Current Best Code.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code here is the current best.  Development is not to be done here, but tests may be run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def AttemptProof(modulus, residue):\n",
    "    def multiplyBy2(modulus,residue,proof):\n",
    "        proof.append(2)\n",
    "        modulus = 2*modulus\n",
    "        residue = 2*residue\n",
    "        return modulus, residue, proof\n",
    "    def divideBy3(modulus,residue,proof):\n",
    "        proof.append(3)\n",
    "        modulus = modulus // 3\n",
    "        residue = (residue - 1) // 3\n",
    "        return modulus, residue, proof\n",
    "    def count3s(modulus):\n",
    "        i = 0\n",
    "        while ((modulus % 3) == 0) and (modulus > 0):\n",
    "            i = i + 1\n",
    "            modulus = modulus // 3\n",
    "        return i\n",
    "    m = modulus\n",
    "    r = residue\n",
    "    proof = ['U', m, r, [], 0]\n",
    "    count = count3s(m)\n",
    "    if ((r % 3) == 2) and ((m % 3) == 0):\n",
    "        proof = ['3-2', m, r, [], 0]\n",
    "    elif ((r % 8) == 5) and ((m % 8) == 0):\n",
    "        proof = ['8-5', m, r, [], 0]\n",
    "    elif ((r % 16) == 3) and ((m % 16) == 0):\n",
    "        proof = ['16-3', m, r, [], 0]\n",
    "    elif ((r % 64) == 25) and ((m % 64) == 0):\n",
    "        proof = ['64-25', m, r, [], 0]\n",
    "    elif ((r % 512) == 33) and ((m % 512) == 0):\n",
    "        proof = ['512-33', m, r, [], 0]\n",
    "    elif ((r % 1024) == 363) and ((m % 1024) == 0):\n",
    "        proof = ['1024-363', m, r, [], 0]\n",
    "    elif ((r % 2) == 0) and ((m % 2) == 0):\n",
    "        proof = ['E', m, r, [], 0]\n",
    "    else:\n",
    "        i = 0\n",
    "        proved = False\n",
    "        while (i < count) and (proved == False):\n",
    "            mod3 = (r % 3)\n",
    "            if mod3 == 1:\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = divideBy3(m,r,proof[3])\n",
    "            elif mod3 == 2:\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = divideBy3(m,r,proof[3])\n",
    "            else:\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = multiplyBy2(m,r,proof[3])\n",
    "                m,r,proof[3] = divideBy3(m,r,proof[3])\n",
    "            if (m < modulus) or ((m == modulus) and (r < residue)):\n",
    "                proved = True\n",
    "            i = i + 1\n",
    "        proof[4] = i\n",
    "        if proved == True:\n",
    "            proof[0] = 'I'\n",
    "    return proof"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime  \n",
    "def SLengthRecords(end, \n",
    "                    start=106241, \n",
    "                    ladderinteger=[106239, 77031, 52527, 35655, 35497, 26623, 23529, \n",
    "                                   17673, 13255, 10971, 6171, 3711, 2919, 2463, 2323, 871, \n",
    "                                   703, 667, 313, 235, 171, 129, 97, 73, 55, 25, 9, 7, 3, 1], \n",
    "                    recordinteger=[1, 3, 7, 9, 25, 27, 73, 97, 129, 171, 231, 313, 327, 703, 871, \n",
    "                                   1161, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, \n",
    "                                   26623, 34239, 35655, 52527, 77031, 106239], \n",
    "                    recordodds=[0, 2, 5, 6, 7, 41, 42, 43, 44, 45, 46, 47, 52, 62, 65, 66, 76, \n",
    "                                79, 87, 96, 98, 101, 102, 103, 113, 114, 119, 125, 129, 130],                    \n",
    "                    printlines = False):\n",
    "                     \n",
    "    starttime = datetime.now().timestamp()\n",
    "    lasttime = starttime\n",
    "    ladderlength = len(ladderinteger) - 1\n",
    "    ladderodds = [recordodds[-i] for i in range(1,len(recordodds)+1)]\n",
    "    currentrecordodds = ladderodds[0]\n",
    "    \n",
    "    # generated by laddergenerator\n",
    "    i1 = ladderinteger[1]\n",
    "    i2 = ladderinteger[2]\n",
    "    i3 = ladderinteger[3]\n",
    "    i4 = ladderinteger[4]\n",
    "    i5 = ladderinteger[5]\n",
    "    i6 = ladderinteger[6]\n",
    "    i7 = ladderinteger[7]\n",
    "    i8 = ladderinteger[8]\n",
    "    i9 = ladderinteger[9]\n",
    "    i10 = ladderinteger[10]\n",
    "    i11 = ladderinteger[11]\n",
    "    i12 = ladderinteger[12]\n",
    "    i13 = ladderinteger[13]\n",
    "    i14 = ladderinteger[14]\n",
    "    i15 = ladderinteger[15]\n",
    "    o1 = ladderodds[1]\n",
    "    o2 = ladderodds[2]\n",
    "    o3 = ladderodds[3]\n",
    "    o4 = ladderodds[4]\n",
    "    o5 = ladderodds[5]\n",
    "    o6 = ladderodds[6]\n",
    "    o7 = ladderodds[7]\n",
    "    o8 = ladderodds[8]\n",
    "    o9 = ladderodds[9]\n",
    "    o10 = ladderodds[10]\n",
    "    o11 = ladderodds[11]\n",
    "    o12 = ladderodds[12]\n",
    "    o13 = ladderodds[13]\n",
    "    o14 = ladderodds[14]\n",
    "    o15 = ladderodds[15]\n",
    "    \n",
    "    # generated by apriorigenerator\n",
    "    skipmodulus = 5184\n",
    "    skip1set = set([5, 13, 25, 31, 37, 41, 53, 61, 71, 77, 85, 95, 103, 109, 121, 125, 133, 143, 149, 157, 167, 175, 181, 185, 197, 205, 217, 221, 229, 233, 239, 247, 253, 265, 269, 277, 287, 293, 301, 311, 319, 325, 329, 341, 349, 359, 365, 373, 377, 383, 391, 397, 409, 415, 421, 431, 437, 445, 455, 463, 469, 473, 485, 493, 503, 509, 517, 521, 527, 541, 553, 557, 565, 581, 589, 601, 607, 613, 617, 629, 637, 647, 653, 661, 665, 671, 679, 685, 697, 701, 709, 719, 725, 733, 743, 751, 757, 761, 773, 781, 793, 797, 805, 809, 815, 823, 829, 841, 845, 853, 863, 869, 877, 887, 895, 901, 905, 917, 925, 935, 941, 949, 953, 959, 967, 973, 985, 989, 997, 1007, 1013, 1021, 1031, 1039, 1045, 1049, 1063, 1069, 1079, 1085, 1093, 1097, 1103, 1117, 1129, 1133, 1141, 1151, 1157, 1165, 1177, 1183, 1189, 1193, 1205, 1213, 1225, 1229, 1237, 1241, 1247, 1255, 1261, 1273, 1277, 1285, 1295, 1301, 1309, 1319, 1327, 1333, 1337, 1349, 1357, 1369, 1373, 1381, 1391, 1399, 1405, 1417, 1421, 1429, 1439, 1445, 1453, 1463, 1471, 1477, 1481, 1493, 1501, 1511, 1517, 1525, 1529, 1535, 1543, 1549, 1561, 1565, 1573, 1583, 1589, 1597, 1607, 1615, 1621, 1625, 1637, 1645, 1655, 1661, 1669, 1673, 1679, 1693, 1705, 1711, 1717, 1727, 1733, 1741, 1753, 1759, 1765, 1769, 1781, 1789, 1799, 1805, 1813, 1817, 1823, 1831, 1837, 1849, 1853, 1861, 1877, 1885, 1895, 1903, 1909, 1913, 1925, 1933, 1945, 1949, 1957, 1961, 1967, 1975, 1981, 1993, 1997, 2005, 2015, 2021, 2029, 2039, 2047, 2053, 2057, 2069, 2077, 2087, 2093, 2101, 2105, 2111, 2119, 2125, 2137, 2141, 2149, 2159, 2165, 2173, 2183, 2191, 2197, 2201, 2213, 2221, 2231, 2237, 2245, 2249, 2255, 2269, 2281, 2285, 2293, 2303, 2309, 2317, 2329, 2335, 2341, 2345, 2359, 2365, 2375, 2381, 2389, 2393, 2399, 2407, 2413, 2425, 2429, 2437, 2447, 2453, 2461, 2471, 2479, 2485, 2489, 2501, 2509, 2521, 2525, 2533, 2537, 2543, 2551, 2557, 2569, 2573, 2581, 2591, 2597, 2605, 2615, 2623, 2629, 2633, 2645, 2653, 2663, 2669, 2677, 2687, 2695, 2701, 2713, 2717, 2725, 2735, 2741, 2749, 2759, 2767, 2773, 2777, 2789, 2797, 2807, 2813, 2821, 2825, 2831, 2845, 2857, 2861, 2869, 2879, 2885, 2893, 2905, 2911, 2917, 2921, 2933, 2941, 2951, 2957, 2965, 2969, 2975, 2983, 2989, 3001, 3007, 3013, 3023, 3029, 3037, 3047, 3055, 3061, 3065, 3077, 3085, 3097, 3101, 3109, 3113, 3119, 3127, 3133, 3145, 3149, 3157, 3173, 3181, 3191, 3199, 3205, 3209, 3221, 3229, 3239, 3245, 3253, 3257, 3263, 3271, 3277, 3289, 3293, 3301, 3311, 3317, 3325, 3335, 3343, 3349, 3353, 3365, 3373, 3383, 3389, 3397, 3401, 3407, 3421, 3433, 3437, 3445, 3455, 3461, 3469, 3481, 3487, 3493, 3497, 3509, 3517, 3527, 3533, 3541, 3545, 3551, 3559, 3565, 3577, 3581, 3589, 3599, 3605, 3613, 3623, 3631, 3637, 3641, 3655, 3661, 3673, 3677, 3685, 3689, 3695, 3703, 3709, 3721, 3725, 3733, 3743, 3749, 3757, 3767, 3775, 3781, 3785, 3797, 3805, 3817, 3821, 3829, 3833, 3839, 3847, 3853, 3865, 3869, 3877, 3887, 3893, 3901, 3911, 3919, 3925, 3929, 3941, 3949, 3959, 3965, 3973, 3983, 3997, 4009, 4013, 4021, 4031, 4037, 4045, 4057, 4063, 4069, 4073, 4085, 4093, 4103, 4109, 4117, 4121, 4127, 4135, 4141, 4153, 4157, 4165, 4175, 4181, 4189, 4199, 4207, 4213, 4217, 4229, 4237, 4249, 4253, 4261, 4265, 4271, 4279, 4285, 4297, 4303, 4309, 4319, 4325, 4333, 4343, 4351, 4357, 4361, 4373, 4381, 4391, 4397, 4405, 4409, 4415, 4423, 4429, 4441, 4445, 4453, 4469, 4477, 4487, 4495, 4501, 4505, 4517, 4525, 4535, 4541, 4549, 4553, 4559, 4573, 4585, 4589, 4597, 4607, 4613, 4621, 4633, 4639, 4645, 4649, 4661, 4669, 4679, 4685, 4693, 4697, 4703, 4711, 4717, 4729, 4733, 4741, 4751, 4757, 4765, 4775, 4783, 4789, 4793, 4805, 4813, 4825, 4829, 4837, 4841, 4847, 4855, 4861, 4873, 4877, 4885, 4895, 4901, 4909, 4919, 4927, 4933, 4937, 4957, 4967, 4973, 4981, 4985, 4991, 4999, 5005, 5017, 5021, 5029, 5039, 5045, 5053, 5063, 5071, 5077, 5081, 5093, 5101, 5113, 5117, 5125, 5129, 5135, 5149, 5161, 5165, 5173, 5183])\n",
    "    skip2set = set([3, 11, 23, 29, 35, 51, 59, 69, 83, 93, 101, 107, 119, 131, 141, 147, 155, 165, 173, 179, 195, 203, 215, 227, 237, 245, 251, 263, 275, 285, 291, 299, 309, 317, 323, 339, 347, 357, 371, 381, 389, 395, 407, 413, 419, 429, 435, 443, 453, 461, 467, 483, 491, 501, 515, 525, 539, 551, 563, 579, 587, 599, 605, 611, 627, 635, 645, 659, 669, 677, 683, 695, 707, 717, 723, 731, 741, 749, 755, 771, 779, 791, 803, 813, 821, 827, 839, 851, 861, 867, 875, 885, 893, 899, 915, 923, 933, 947, 957, 965, 971, 983, 995, 1005, 1011, 1019, 1029, 1037, 1043, 1061, 1067, 1077, 1091, 1101, 1115, 1127, 1139, 1149, 1155, 1163, 1175, 1181, 1187, 1203, 1211, 1223, 1235, 1245, 1253, 1259, 1271, 1283, 1293, 1299, 1307, 1317, 1325, 1331, 1347, 1355, 1367, 1379, 1389, 1397, 1403, 1415, 1427, 1437, 1443, 1451, 1461, 1469, 1475, 1491, 1499, 1509, 1523, 1533, 1541, 1547, 1559, 1571, 1581, 1587, 1595, 1605, 1613, 1619, 1635, 1643, 1653, 1667, 1677, 1691, 1703, 1709, 1715, 1725, 1731, 1739, 1751, 1757, 1763, 1779, 1787, 1797, 1811, 1821, 1829, 1835, 1847, 1859, 1875, 1883, 1893, 1901, 1907, 1923, 1931, 1943, 1955, 1965, 1973, 1979, 1991, 2003, 2013, 2019, 2027, 2037, 2045, 2051, 2067, 2075, 2085, 2099, 2109, 2117, 2123, 2135, 2147, 2157, 2163, 2171, 2181, 2189, 2195, 2211, 2219, 2229, 2243, 2253, 2267, 2279, 2291, 2301, 2307, 2315, 2327, 2333, 2339, 2357, 2363, 2373, 2387, 2397, 2405, 2411, 2423, 2435, 2445, 2451, 2459, 2469, 2477, 2483, 2499, 2507, 2519, 2531, 2541, 2549, 2555, 2567, 2579, 2589, 2595, 2603, 2613, 2621, 2627, 2643, 2651, 2661, 2675, 2685, 2693, 2699, 2711, 2723, 2733, 2739, 2747, 2757, 2765, 2771, 2787, 2795, 2805, 2819, 2829, 2843, 2855, 2867, 2877, 2883, 2891, 2903, 2909, 2915, 2931, 2939, 2949, 2963, 2973, 2981, 2987, 2999, 3005, 3011, 3021, 3027, 3035, 3045, 3053, 3059, 3075, 3083, 3095, 3107, 3117, 3125, 3131, 3143, 3155, 3171, 3179, 3189, 3197, 3203, 3219, 3227, 3237, 3251, 3261, 3269, 3275, 3287, 3299, 3309, 3315, 3323, 3333, 3341, 3347, 3363, 3371, 3381, 3395, 3405, 3419, 3431, 3443, 3453, 3459, 3467, 3479, 3485, 3491, 3507, 3515, 3525, 3539, 3549, 3557, 3563, 3575, 3587, 3597, 3603, 3611, 3621, 3629, 3635, 3653, 3659, 3671, 3683, 3693, 3701, 3707, 3719, 3731, 3741, 3747, 3755, 3765, 3773, 3779, 3795, 3803, 3815, 3827, 3837, 3845, 3851, 3863, 3875, 3885, 3891, 3899, 3909, 3917, 3923, 3939, 3947, 3957, 3971, 3981, 3995, 4007, 4019, 4029, 4035, 4043, 4055, 4061, 4067, 4083, 4091, 4101, 4115, 4125, 4133, 4139, 4151, 4163, 4173, 4179, 4187, 4197, 4205, 4211, 4227, 4235, 4247, 4259, 4269, 4277, 4283, 4295, 4301, 4307, 4317, 4323, 4331, 4341, 4349, 4355, 4371, 4379, 4389, 4403, 4413, 4421, 4427, 4439, 4451, 4467, 4475, 4485, 4493, 4499, 4515, 4523, 4533, 4547, 4557, 4571, 4583, 4595, 4605, 4611, 4619, 4631, 4637, 4643, 4659, 4667, 4677, 4691, 4701, 4709, 4715, 4727, 4739, 4749, 4755, 4763, 4773, 4781, 4787, 4803, 4811, 4823, 4835, 4845, 4853, 4859, 4871, 4883, 4893, 4899, 4907, 4917, 4925, 4931, 4955, 4965, 4979, 4989, 4997, 5003, 5015, 5027, 5037, 5043, 5051, 5061, 5069, 5075, 5091, 5099, 5111, 5123, 5133, 5147, 5159, 5171, 5181])\n",
    "    skip3set = set([21, 49, 67, 91, 99, 117, 139, 153, 163, 193, 213, 243, 261, 283, 307, 337, 345, 355, 387, 405, 427, 451, 481, 499, 537, 549, 577, 597, 625, 643, 675, 693, 715, 729, 739, 769, 789, 819, 837, 859, 883, 913, 921, 931, 963, 981, 1003, 1027, 1059, 1075, 1113, 1125, 1147, 1173, 1201, 1221, 1251, 1269, 1291, 1305, 1315, 1345, 1365, 1387, 1395, 1413, 1435, 1459, 1489, 1497, 1507, 1539, 1557, 1579, 1603, 1633, 1651, 1689, 1701, 1723, 1749, 1777, 1795, 1827, 1845, 1873, 1881, 1891, 1921, 1941, 1971, 1989, 2011, 2035, 2065, 2073, 2083, 2115, 2133, 2155, 2179, 2209, 2227, 2265, 2277, 2299, 2325, 2355, 2371, 2403, 2421, 2443, 2457, 2467, 2497, 2517, 2547, 2565, 2587, 2611, 2641, 2649, 2659, 2683, 2691, 2709, 2731, 2755, 2785, 2803, 2841, 2853, 2875, 2901, 2929, 2947, 2979, 2997, 3019, 3033, 3043, 3073, 3093, 3123, 3141, 3169, 3187, 3217, 3225, 3235, 3267, 3285, 3307, 3331, 3361, 3379, 3417, 3429, 3451, 3477, 3505, 3523, 3555, 3573, 3595, 3609, 3619, 3651, 3669, 3699, 3717, 3739, 3763, 3793, 3801, 3813, 3843, 3861, 3883, 3907, 3937, 3955, 3979, 3993, 4005, 4027, 4053, 4081, 4099, 4131, 4149, 4171, 4185, 4195, 4225, 4245, 4275, 4293, 4315, 4339, 4369, 4377, 4387, 4419, 4437, 4465, 4483, 4513, 4531, 4569, 4581, 4603, 4629, 4657, 4675, 4707, 4725, 4747, 4761, 4771, 4801, 4821, 4851, 4869, 4891, 4915, 4953, 4963, 4995, 5013, 5035, 5059, 5089, 5109, 5145, 5157, 5179])\n",
    "    skip4set = set([19, 47, 65, 89, 115, 137, 161, 191, 211, 259, 281, 305, 335, 353, 403, 425, 449, 479, 497, 535, 547, 575, 595, 623, 641, 691, 713, 737, 767, 787, 835, 857, 881, 911, 929, 979, 1001, 1025, 1057, 1073, 1111, 1123, 1145, 1171, 1199, 1219, 1267, 1289, 1313, 1343, 1363, 1385, 1411, 1433, 1457, 1487, 1505, 1555, 1577, 1601, 1631, 1649, 1687, 1699, 1721, 1747, 1775, 1793, 1843, 1871, 1889, 1919, 1939, 1987, 2009, 2033, 2063, 2081, 2131, 2153, 2177, 2207, 2225, 2263, 2275, 2297, 2323, 2353, 2369, 2419, 2441, 2465, 2495, 2515, 2563, 2585, 2609, 2639, 2657, 2681, 2707, 2729, 2753, 2783, 2801, 2839, 2851, 2873, 2899, 2927, 2945, 2995, 3017, 3041, 3071, 3091, 3139, 3167, 3185, 3215, 3233, 3283, 3305, 3329, 3359, 3377, 3415, 3427, 3449, 3475, 3503, 3521, 3571, 3593, 3617, 3649, 3667, 3715, 3737, 3761, 3791, 3811, 3859, 3881, 3905, 3935, 3953, 3977, 3991, 4003, 4025, 4051, 4079, 4097, 4147, 4169, 4193, 4223, 4243, 4291, 4313, 4337, 4367, 4385, 4435, 4463, 4481, 4511, 4529, 4567, 4579, 4601, 4627, 4655, 4673, 4723, 4745, 4769, 4799, 4819, 4867, 4889, 4913, 4951, 4961, 5011, 5033, 5057, 5087, 5107, 5143, 5155, 5177])\n",
    "    skip5set = set([17, 45, 113, 189, 209, 257, 333, 401, 477, 533, 545, 573, 593, 621, 689, 765, 785, 833, 909, 977, 1055, 1109, 1121, 1169, 1197, 1217, 1265, 1341, 1361, 1409, 1485, 1553, 1629, 1685, 1697, 1745, 1773, 1841, 1869, 1917, 1937, 1985, 2061, 2129, 2205, 2261, 2273, 2321, 2351, 2417, 2493, 2513, 2561, 2637, 2705, 2781, 2837, 2849, 2897, 2925, 2993, 3069, 3089, 3137, 3165, 3213, 3281, 3357, 3413, 3425, 3473, 3501, 3569, 3647, 3665, 3713, 3789, 3809, 3857, 3933, 3989, 4001, 4049, 4077, 4145, 4221, 4241, 4289, 4365, 4433, 4461, 4509, 4565, 4577, 4625, 4653, 4721, 4797, 4817, 4865, 4949, 5009, 5085, 5105, 5141, 5153])\n",
    "    skip6set = set([531, 571, 1053, 1107, 1683, 1867, 2259, 2349, 2835, 3163, 3411, 3645, 3987, 4459, 4563, 4947, 5139])\n",
    "    skip7set = set([569, 1865, 3161, 4457, 4945])\n",
    "    skip8set = set([4943])\n",
    "    skip9set = set([4941]) \n",
    "    \n",
    "    # generated by oddslookupgenerator with input 8000 and 8\n",
    "    smalloddssize = 8000\n",
    "    smallodds1 = dict([(1, 0), (3, 2), (5, 1), (7, 5), (9, 6), (11, 4), (13, 2), (15, 5), (17, 3), (19, 6), (21, 1), (23, 4), (25, 7), (27, 41), (29, 5), (31, 39), (33, 8), (35, 3), (37, 6), (39, 11), (41, 40), (43, 9), (45, 4), (47, 38), (49, 7), (51, 7), (53, 2), (55, 41), (57, 10), (59, 10), (61, 5), (63, 39), (65, 8), (67, 8), (69, 3), (71, 37), (73, 42), (75, 3), (77, 6), (79, 11), (81, 6), (83, 40), (85, 1), (87, 9), (89, 9), (91, 33), (93, 4), (95, 38), (97, 43), (99, 7), (101, 7), (103, 31), (105, 12), (107, 36), (109, 41), (111, 24), (113, 2), (115, 10), (117, 5), (119, 10), (121, 34), (123, 15), (125, 39), (127, 15), (129, 44), (131, 8), (133, 8), (135, 13), (137, 32), (139, 13), (141, 3), (143, 37), (145, 42), (147, 42), (149, 6), (151, 3), (153, 11), (155, 30), (157, 11), (159, 18), (161, 35), (163, 6), (165, 40), (167, 23), (169, 16), (171, 45), (173, 9), (175, 28), (177, 9), (179, 9), (181, 4), (183, 33), (185, 14), (187, 14), (189, 38), (191, 14), (193, 43), (195, 43), (197, 7), (199, 43), (201, 4), (203, 12), (205, 7), (207, 31), (209, 12), (211, 12), (213, 2), (215, 36), (217, 7), (219, 17), (221, 41), (223, 24), (225, 17), (227, 2), (229, 10), (231, 46), (233, 29), (235, 46), (237, 10), (239, 17), (241, 5), (243, 34), (245, 5), (247, 15), (249, 15), (251, 22), (253, 39), (255, 15), (257, 44), (259, 44), (261, 8), (263, 27), (265, 44), (267, 5), (269, 8), (271, 13), (273, 8), (275, 32), (277, 3), (279, 13), (281, 13), (283, 20), (285, 37), (287, 13), (289, 8), (291, 42), (293, 42), (295, 18), (297, 25), (299, 42), (301, 3), (303, 13), (305, 11), (307, 11), (309, 6), (311, 30), (313, 47), (315, 11), (317, 11), (319, 18), (321, 6), (323, 35), (325, 6), (327, 52), (329, 16), (331, 6), (333, 40), (335, 23), (337, 40), (339, 16), (341, 1), (343, 45), (345, 45), (347, 45), (349, 9), (351, 28), (353, 45), (355, 9), (357, 9), (359, 16), (361, 14), (363, 14), (365, 33), (367, 14), (369, 4), (371, 14), (373, 4), (375, 14), (377, 21), (379, 19), (381, 38), (383, 14), (385, 9), (387, 43), (389, 43), (391, 43), (393, 19), (395, 26), (397, 7), (399, 43), (401, 4), (403, 4), (405, 7), (407, 12), (409, 12), (411, 48), (413, 31), (415, 48), (417, 48), (419, 12), (421, 12), (423, 9), (425, 19), (427, 17), (429, 36), (431, 12), (433, 7), (435, 7), (437, 41), (439, 17), (441, 7), (443, 17), (445, 24), (447, 34), (449, 41), (451, 17), (453, 2), (455, 12), (457, 46), (459, 46), (461, 10), (463, 46), (465, 10), (467, 29), (469, 5), (471, 46), (473, 10), (475, 7), (477, 10), (479, 17), (481, 15), (483, 5), (485, 34), (487, 51), (489, 15), (491, 51), (493, 15), (495, 34), (497, 5), (499, 15), (501, 39), (503, 22), (505, 20), (507, 10), (509, 15), (511, 20), (513, 10), (515, 44), (517, 44), (519, 20), (521, 44), (523, 44), (525, 8), (527, 27), (529, 8), (531, 44), (533, 8), (535, 5), (537, 5), (539, 15), (541, 13), (543, 49), (545, 13), (547, 8), (549, 32), (551, 13), (553, 49), (555, 8), (557, 13), (559, 30), (561, 13), (563, 13), (565, 3), (567, 20), (569, 18), (571, 8), (573, 37), (575, 13), (577, 8), (579, 8), (581, 42), (583, 8), (585, 18), (587, 42), (589, 42), (591, 18), (593, 25), (595, 25), (597, 6), (599, 42), (601, 18), (603, 23), (605, 3), (607, 13), (609, 47), (611, 11), (613, 11), (615, 23), (617, 47), (619, 47), (621, 30), (623, 47), (625, 6), (627, 47), (629, 11), (631, 11), (633, 8), (635, 8), (637, 18), (639, 47), (641, 16), (643, 6), (645, 35), (647, 11), (649, 52), (651, 35), (653, 6), (655, 52), (657, 16), (659, 16), (661, 40), (663, 6), (665, 16), (667, 52), (669, 23), (671, 33), (673, 21), (675, 40), (677, 16), (679, 21), (681, 21), (683, 11), (685, 45), (687, 11), (689, 45), (691, 45), (693, 9), (695, 45), (697, 45), (699, 21), (701, 28), (703, 62), (705, 9), (707, 45), (709, 9), (711, 21), (713, 6), (715, 6), (717, 9), (719, 16), (721, 14), (723, 14), (725, 4), (727, 14), (729, 9), (731, 50), (733, 33), (735, 14), (737, 50), (739, 4), (741, 14), (743, 33), (745, 31), (747, 14), (749, 14), (751, 50), (753, 4), (755, 21), (757, 38), (759, 19), (761, 9), (763, 55), (765, 14), (767, 19), (769, 9), (771, 9), (773, 43), (775, 55), (777, 9), (779, 19), (781, 43), (783, 43), (785, 43), (787, 19), (789, 7), (791, 26), (793, 26), (795, 36), (797, 43), (799, 24), (801, 19), (803, 4), (805, 4), (807, 24), (809, 14), (811, 48), (813, 12), (815, 48), (817, 12), (819, 12), (821, 7), (823, 48), (825, 48), (827, 12), (829, 31), (831, 48), (833, 7), (835, 48), (837, 12), (839, 29), (841, 12), (843, 12), (845, 12), (847, 9), (849, 19), (851, 19), (853, 2), (855, 17), (857, 7), (859, 53), (861, 36), (863, 12), (865, 53), (867, 7), (869, 7), (871, 65), (873, 53), (875, 7), (877, 17), (879, 53), (881, 41), (883, 7), (885, 41), (887, 17), (889, 53), (891, 14), (893, 24), (895, 34), (897, 22), (899, 41), (901, 17), (903, 41), (905, 22), (907, 17), (909, 2), (911, 12), (913, 46), (915, 46), (917, 10), (919, 46), (921, 46), (923, 22), (925, 46), (927, 41), (929, 46), (931, 10), (933, 29), (935, 46), (937, 63), (939, 29), (941, 46), (943, 10), (945, 10), (947, 10), (949, 10), (951, 7), (953, 7), (955, 7), (957, 17), (959, 46), (961, 15), (963, 15), (965, 5), (967, 51), (969, 15), (971, 10), (973, 34), (975, 51), (977, 34), (979, 15), (981, 5), (983, 51), (985, 5), (987, 10), (989, 15), (991, 34), (993, 32), (995, 5), (997, 15), (999, 15)])\n",
    "    smallodds2 = dict([(1001, 51), (1003, 12), (1005, 22), (1007, 32), (1009, 39), (1011, 20), (1013, 39), (1015, 10), (1017, 56), (1019, 20), (1021, 15), (1023, 20), (1025, 10), (1027, 10), (1029, 44), (1031, 10), (1033, 56), (1035, 44), (1037, 44), (1039, 20), (1041, 44), (1043, 44), (1045, 8), (1047, 44), (1049, 20), (1051, 32), (1053, 27), (1055, 61), (1057, 27), (1059, 8), (1061, 44), (1063, 25), (1065, 25), (1067, 20), (1069, 5), (1071, 61), (1073, 5), (1075, 5), (1077, 8), (1079, 15), (1081, 49), (1083, 49), (1085, 13), (1087, 49), (1089, 13), (1091, 13), (1093, 8), (1095, 25), (1097, 49), (1099, 8), (1101, 32), (1103, 13), (1105, 32), (1107, 49), (1109, 3), (1111, 8), (1113, 49), (1115, 32), (1117, 13), (1119, 30), (1121, 13), (1123, 13), (1125, 13), (1127, 49), (1129, 10), (1131, 10), (1133, 20), (1135, 20), (1137, 3), (1139, 18), (1141, 37), (1143, 8), (1145, 54), (1147, 18), (1149, 13), (1151, 18), (1153, 54), (1155, 8), (1157, 8), (1159, 18), (1161, 66), (1163, 54), (1165, 42), (1167, 8), (1169, 18), (1171, 18), (1173, 42), (1175, 42), (1177, 8), (1179, 18), (1181, 18), (1183, 30), (1185, 54), (1187, 25), (1189, 25), (1191, 15), (1193, 35), (1195, 42), (1197, 42), (1199, 23), (1201, 18), (1203, 18), (1205, 3), (1207, 23), (1209, 18), (1211, 23), (1213, 13), (1215, 59), (1217, 47), (1219, 47), (1221, 11), (1223, 47), (1225, 47), (1227, 47), (1229, 11), (1231, 23), (1233, 47), (1235, 47), (1237, 6), (1239, 47), (1241, 11), (1243, 23), (1245, 30), (1247, 47), (1249, 64), (1251, 6), (1253, 47), (1255, 30), (1257, 11), (1259, 28), (1261, 11), (1263, 64), (1265, 11), (1267, 8), (1269, 11), (1271, 8), (1273, 8), (1275, 28), (1277, 18), (1279, 47), (1281, 16), (1283, 16), (1285, 6), (1287, 52), (1289, 52), (1291, 16), (1293, 35), (1295, 11), (1297, 35), (1299, 52), (1301, 6), (1303, 35), (1305, 16), (1307, 64), (1309, 52), (1311, 35), (1313, 6), (1315, 16), (1317, 16), (1319, 52), (1321, 35), (1323, 16), (1325, 6), (1327, 16), (1329, 16), (1331, 16), (1333, 40), (1335, 52), (1337, 13), (1339, 6), (1341, 23), (1343, 33), (1345, 40), (1347, 21), (1349, 40), (1351, 57), (1353, 11), (1355, 40), (1357, 16), (1359, 21), (1361, 16), (1363, 21), (1365, 1), (1367, 11), (1369, 11), (1371, 40), (1373, 45), (1375, 11), (1377, 57), (1379, 45), (1381, 45), (1383, 33), (1385, 21), (1387, 21), (1389, 45), (1391, 40), (1393, 9), (1395, 45), (1397, 9), (1399, 21), (1401, 33), (1403, 45), (1405, 28), (1407, 62), (1409, 28), (1411, 9), (1413, 45), (1415, 9), (1417, 26), (1419, 45), (1421, 9), (1423, 21), (1425, 6), (1427, 6), (1429, 9), (1431, 6), (1433, 6), (1435, 26), (1437, 16), (1439, 45), (1441, 50), (1443, 14), (1445, 14), (1447, 16), (1449, 50), (1451, 50), (1453, 14), (1455, 50), (1457, 9), (1459, 9), (1461, 33), (1463, 50), (1465, 9), (1467, 50), (1469, 14), (1471, 62), (1473, 33), (1475, 50), (1477, 4), (1479, 33), (1481, 9), (1483, 50), (1485, 14), (1487, 33), (1489, 14), (1491, 31), (1493, 4), (1495, 14), (1497, 14), (1499, 14), (1501, 14), (1503, 50), (1505, 11), (1507, 4), (1509, 21), (1511, 31), (1513, 21), (1515, 50), (1517, 19), (1519, 55), (1521, 38), (1523, 9), (1525, 38), (1527, 55), (1529, 19), (1531, 19), (1533, 14), (1535, 19), (1537, 55), (1539, 9), (1541, 9), (1543, 38), (1545, 19), (1547, 9), (1549, 43), (1551, 55), (1553, 43), (1555, 9), (1557, 43), (1559, 19), (1561, 19), (1563, 55), (1565, 43), (1567, 19), (1569, 9), (1571, 43), (1573, 19), (1575, 19), (1577, 31), (1579, 43), (1581, 26), (1583, 60), (1585, 26), (1587, 26), (1589, 7), (1591, 36), (1593, 43), (1595, 24), (1597, 43), (1599, 24), (1601, 19), (1603, 19), (1605, 4), (1607, 60), (1609, 24), (1611, 4), (1613, 4), (1615, 24), (1617, 14), (1619, 14), (1621, 7), (1623, 48), (1625, 48), (1627, 24), (1629, 12), (1631, 48), (1633, 48), (1635, 12), (1637, 12), (1639, 36), (1641, 24), (1643, 24), (1645, 48), (1647, 48), (1649, 7), (1651, 48), (1653, 31), (1655, 12), (1657, 24), (1659, 12), (1661, 48), (1663, 24), (1665, 65), (1667, 7), (1669, 48), (1671, 12), (1673, 31), (1675, 48), (1677, 12), (1679, 29), (1681, 12), (1683, 12), (1685, 12), (1687, 12), (1689, 9), (1691, 48), (1693, 9), (1695, 65), (1697, 9), (1699, 19), (1701, 19), (1703, 19), (1705, 48), (1707, 53), (1709, 17), (1711, 53), (1713, 7), (1715, 7), (1717, 36), (1719, 53), (1721, 17), (1723, 17), (1725, 12), (1727, 17), (1729, 36), (1731, 53), (1733, 7), (1735, 36), (1737, 36), (1739, 17), (1741, 7), (1743, 65), (1745, 53), (1747, 53), (1749, 41), (1751, 7), (1753, 17), (1755, 12), (1757, 17), (1759, 53), (1761, 36), (1763, 41), (1765, 7), (1767, 53), (1769, 17), (1771, 17), (1773, 17), (1775, 29), (1777, 41), (1779, 53), (1781, 24), (1783, 14), (1785, 7), (1787, 14), (1789, 34), (1791, 34), (1793, 41), (1795, 22), (1797, 41), (1799, 22), (1801, 58), (1803, 12), (1805, 17), (1807, 41), (1809, 17), (1811, 22), (1813, 2), (1815, 17), (1817, 22), (1819, 58), (1821, 12), (1823, 58), (1825, 12), (1827, 46), (1829, 46), (1831, 22), (1833, 12), (1835, 46), (1837, 46), (1839, 58), (1841, 46), (1843, 46), (1845, 10), (1847, 22), (1849, 22), (1851, 46), (1853, 46), (1855, 41), (1857, 10), (1859, 46), (1861, 10), (1863, 22), (1865, 22), (1867, 10), (1869, 29), (1871, 46), (1873, 29), (1875, 63), (1877, 5), (1879, 29), (1881, 10), (1883, 29), (1885, 46), (1887, 10), (1889, 27), (1891, 10), (1893, 10), (1895, 63), (1897, 22), (1899, 22), (1901, 7), (1903, 46), (1905, 10), (1907, 7), (1909, 10), (1911, 7), (1913, 27), (1915, 63), (1917, 17), (1919, 46), (1921, 51), (1923, 15), (1925, 15), (1927, 15), (1929, 17), (1931, 51), (1933, 5), (1935, 51), (1937, 15), (1939, 15), (1941, 34), (1943, 10), (1945, 10), (1947, 27), (1949, 51), (1951, 63), (1953, 10), (1955, 34), (1957, 15), (1959, 27), (1961, 63), (1963, 27), (1965, 51), (1967, 34), (1969, 5), (1971, 5), (1973, 15), (1975, 10), (1977, 51), (1979, 51), (1981, 34), (1983, 15), (1985, 15), (1987, 32), (1989, 5), (1991, 15), (1993, 15), (1995, 15), (1997, 15), (1999, 15)])\n",
    "    smallodds3 = dict([(2001, 15), (2003, 51), (2005, 39), (2007, 12), (2009, 5), (2011, 12), (2013, 22), (2015, 32), (2017, 22), (2019, 39), (2021, 20), (2023, 56), (2025, 56), (2027, 56), (2029, 10), (2031, 20), (2033, 39), (2035, 56), (2037, 15), (2039, 20), (2041, 20), (2043, 56), (2045, 20), (2047, 56), (2049, 56), (2051, 10), (2053, 10), (2055, 10), (2057, 39), (2059, 10), (2061, 44), (2063, 10), (2065, 44), (2067, 56), (2069, 44), (2071, 44), (2073, 10), (2075, 32), (2077, 20), (2079, 15), (2081, 20), (2083, 44), (2085, 44), (2087, 39), (2089, 20), (2091, 10), (2093, 44), (2095, 37), (2097, 20), (2099, 20), (2101, 8), (2103, 32), (2105, 44), (2107, 56), (2109, 27), (2111, 61), (2113, 27), (2115, 27), (2117, 8), (2119, 27), (2121, 37), (2123, 8), (2125, 44), (2127, 25), (2129, 44), (2131, 25), (2133, 8), (2135, 20), (2137, 20), (2139, 25), (2141, 5), (2143, 61), (2145, 25), (2147, 5), (2149, 5), (2151, 37), (2153, 25), (2155, 61), (2157, 15), (2159, 44), (2161, 8), (2163, 49), (2165, 13), (2167, 49), (2169, 25), (2171, 15), (2173, 49), (2175, 25), (2177, 49), (2179, 13), (2181, 13), (2183, 49), (2185, 37), (2187, 25), (2189, 8), (2191, 25), (2193, 49), (2195, 49), (2197, 32), (2199, 8), (2201, 49), (2203, 15), (2205, 13), (2207, 61), (2209, 25), (2211, 32), (2213, 49), (2215, 42), (2217, 25), (2219, 32), (2221, 8), (2223, 66), (2225, 49), (2227, 49), (2229, 13), (2231, 32), (2233, 49), (2235, 13), (2237, 30), (2239, 49), (2241, 13), (2243, 13), (2245, 13), (2247, 25), (2249, 13), (2251, 10), (2253, 13), (2255, 49), (2257, 10), (2259, 10), (2261, 3), (2263, 10), (2265, 20), (2267, 30), (2269, 20), (2271, 20), (2273, 49), (2275, 3), (2277, 18), (2279, 54), (2281, 54), (2283, 18), (2285, 8), (2287, 42), (2289, 37), (2291, 54), (2293, 37), (2295, 18), (2297, 18), (2299, 54), (2301, 13), (2303, 18), (2305, 37), (2307, 54), (2309, 8), (2311, 54), (2313, 37), (2315, 37), (2317, 8), (2319, 18), (2321, 8), (2323, 66), (2325, 42), (2327, 54), (2329, 54), (2331, 37), (2333, 8), (2335, 30), (2337, 18), (2339, 18), (2341, 18), (2343, 54), (2345, 54), (2347, 37), (2349, 42), (2351, 18), (2353, 8), (2355, 8), (2357, 42), (2359, 18), (2361, 18), (2363, 18), (2365, 18), (2367, 30), (2369, 42), (2371, 54), (2373, 25), (2375, 59), (2377, 15), (2379, 25), (2381, 25), (2383, 15), (2385, 35), (2387, 35), (2389, 6), (2391, 42), (2393, 23), (2395, 8), (2397, 42), (2399, 23), (2401, 59), (2403, 18), (2405, 18), (2407, 23), (2409, 42), (2411, 59), (2413, 23), (2415, 42), (2417, 3), (2419, 18), (2421, 3), (2423, 23), (2425, 59), (2427, 42), (2429, 13), (2431, 59), (2433, 13), (2435, 47), (2437, 47), (2439, 47), (2441, 23), (2443, 13), (2445, 11), (2447, 47), (2449, 47), (2451, 47), (2453, 11), (2455, 47), (2457, 47), (2459, 35), (2461, 23), (2463, 76), (2465, 23), (2467, 47), (2469, 47), (2471, 47), (2473, 42), (2475, 23), (2477, 47), (2479, 13), (2481, 11), (2483, 11), (2485, 30), (2487, 23), (2489, 11), (2491, 35), (2493, 47), (2495, 23), (2497, 30), (2499, 64), (2501, 6), (2503, 20), (2505, 30), (2507, 11), (2509, 47), (2511, 30), (2513, 47), (2515, 11), (2517, 11), (2519, 28), (2521, 11), (2523, 47), (2525, 11), (2527, 64), (2529, 23), (2531, 11), (2533, 8), (2535, 28), (2537, 47), (2539, 64), (2541, 8), (2543, 64), (2545, 11), (2547, 8), (2549, 18), (2551, 28), (2553, 64), (2555, 18), (2557, 47), (2559, 40), (2561, 52), (2563, 16), (2565, 16), (2567, 52), (2569, 16), (2571, 16), (2573, 6), (2575, 52), (2577, 6), (2579, 52), (2581, 35), (2583, 16), (2585, 16), (2587, 52), (2589, 11), (2591, 16), (2593, 11), (2595, 35), (2597, 52), (2599, 52), (2601, 64), (2603, 35), (2605, 35), (2607, 28), (2609, 16), (2611, 16), (2613, 6), (2615, 64), (2617, 28), (2619, 35), (2621, 52), (2623, 35), (2625, 6), (2627, 6), (2629, 16), (2631, 69), (2633, 11), (2635, 16), (2637, 16), (2639, 52), (2641, 35), (2643, 35), (2645, 40), (2647, 16), (2649, 33), (2651, 52), (2653, 6), (2655, 16), (2657, 16), (2659, 16), (2661, 16), (2663, 28), (2665, 16), (2667, 13), (2669, 52), (2671, 13), (2673, 40), (2675, 13), (2677, 23), (2679, 6), (2681, 13), (2683, 23), (2685, 33), (2687, 33), (2689, 23), (2691, 40), (2693, 21), (2695, 6), (2697, 57), (2699, 21), (2701, 40), (2703, 57), (2705, 11), (2707, 11), (2709, 16), (2711, 40), (2713, 57), (2715, 33), (2717, 21), (2719, 21), (2721, 21), (2723, 16), (2725, 21), (2727, 45), (2729, 57), (2731, 40), (2733, 11), (2735, 57), (2737, 11), (2739, 11), (2741, 45), (2743, 40), (2745, 11), (2747, 21), (2749, 11), (2751, 62), (2753, 45), (2755, 57), (2757, 45), (2759, 57), (2761, 45), (2763, 11), (2765, 45), (2767, 33), (2769, 21), (2771, 21), (2773, 9), (2775, 21), (2777, 45), (2779, 57), (2781, 45), (2783, 40), (2785, 21), (2787, 9), (2789, 45), (2791, 21), (2793, 38), (2795, 21), (2797, 21), (2799, 21), (2801, 9), (2803, 33), (2805, 28), (2807, 45), (2809, 57), (2811, 18), (2813, 62), (2815, 57), (2817, 28), (2819, 28), (2821, 9), (2823, 18), (2825, 28), (2827, 38), (2829, 45), (2831, 9), (2833, 45), (2835, 26), (2837, 9), (2839, 45), (2841, 26), (2843, 62), (2845, 21), (2847, 62), (2849, 21), (2851, 6), (2853, 6), (2855, 45), (2857, 62), (2859, 26), (2861, 6), (2863, 26), (2865, 6), (2867, 6), (2869, 9), (2871, 26), (2873, 62), (2875, 16), (2877, 16), (2879, 45), (2881, 9), (2883, 50), (2885, 14), (2887, 45), (2889, 50), (2891, 14), (2893, 14), (2895, 16), (2897, 50), (2899, 50), (2901, 4), (2903, 50), (2905, 14), (2907, 50), (2909, 14), (2911, 50), (2913, 38), (2915, 9), (2917, 9), (2919, 79), (2921, 26), (2923, 50), (2925, 50), (2927, 62), (2929, 33), (2931, 9), (2933, 33), (2935, 50), (2937, 16), (2939, 26), (2941, 14), (2943, 62), (2945, 26), (2947, 33), (2949, 50), (2951, 33), (2953, 43), (2955, 50), (2957, 4), (2959, 33), (2961, 9), (2963, 9), (2965, 14), (2967, 50), (2969, 50), (2971, 14), (2973, 33), (2975, 14), (2977, 50), (2979, 14), (2981, 31), (2983, 50), (2985, 50), (2987, 14), (2989, 14), (2991, 14), (2993, 14), (2995, 14), (2997, 14), (2999, 14)])\n",
    "    smallodds4 = dict([(3001, 11), (3003, 11), (3005, 50), (3007, 55), (3009, 11), (3011, 11), (3013, 4), (3015, 31), (3017, 11), (3019, 21), (3021, 21), (3023, 31), (3025, 21), (3027, 21), (3029, 38), (3031, 50), (3033, 4), (3035, 55), (3037, 19), (3039, 55), (3041, 55), (3043, 38), (3045, 9), (3047, 19), (3049, 43), (3051, 55), (3053, 55), (3055, 31), (3057, 38), (3059, 19), (3061, 14), (3063, 19), (3065, 55), (3067, 19), (3069, 19), (3071, 55), (3073, 38), (3075, 55), (3077, 9), (3079, 55), (3081, 55), (3083, 9), (3085, 9), (3087, 38), (3089, 9), (3091, 19), (3093, 43), (3095, 9), (3097, 67), (3099, 48), (3101, 55), (3103, 31), (3105, 55), (3107, 43), (3109, 9), (3111, 9), (3113, 31), (3115, 19), (3117, 19), (3119, 14), (3121, 19), (3123, 19), (3125, 43), (3127, 55), (3129, 38), (3131, 38), (3133, 43), (3135, 19), (3137, 9), (3139, 9), (3141, 43), (3143, 36), (3145, 19), (3147, 43), (3149, 19), (3151, 19), (3153, 19), (3155, 31), (3157, 7), (3159, 43), (3161, 55), (3163, 16), (3165, 26), (3167, 60), (3169, 16), (3171, 26), (3173, 26), (3175, 72), (3177, 16), (3179, 26), (3181, 36), (3183, 19), (3185, 7), (3187, 43), (3189, 43), (3191, 24), (3193, 9), (3195, 24), (3197, 24), (3199, 60), (3201, 60), (3203, 19), (3205, 19), (3207, 14), (3209, 24), (3211, 43), (3213, 4), (3215, 60), (3217, 24), (3219, 24), (3221, 4), (3223, 4), (3225, 19), (3227, 36), (3229, 24), (3231, 60), (3233, 60), (3235, 14), (3237, 14), (3239, 43), (3241, 60), (3243, 14), (3245, 48), (3247, 14), (3249, 48), (3251, 48), (3253, 12), (3255, 24), (3257, 14), (3259, 14), (3261, 48), (3263, 24), (3265, 48), (3267, 48), (3269, 12), (3271, 48), (3273, 48), (3275, 48), (3277, 12), (3279, 36), (3281, 24), (3283, 24), (3285, 7), (3287, 24), (3289, 48), (3291, 48), (3293, 48), (3295, 48), (3297, 43), (3299, 7), (3301, 48), (3303, 24), (3305, 14), (3307, 24), (3309, 12), (3311, 60), (3313, 31), (3315, 24), (3317, 31), (3319, 12), (3321, 36), (3323, 41), (3325, 48), (3327, 24), (3329, 31), (3331, 65), (3333, 7), (3335, 65), (3337, 21), (3339, 31), (3341, 48), (3343, 12), (3345, 48), (3347, 31), (3349, 12), (3351, 48), (3353, 12), (3355, 31), (3357, 29), (3359, 48), (3361, 12), (3363, 12), (3365, 12), (3367, 29), (3369, 65), (3371, 24), (3373, 12), (3375, 48), (3377, 9), (3379, 9), (3381, 12), (3383, 48), (3385, 65), (3387, 12), (3389, 9), (3391, 65), (3393, 12), (3395, 9), (3397, 19), (3399, 41), (3401, 29), (3403, 19), (3405, 19), (3407, 19), (3409, 48), (3411, 48), (3413, 2), (3415, 53), (3417, 17), (3419, 53), (3421, 17), (3423, 53), (3425, 17), (3427, 7), (3429, 7), (3431, 41), (3433, 53), (3435, 53), (3437, 53), (3439, 53), (3441, 36), (3443, 17), (3445, 36), (3447, 17), (3449, 53), (3451, 17), (3453, 12), (3455, 17), (3457, 12), (3459, 36), (3461, 53), (3463, 36), (3465, 53), (3467, 53), (3469, 7), (3471, 36), (3473, 36), (3475, 36), (3477, 7), (3479, 17), (3481, 17), (3483, 29), (3485, 65), (3487, 46), (3489, 29), (3491, 53), (3493, 53), (3495, 17), (3497, 36), (3499, 46), (3501, 7), (3503, 29), (3505, 17), (3507, 17), (3509, 17), (3511, 12), (3513, 17), (3515, 53), (3517, 53), (3519, 26), (3521, 36), (3523, 36), (3525, 41), (3527, 17), (3529, 17), (3531, 34), (3533, 7), (3535, 53), (3537, 7), (3539, 17), (3541, 41), (3543, 17), (3545, 17), (3547, 17), (3549, 17), (3551, 29), (3553, 17), (3555, 41), (3557, 53), (3559, 14), (3561, 14), (3563, 58), (3565, 14), (3567, 70), (3569, 24), (3571, 7), (3573, 24), (3575, 14), (3577, 24), (3579, 24), (3581, 34), (3583, 34), (3585, 24), (3587, 41), (3589, 22), (3591, 53), (3593, 7), (3595, 22), (3597, 41), (3599, 22), (3601, 41), (3603, 58), (3605, 17), (3607, 12), (3609, 12), (3611, 22), (3613, 41), (3615, 22), (3617, 58), (3619, 17), (3621, 22), (3623, 41), (3625, 22), (3627, 17), (3629, 17), (3631, 34), (3633, 22), (3635, 22), (3637, 2), (3639, 58), (3641, 41), (3643, 58), (3645, 12), (3647, 58), (3649, 12), (3651, 12), (3653, 46), (3655, 41), (3657, 41), (3659, 46), (3661, 46), (3663, 22), (3665, 12), (3667, 12), (3669, 10), (3671, 46), (3673, 58), (3675, 34), (3677, 46), (3679, 58), (3681, 46), (3683, 46), (3685, 46), (3687, 12), (3689, 34), (3691, 22), (3693, 22), (3695, 75), (3697, 10), (3699, 22), (3701, 46), (3703, 46), (3705, 58), (3707, 46), (3709, 41), (3711, 87), (3713, 22), (3715, 10), (3717, 46), (3719, 12), (3721, 22), (3723, 46), (3725, 10), (3727, 22), (3729, 22), (3731, 22), (3733, 29), (3735, 10), (3737, 34), (3739, 39), (3741, 46), (3743, 22), (3745, 58), (3747, 29), (3749, 63), (3751, 19), (3753, 58), (3755, 19), (3757, 29), (3759, 29), (3761, 10), (3763, 10), (3765, 46), (3767, 29), (3769, 39), (3771, 39), (3773, 10), (3775, 29), (3777, 46), (3779, 27), (3781, 10), (3783, 46), (3785, 46), (3787, 27), (3789, 10), (3791, 63), (3793, 22), (3795, 22), (3797, 10), (3799, 22), (3801, 7), (3803, 27), (3805, 7), (3807, 46), (3809, 63), (3811, 10), (3813, 7), (3815, 63), (3817, 27), (3819, 7), (3821, 7), (3823, 63), (3825, 10), (3827, 27), (3829, 17), (3831, 63), (3833, 17), (3835, 46), (3837, 46), (3839, 39), (3841, 10), (3843, 51), (3845, 15), (3847, 51), (3849, 46), (3851, 51), (3853, 15), (3855, 15), (3857, 15), (3859, 17), (3861, 5), (3863, 51), (3865, 51), (3867, 27), (3869, 51), (3871, 39), (3873, 15), (3875, 15), (3877, 15), (3879, 51), (3881, 51), (3883, 15), (3885, 10), (3887, 15), (3889, 10), (3891, 10), (3893, 34), (3895, 27), (3897, 51), (3899, 51), (3901, 51), (3903, 63), (3905, 34), (3907, 10), (3909, 34), (3911, 27), (3913, 51), (3915, 34), (3917, 15), (3919, 27), (3921, 15), (3923, 63), (3925, 5), (3927, 27), (3929, 34), (3931, 27), (3933, 51), (3935, 34), (3937, 44), (3939, 5), (3941, 5), (3943, 63), (3945, 34), (3947, 68), (3949, 10), (3951, 24), (3953, 15), (3955, 51), (3957, 15), (3959, 51), (3961, 15), (3963, 15), (3965, 34), (3967, 15), (3969, 51), (3971, 15), (3973, 32), (3975, 15), (3977, 51), (3979, 32), (3981, 5), (3983, 15), (3985, 15), (3987, 15), (3989, 15), (3991, 15), (3993, 15), (3995, 27), (3997, 15), (3999, 68)])\n",
    "    smallodds5 = dict([(4001, 12), (4003, 15), (4005, 51), (4007, 12), (4009, 56), (4011, 68), (4013, 12), (4015, 12), (4017, 5), (4019, 5), (4021, 22), (4023, 12), (4025, 22), (4027, 22), (4029, 32), (4031, 32), (4033, 22), (4035, 22), (4037, 39), (4039, 51), (4041, 51), (4043, 5), (4045, 20), (4047, 56), (4049, 20), (4051, 56), (4053, 39), (4055, 56), (4057, 39), (4059, 20), (4061, 10), (4063, 20), (4065, 44), (4067, 39), (4069, 56), (4071, 56), (4073, 32), (4075, 56), (4077, 20), (4079, 20), (4081, 15), (4083, 20), (4085, 15), (4087, 56), (4089, 20), (4091, 44), (4093, 20), (4095, 56), (4097, 39), (4099, 56), (4101, 10), (4103, 56), (4105, 56), (4107, 10), (4109, 10), (4111, 10), (4113, 10), (4115, 39), (4117, 44), (4119, 10), (4121, 20), (4123, 32), (4125, 10), (4127, 61), (4129, 68), (4131, 44), (4133, 56), (4135, 32), (4137, 32), (4139, 56), (4141, 44), (4143, 20), (4145, 10), (4147, 10), (4149, 44), (4151, 32), (4153, 20), (4155, 20), (4157, 20), (4159, 15), (4161, 20), (4163, 20), (4165, 44), (4167, 39), (4169, 56), (4171, 44), (4173, 44), (4175, 39), (4177, 44), (4179, 20), (4181, 8), (4183, 10), (4185, 10), (4187, 20), (4189, 44), (4191, 37), (4193, 20), (4195, 20), (4197, 20), (4199, 20), (4201, 20), (4203, 20), (4205, 32), (4207, 37), (4209, 8), (4211, 44), (4213, 27), (4215, 56), (4217, 17), (4219, 56), (4221, 61), (4223, 56), (4225, 17), (4227, 27), (4229, 27), (4231, 10), (4233, 73), (4235, 17), (4237, 8), (4239, 27), (4241, 37), (4243, 37), (4245, 44), (4247, 8), (4249, 44), (4251, 27), (4253, 25), (4255, 73), (4257, 10), (4259, 44), (4261, 25), (4263, 44), (4265, 61), (4267, 44), (4269, 20), (4271, 61), (4273, 20), (4275, 20), (4277, 5), (4279, 25), (4281, 44), (4283, 44), (4285, 61), (4287, 44), (4289, 25), (4291, 25), (4293, 5), (4295, 25), (4297, 5), (4299, 20), (4301, 5), (4303, 37), (4305, 25), (4307, 25), (4309, 8), (4311, 61), (4313, 15), (4315, 44), (4317, 15), (4319, 44), (4321, 61), (4323, 8), (4325, 49), (4327, 61), (4329, 15), (4331, 44), (4333, 49), (4335, 20), (4337, 13), (4339, 25), (4341, 13), (4343, 15), (4345, 15), (4347, 66), (4349, 49), (4351, 25), (4353, 49), (4355, 49), (4357, 13), (4359, 61), (4361, 49), (4363, 49), (4365, 13), (4367, 49), (4369, 13), (4371, 37), (4373, 8), (4375, 25), (4377, 25), (4379, 78), (4381, 25), (4383, 25), (4385, 49), (4387, 49), (4389, 49), (4391, 61), (4393, 49), (4395, 44), (4397, 8), (4399, 34), (4401, 49), (4403, 49), (4405, 32), (4407, 15), (4409, 25), (4411, 13), (4413, 13), (4415, 61), (4417, 32), (4419, 25), (4421, 32), (4423, 25), (4425, 13), (4427, 32), (4429, 49), (4431, 42), (4433, 49), (4435, 25), (4437, 3), (4439, 32), (4441, 66), (4443, 32), (4445, 8), (4447, 66), (4449, 22), (4451, 49), (4453, 49), (4455, 32), (4457, 13), (4459, 13), (4461, 32), (4463, 13), (4465, 13), (4467, 49), (4469, 13), (4471, 13), (4473, 32), (4475, 49), (4477, 30), (4479, 49), (4481, 13), (4483, 13), (4485, 13), (4487, 13), (4489, 30), (4491, 66), (4493, 13), (4495, 25), (4497, 13), (4499, 13), (4501, 13), (4503, 10), (4505, 10), (4507, 30), (4509, 49), (4511, 54), (4513, 66), (4515, 10), (4517, 10), (4519, 30), (4521, 66), (4523, 30), (4525, 10), (4527, 10), (4529, 20), (4531, 20), (4533, 20), (4535, 30), (4537, 20), (4539, 66), (4541, 20), (4543, 66), (4545, 49), (4547, 49), (4549, 3), (4551, 66), (4553, 54), (4555, 18), (4557, 18), (4559, 54), (4561, 18), (4563, 54), (4565, 37), (4567, 18), (4569, 8), (4571, 18), (4573, 8), (4575, 42), (4577, 54), (4579, 37), (4581, 54), (4583, 30), (4585, 54), (4587, 42), (4589, 18), (4591, 61), (4593, 37), (4595, 18), (4597, 13), (4599, 54), (4601, 18), (4603, 42), (4605, 18), (4607, 54), (4609, 13), (4611, 37), (4613, 54), (4615, 30), (4617, 37), (4619, 54), (4621, 8), (4623, 54), (4625, 8), (4627, 37), (4629, 8), (4631, 37), (4633, 37), (4635, 30), (4637, 18), (4639, 30), (4641, 18), (4643, 8), (4645, 66), (4647, 18), (4649, 47), (4651, 8), (4653, 54), (4655, 30), (4657, 54), (4659, 54), (4661, 42), (4663, 37), (4665, 47), (4667, 8), (4669, 8), (4671, 30), (4673, 18), (4675, 18), (4677, 18), (4679, 13), (4681, 13), (4683, 18), (4685, 18), (4687, 54), (4689, 54), (4691, 54), (4693, 42), (4695, 37), (4697, 37), (4699, 27), (4701, 42), (4703, 18), (4705, 18), (4707, 8), (4709, 8), (4711, 18), (4713, 54), (4715, 35), (4717, 18), (4719, 35), (4721, 42), (4723, 18), (4725, 18), (4727, 18), (4729, 18), (4731, 18), (4733, 30), (4735, 54), (4737, 18), (4739, 42), (4741, 54), (4743, 18), (4745, 15), (4747, 54), (4749, 25), (4751, 59), (4753, 15), (4755, 15), (4757, 25), (4759, 25), (4761, 8), (4763, 71), (4765, 15), (4767, 35), (4769, 25), (4771, 35), (4773, 35), (4775, 18), (4777, 35), (4779, 25), (4781, 42), (4783, 25), (4785, 23), (4787, 23), (4789, 42), (4791, 8), (4793, 23), (4795, 59), (4797, 23), (4799, 59), (4801, 42), (4803, 59), (4805, 18), (4807, 42), (4809, 13), (4811, 13), (4813, 18), (4815, 23), (4817, 42), (4819, 42), (4821, 3), (4823, 59), (4825, 18), (4827, 35), (4829, 23), (4831, 42), (4833, 23), (4835, 3), (4837, 18), (4839, 59), (4841, 35), (4843, 59), (4845, 23), (4847, 59), (4849, 3), (4851, 59), (4853, 13), (4855, 42), (4857, 59), (4859, 42), (4861, 59), (4863, 30), (4865, 13), (4867, 13), (4869, 47), (4871, 13), (4873, 42), (4875, 42), (4877, 47), (4879, 47), (4881, 47), (4883, 23), (4885, 11), (4887, 13), (4889, 13), (4891, 64), (4893, 47), (4895, 23), (4897, 59), (4899, 47), (4901, 47), (4903, 35), (4905, 59), (4907, 47), (4909, 47), (4911, 42), (4913, 47), (4915, 47), (4917, 11), (4919, 35), (4921, 23), (4923, 23), (4925, 23), (4927, 76), (4929, 11), (4931, 23), (4933, 47), (4935, 71), (4937, 47), (4939, 47), (4941, 47), (4943, 47), (4945, 42), (4947, 42), (4949, 6), (4951, 23), (4953, 11), (4955, 23), (4957, 47), (4959, 13), (4961, 23), (4963, 11), (4965, 11), (4967, 59), (4969, 23), (4971, 23), (4973, 23), (4975, 23), (4977, 30), (4979, 11), (4981, 30), (4983, 35), (4985, 40), (4987, 59), (4989, 47), (4991, 23), (4993, 59), (4995, 30), (4997, 64), (4999, 30)])\n",
    "    smallodds6 = dict([(5001, 20), (5003, 64), (5005, 6), (5007, 20), (5009, 30), (5011, 30), (5013, 47), (5015, 11), (5017, 11), (5019, 20), (5021, 30), (5023, 30), (5025, 40), (5027, 47), (5029, 11), (5031, 40), (5033, 30), (5035, 47), (5037, 28), (5039, 47), (5041, 11), (5043, 11), (5045, 11), (5047, 47), (5049, 28), (5051, 28), (5053, 64), (5055, 28), (5057, 23), (5059, 23), (5061, 11), (5063, 47), (5065, 23), (5067, 8), (5069, 8), (5071, 28), (5073, 8), (5075, 47), (5077, 11), (5079, 64), (5081, 11), (5083, 28), (5085, 8), (5087, 64), (5089, 28), (5091, 11), (5093, 8), (5095, 23), (5097, 64), (5099, 40), (5101, 28), (5103, 28), (5105, 18), (5107, 64), (5109, 18), (5111, 18), (5113, 47), (5115, 18), (5117, 47), (5119, 40), (5121, 11), (5123, 52), (5125, 16), (5127, 52), (5129, 52), (5131, 16), (5133, 16), (5135, 52), (5137, 16), (5139, 16), (5141, 6), (5143, 16), (5145, 18), (5147, 40), (5149, 52), (5151, 30), (5153, 52), (5155, 6), (5157, 52), (5159, 52), (5161, 40), (5163, 16), (5165, 16), (5167, 64), (5169, 16), (5171, 16), (5173, 35), (5175, 52), (5177, 16), (5179, 40), (5181, 11), (5183, 16), (5185, 11), (5187, 11), (5189, 35), (5191, 23), (5193, 28), (5195, 35), (5197, 52), (5199, 52), (5201, 52), (5203, 64), (5205, 6), (5207, 35), (5209, 11), (5211, 47), (5213, 35), (5215, 28), (5217, 52), (5219, 16), (5221, 16), (5223, 18), (5225, 28), (5227, 16), (5229, 64), (5231, 45), (5233, 6), (5235, 28), (5237, 52), (5239, 35), (5241, 28), (5243, 16), (5245, 35), (5247, 28), (5249, 45), (5251, 6), (5253, 6), (5255, 28), (5257, 64), (5259, 35), (5261, 16), (5263, 69), (5265, 11), (5267, 11), (5269, 16), (5271, 16), (5273, 52), (5275, 35), (5277, 52), (5279, 25), (5281, 16), (5283, 35), (5285, 35), (5287, 25), (5289, 16), (5291, 16), (5293, 16), (5295, 52), (5297, 33), (5299, 33), (5301, 6), (5303, 52), (5305, 33), (5307, 52), (5309, 16), (5311, 33), (5313, 16), (5315, 16), (5317, 16), (5319, 16), (5321, 16), (5323, 16), (5325, 16), (5327, 28), (5329, 16), (5331, 16), (5333, 40), (5335, 13), (5337, 16), (5339, 13), (5341, 52), (5343, 13), (5345, 57), (5347, 40), (5349, 13), (5351, 69), (5353, 13), (5355, 33), (5357, 6), (5359, 69), (5361, 23), (5363, 13), (5365, 23), (5367, 23), (5369, 23), (5371, 45), (5373, 33), (5375, 33), (5377, 23), (5379, 23), (5381, 40), (5383, 23), (5385, 52), (5387, 52), (5389, 21), (5391, 6), (5393, 21), (5395, 57), (5397, 40), (5399, 21), (5401, 57), (5403, 23), (5405, 57), (5407, 21), (5409, 40), (5411, 11), (5413, 11), (5415, 11), (5417, 21), (5419, 11), (5421, 40), (5423, 21), (5425, 57), (5427, 57), (5429, 16), (5431, 33), (5433, 57), (5435, 40), (5437, 21), (5439, 21), (5441, 16), (5443, 21), (5445, 16), (5447, 33), (5449, 57), (5451, 16), (5453, 21), (5455, 45), (5457, 21), (5459, 57), (5461, 1), (5463, 40), (5465, 57), (5467, 40), (5469, 11), (5471, 57), (5473, 57), (5475, 11), (5477, 11), (5479, 69), (5481, 11), (5483, 40), (5485, 40), (5487, 16), (5489, 45), (5491, 11), (5493, 45), (5495, 21), (5497, 33), (5499, 21), (5501, 11), (5503, 62), (5505, 69), (5507, 45), (5509, 57), (5511, 45), (5513, 33), (5515, 57), (5517, 45), (5519, 57), (5521, 45), (5523, 45), (5525, 45), (5527, 11), (5529, 11), (5531, 11), (5533, 33), (5535, 45), (5537, 21), (5539, 21), (5541, 21), (5543, 74), (5545, 16), (5547, 16), (5549, 21), (5551, 21), (5553, 45), (5555, 45), (5557, 45), (5559, 57), (5561, 45), (5563, 40), (5565, 40), (5567, 86), (5569, 45), (5571, 21), (5573, 9), (5575, 21), (5577, 11), (5579, 11), (5581, 45), (5583, 21), (5585, 45), (5587, 38), (5589, 9), (5591, 21), (5593, 21), (5595, 45), (5597, 21), (5599, 21), (5601, 21), (5603, 9), (5605, 33), (5607, 21), (5609, 38), (5611, 57), (5613, 45), (5615, 21), (5617, 28), (5619, 57), (5621, 28), (5623, 18), (5625, 57), (5627, 18), (5629, 62), (5631, 57), (5633, 18), (5635, 28), (5637, 28), (5639, 28), (5641, 11), (5643, 28), (5645, 9), (5647, 18), (5649, 9), (5651, 28), (5653, 45), (5655, 38), (5657, 38), (5659, 21), (5661, 9), (5663, 28), (5665, 45), (5667, 45), (5669, 26), (5671, 26), (5673, 74), (5675, 45), (5677, 45), (5679, 57), (5681, 26), (5683, 26), (5685, 9), (5687, 62), (5689, 45), (5691, 62), (5693, 21), (5695, 62), (5697, 21), (5699, 21), (5701, 6), (5703, 16), (5705, 26), (5707, 6), (5709, 6), (5711, 45), (5713, 62), (5715, 62), (5717, 9), (5719, 26), (5721, 26), (5723, 62), (5725, 6), (5727, 26), (5729, 6), (5731, 6), (5733, 6), (5735, 62), (5737, 38), (5739, 62), (5741, 26), (5743, 26), (5745, 9), (5747, 62), (5749, 16), (5751, 16), (5753, 45), (5755, 16), (5757, 45), (5759, 38), (5761, 62), (5763, 9), (5765, 50), (5767, 16), (5769, 62), (5771, 50), (5773, 14), (5775, 45), (5777, 50), (5779, 50), (5781, 14), (5783, 14), (5785, 26), (5787, 26), (5789, 16), (5791, 38), (5793, 16), (5795, 50), (5797, 50), (5799, 74), (5801, 26), (5803, 62), (5805, 50), (5807, 38), (5809, 14), (5811, 14), (5813, 14), (5815, 50), (5817, 50), (5819, 50), (5821, 50), (5823, 50), (5825, 14), (5827, 38), (5829, 9), (5831, 14), (5833, 26), (5835, 26), (5837, 9), (5839, 79), (5841, 26), (5843, 26), (5845, 33), (5847, 50), (5849, 50), (5851, 50), (5853, 50), (5855, 62), (5857, 50), (5859, 33), (5861, 9), (5863, 45), (5865, 35), (5867, 26), (5869, 50), (5871, 26), (5873, 33), (5875, 16), (5877, 14), (5879, 26), (5881, 14), (5883, 50), (5885, 62), (5887, 43), (5889, 33), (5891, 26), (5893, 33), (5895, 26), (5897, 26), (5899, 14), (5901, 50), (5903, 33), (5905, 50), (5907, 43), (5909, 4), (5911, 50), (5913, 26), (5915, 62), (5917, 33), (5919, 62), (5921, 67), (5923, 9), (5925, 9), (5927, 23), (5929, 67), (5931, 9), (5933, 50), (5935, 33), (5937, 50), (5939, 50), (5941, 14), (5943, 14), (5945, 14), (5947, 50), (5949, 33), (5951, 14), (5953, 14), (5955, 50), (5957, 14), (5959, 43), (5961, 14), (5963, 14), (5965, 31), (5967, 50), (5969, 31), (5971, 50), (5973, 4), (5975, 14), (5977, 14), (5979, 16), (5981, 14), (5983, 14), (5985, 31), (5987, 14), (5989, 14), (5991, 31), (5993, 26), (5995, 26), (5997, 14), (5999, 67)])\n",
    "    smallodds7 = dict([(6001, 14), (6003, 11), (6005, 14), (6007, 11), (6009, 31), (6011, 11), (6013, 50), (6015, 55), (6017, 67), (6019, 11), (6021, 11), (6023, 11), (6025, 31), (6027, 67), (6029, 4), (6031, 31), (6033, 11), (6035, 11), (6037, 21), (6039, 21), (6041, 21), (6043, 43), (6045, 31), (6047, 31), (6049, 21), (6051, 21), (6053, 21), (6055, 31), (6057, 67), (6059, 50), (6061, 50), (6063, 50), (6065, 4), (6067, 4), (6069, 19), (6071, 55), (6073, 19), (6075, 19), (6077, 55), (6079, 21), (6081, 19), (6083, 55), (6085, 38), (6087, 55), (6089, 19), (6091, 9), (6093, 9), (6095, 19), (6097, 9), (6099, 43), (6101, 38), (6103, 55), (6105, 38), (6107, 55), (6109, 55), (6111, 31), (6113, 55), (6115, 38), (6117, 19), (6119, 19), (6121, 62), (6123, 67), (6125, 19), (6127, 19), (6129, 14), (6131, 55), (6133, 14), (6135, 19), (6137, 43), (6139, 43), (6141, 19), (6143, 55), (6145, 14), (6147, 38), (6149, 55), (6151, 38), (6153, 31), (6155, 55), (6157, 9), (6159, 55), (6161, 9), (6163, 55), (6165, 9), (6167, 9), (6169, 38), (6171, 96), (6173, 38), (6175, 50), (6177, 38), (6179, 9), (6181, 19), (6183, 55), (6185, 31), (6187, 19), (6189, 9), (6191, 60), (6193, 67), (6195, 67), (6197, 43), (6199, 48), (6201, 9), (6203, 31), (6205, 55), (6207, 31), (6209, 55), (6211, 55), (6213, 43), (6215, 19), (6217, 38), (6219, 43), (6221, 9), (6223, 9), (6225, 9), (6227, 31), (6229, 43), (6231, 19), (6233, 19), (6235, 67), (6237, 19), (6239, 14), (6241, 14), (6243, 19), (6245, 19), (6247, 67), (6249, 55), (6251, 38), (6253, 55), (6255, 38), (6257, 43), (6259, 38), (6261, 43), (6263, 38), (6265, 28), (6267, 19), (6269, 19), (6271, 38), (6273, 19), (6275, 9), (6277, 9), (6279, 36), (6281, 19), (6283, 55), (6285, 43), (6287, 36), (6289, 19), (6291, 19), (6293, 19), (6295, 43), (6297, 19), (6299, 19), (6301, 19), (6303, 55), (6305, 19), (6307, 19), (6309, 31), (6311, 36), (6313, 55), (6315, 19), (6317, 43), (6319, 72), (6321, 55), (6323, 55), (6325, 26), (6327, 16), (6329, 55), (6331, 16), (6333, 60), (6335, 55), (6337, 16), (6339, 16), (6341, 26), (6343, 16), (6345, 26), (6347, 9), (6349, 26), (6351, 72), (6353, 16), (6355, 16), (6357, 7), (6359, 26), (6361, 36), (6363, 26), (6365, 36), (6367, 19), (6369, 36), (6371, 7), (6373, 43), (6375, 72), (6377, 26), (6379, 26), (6381, 24), (6383, 72), (6385, 43), (6387, 9), (6389, 43), (6391, 24), (6393, 60), (6395, 43), (6397, 24), (6399, 60), (6401, 43), (6403, 60), (6405, 19), (6407, 60), (6409, 43), (6411, 14), (6413, 19), (6415, 14), (6417, 19), (6419, 24), (6421, 4), (6423, 43), (6425, 43), (6427, 24), (6429, 60), (6431, 43), (6433, 19), (6435, 24), (6437, 24), (6439, 60), (6441, 43), (6443, 24), (6445, 4), (6447, 24), (6449, 19), (6451, 19), (6453, 4), (6455, 36), (6457, 60), (6459, 24), (6461, 24), (6463, 60), (6465, 4), (6467, 60), (6469, 14), (6471, 60), (6473, 43), (6475, 14), (6477, 14), (6479, 43), (6481, 60), (6483, 60), (6485, 7), (6487, 14), (6489, 14), (6491, 60), (6493, 48), (6495, 14), (6497, 43), (6499, 48), (6501, 48), (6503, 19), (6505, 48), (6507, 14), (6509, 24), (6511, 24), (6513, 12), (6515, 14), (6517, 12), (6519, 14), (6521, 65), (6523, 72), (6525, 48), (6527, 24), (6529, 60), (6531, 48), (6533, 48), (6535, 48), (6537, 36), (6539, 60), (6541, 12), (6543, 48), (6545, 48), (6547, 48), (6549, 12), (6551, 48), (6553, 48), (6555, 14), (6557, 36), (6559, 14), (6561, 24), (6563, 24), (6565, 24), (6567, 24), (6569, 77), (6571, 19), (6573, 24), (6575, 24), (6577, 48), (6579, 48), (6581, 48), (6583, 48), (6585, 48), (6587, 60), (6589, 48), (6591, 89), (6593, 43), (6595, 43), (6597, 7), (6599, 33), (6601, 24), (6603, 12), (6605, 48), (6607, 24), (6609, 48), (6611, 14), (6613, 31), (6615, 24), (6617, 12), (6619, 48), (6621, 12), (6623, 60), (6625, 24), (6627, 31), (6629, 24), (6631, 48), (6633, 24), (6635, 24), (6637, 12), (6639, 24), (6641, 31), (6643, 36), (6645, 48), (6647, 41), (6649, 60), (6651, 12), (6653, 24), (6655, 60), (6657, 60), (6659, 31), (6661, 65), (6663, 21), (6665, 31), (6667, 65), (6669, 7), (6671, 65), (6673, 7), (6675, 21), (6677, 48), (6679, 31), (6681, 31), (6683, 31), (6685, 12), (6687, 14), (6689, 12), (6691, 48), (6693, 31), (6695, 12), (6697, 31), (6699, 48), (6701, 48), (6703, 31), (6705, 12), (6707, 12), (6709, 12), (6711, 31), (6713, 48), (6715, 48), (6717, 29), (6719, 48), (6721, 12), (6723, 12), (6725, 12), (6727, 14), (6729, 48), (6731, 12), (6733, 12), (6735, 29), (6737, 65), (6739, 65), (6741, 12), (6743, 24), (6745, 24), (6747, 65), (6749, 12), (6751, 48), (6753, 24), (6755, 9), (6757, 9), (6759, 19), (6761, 29), (6763, 9), (6765, 48), (6767, 53), (6769, 12), (6771, 65), (6773, 9), (6775, 12), (6777, 29), (6779, 29), (6781, 65), (6783, 65), (6785, 29), (6787, 12), (6789, 9), (6791, 9), (6793, 24), (6795, 9), (6797, 19), (6799, 41), (6801, 29), (6803, 29), (6805, 19), (6807, 19), (6809, 65), (6811, 31), (6813, 19), (6815, 65), (6817, 48), (6819, 48), (6821, 48), (6823, 41), (6825, 41), (6827, 65), (6829, 53), (6831, 12), (6833, 17), (6835, 17), (6837, 17), (6839, 53), (6841, 17), (6843, 48), (6845, 53), (6847, 19), (6849, 17), (6851, 17), (6853, 7), (6855, 29), (6857, 17), (6859, 19), (6861, 7), (6863, 41), (6865, 53), (6867, 53), (6869, 36), (6871, 53), (6873, 7), (6875, 29), (6877, 53), (6879, 53), (6881, 41), (6883, 36), (6885, 17), (6887, 60), (6889, 65), (6891, 53), (6893, 17), (6895, 29), (6897, 36), (6899, 53), (6901, 12), (6903, 17), (6905, 41), (6907, 41), (6909, 17), (6911, 53), (6913, 12), (6915, 12), (6917, 36), (6919, 82), (6921, 24), (6923, 29), (6925, 53), (6927, 36), (6929, 53), (6931, 53), (6933, 7), (6935, 53), (6937, 65), (6939, 29), (6941, 36), (6943, 94), (6945, 12), (6947, 36), (6949, 36), (6951, 38), (6953, 29), (6955, 53), (6957, 17), (6959, 29), (6961, 17), (6963, 17), (6965, 7), (6967, 29), (6969, 17), (6971, 17), (6973, 65), (6975, 46), (6977, 7), (6979, 29), (6981, 53), (6983, 29), (6985, 36), (6987, 53), (6989, 53), (6991, 17), (6993, 36), (6995, 36), (6997, 41), (6999, 46)])\n",
    "    smallodds8 = dict([(7001, 7), (7003, 53), (7005, 7), (7007, 29), (7009, 65), (7011, 17), (7013, 17), (7015, 65), (7017, 70), (7019, 12), (7021, 12), (7023, 70), (7025, 17), (7027, 17), (7029, 17), (7031, 53), (7033, 36), (7035, 36), (7037, 53), (7039, 26), (7041, 17), (7043, 36), (7045, 36), (7047, 36), (7049, 26), (7051, 17), (7053, 41), (7055, 17), (7057, 17), (7059, 17), (7061, 7), (7063, 34), (7065, 34), (7067, 17), (7069, 53), (7071, 17), (7073, 34), (7075, 7), (7077, 17), (7079, 34), (7081, 34), (7083, 17), (7085, 17), (7087, 17), (7089, 17), (7091, 17), (7093, 17), (7095, 17), (7097, 17), (7099, 17), (7101, 29), (7103, 53), (7105, 17), (7107, 17), (7109, 41), (7111, 53), (7113, 14), (7115, 17), (7117, 53), (7119, 14), (7121, 53), (7123, 14), (7125, 24), (7127, 58), (7129, 41), (7131, 70), (7133, 14), (7135, 70), (7137, 14), (7139, 24), (7141, 7), (7143, 70), (7145, 70), (7147, 34), (7149, 14), (7151, 34), (7153, 24), (7155, 24), (7157, 34), (7159, 24), (7161, 46), (7163, 17), (7165, 34), (7167, 70), (7169, 24), (7171, 24), (7173, 41), (7175, 24), (7177, 24), (7179, 41), (7181, 22), (7183, 53), (7185, 22), (7187, 7), (7189, 41), (7191, 22), (7193, 58), (7195, 41), (7197, 22), (7199, 58), (7201, 58), (7203, 41), (7205, 58), (7207, 22), (7209, 22), (7211, 41), (7213, 12), (7215, 22), (7217, 12), (7219, 12), (7221, 17), (7223, 22), (7225, 12), (7227, 46), (7229, 41), (7231, 22), (7233, 58), (7235, 58), (7237, 17), (7239, 12), (7241, 34), (7243, 17), (7245, 22), (7247, 41), (7249, 22), (7251, 22), (7253, 2), (7255, 17), (7257, 22), (7259, 58), (7261, 17), (7263, 34), (7265, 58), (7267, 22), (7269, 22), (7271, 58), (7273, 46), (7275, 46), (7277, 58), (7279, 63), (7281, 2), (7283, 41), (7285, 12), (7287, 58), (7289, 41), (7291, 58), (7293, 58), (7295, 29), (7297, 58), (7299, 12), (7301, 12), (7303, 58), (7305, 70), (7307, 12), (7309, 46), (7311, 41), (7313, 41), (7315, 41), (7317, 46), (7319, 46), (7321, 12), (7323, 58), (7325, 22), (7327, 34), (7329, 34), (7331, 12), (7333, 12), (7335, 24), (7337, 63), (7339, 70), (7341, 46), (7343, 22), (7345, 58), (7347, 58), (7349, 46), (7351, 34), (7353, 58), (7355, 34), (7357, 58), (7359, 51), (7361, 46), (7363, 46), (7365, 46), (7367, 41), (7369, 12), (7371, 12), (7373, 46), (7375, 12), (7377, 34), (7379, 34), (7381, 10), (7383, 22), (7385, 22), (7387, 22), (7389, 22), (7391, 75), (7393, 17), (7395, 10), (7397, 22), (7399, 31), (7401, 22), (7403, 70), (7405, 46), (7407, 17), (7409, 46), (7411, 58), (7413, 46), (7415, 46), (7417, 41), (7419, 22), (7421, 41), (7423, 87), (7425, 46), (7427, 22), (7429, 10), (7431, 22), (7433, 22), (7435, 12), (7437, 46), (7439, 12), (7441, 46), (7443, 22), (7445, 10), (7447, 46), (7449, 39), (7451, 58), (7453, 22), (7455, 22), (7457, 22), (7459, 22), (7461, 22), (7463, 22), (7465, 22), (7467, 22), (7469, 10), (7471, 22), (7473, 34), (7475, 34), (7477, 29), (7479, 39), (7481, 58), (7483, 10), (7485, 46), (7487, 22), (7489, 29), (7491, 58), (7493, 29), (7495, 22), (7497, 19), (7499, 29), (7501, 63), (7503, 19), (7505, 63), (7507, 58), (7509, 5), (7511, 19), (7513, 29), (7515, 75), (7517, 29), (7519, 29), (7521, 12), (7523, 10), (7525, 10), (7527, 53), (7529, 19), (7531, 19), (7533, 29), (7535, 29), (7537, 46), (7539, 39), (7541, 46), (7543, 39), (7545, 22), (7547, 39), (7549, 10), (7551, 29), (7553, 46), (7555, 46), (7557, 27), (7559, 46), (7561, 27), (7563, 27), (7565, 10), (7567, 46), (7569, 46), (7571, 46), (7573, 10), (7575, 27), (7577, 27), (7579, 46), (7581, 63), (7583, 27), (7585, 46), (7587, 22), (7589, 22), (7591, 63), (7593, 63), (7595, 46), (7597, 22), (7599, 17), (7601, 7), (7603, 7), (7605, 7), (7607, 27), (7609, 7), (7611, 46), (7613, 46), (7615, 17), (7617, 63), (7619, 63), (7621, 10), (7623, 22), (7625, 27), (7627, 27), (7629, 7), (7631, 63), (7633, 7), (7635, 27), (7637, 10), (7639, 7), (7641, 7), (7643, 22), (7645, 7), (7647, 63), (7649, 39), (7651, 10), (7653, 27), (7655, 27), (7657, 27), (7659, 63), (7661, 63), (7663, 29), (7665, 17), (7667, 17), (7669, 17), (7671, 46), (7673, 17), (7675, 63), (7677, 46), (7679, 39), (7681, 63), (7683, 10), (7685, 51), (7687, 17), (7689, 17), (7691, 51), (7693, 15), (7695, 51), (7697, 15), (7699, 46), (7701, 15), (7703, 51), (7705, 51), (7707, 22), (7709, 15), (7711, 46), (7713, 27), (7715, 15), (7717, 17), (7719, 15), (7721, 39), (7723, 15), (7725, 51), (7727, 29), (7729, 51), (7731, 51), (7733, 5), (7735, 27), (7737, 63), (7739, 51), (7741, 51), (7743, 39), (7745, 15), (7747, 15), (7749, 15), (7751, 63), (7753, 51), (7755, 15), (7757, 15), (7759, 51), (7761, 51), (7763, 51), (7765, 34), (7767, 15), (7769, 39), (7771, 39), (7773, 10), (7775, 15), (7777, 27), (7779, 10), (7781, 10), (7783, 27), (7785, 80), (7787, 22), (7789, 27), (7791, 22), (7793, 34), (7795, 51), (7797, 51), (7799, 51), (7801, 51), (7803, 51), (7805, 63), (7807, 27), (7809, 51), (7811, 34), (7813, 10), (7815, 46), (7817, 46), (7819, 10), (7821, 34), (7823, 27), (7825, 51), (7827, 51), (7829, 15), (7831, 34), (7833, 17), (7835, 17), (7837, 27), (7839, 27), (7841, 15), (7843, 15), (7845, 63), (7847, 44), (7849, 44), (7851, 27), (7853, 27), (7855, 27), (7857, 34), (7859, 34), (7861, 51), (7863, 27), (7865, 15), (7867, 15), (7869, 34), (7871, 27), (7873, 51), (7875, 44), (7877, 5), (7879, 51), (7881, 51), (7883, 27), (7885, 5), (7887, 63), (7889, 34), (7891, 34), (7893, 15), (7895, 68), (7897, 10), (7899, 34), (7901, 10), (7903, 24), (7905, 68), (7907, 15), (7909, 51), (7911, 24), (7913, 34), (7915, 34), (7917, 51), (7919, 24), (7921, 15), (7923, 15), (7925, 34), (7927, 15), (7929, 51), (7931, 24), (7933, 15), (7935, 44), (7937, 15), (7939, 51), (7941, 15), (7943, 51), (7945, 44), (7947, 15), (7949, 32), (7951, 15), (7953, 32), (7955, 51), (7957, 5), (7959, 32), (7961, 51), (7963, 92), (7965, 15), (7967, 32), (7969, 15), (7971, 15), (7973, 15), (7975, 51), (7977, 15), (7979, 15), (7981, 15), (7983, 15), (7985, 15), (7987, 15), (7989, 15), (7991, 27), (7993, 27), (7995, 15), (7997, 15), (7999, 68)])    \n",
    "    s1 = 0;s2=0\n",
    "    i = start\n",
    "    while i < end:\n",
    "       \n",
    "        # generated by apriorigenerator\n",
    "        r = (i % skipmodulus)\n",
    "        if r in skip1set: i = i + 2\n",
    "        elif r in skip2set: i = i + 4\n",
    "        elif r in skip3set: i = i + 6\n",
    "        elif r in skip4set: i = i + 8\n",
    "        elif r in skip5set: i = i + 10\n",
    "        elif r in skip6set: i = i + 12\n",
    "        elif r in skip7set: i = i + 14\n",
    "        elif r in skip8set: i = i + 16\n",
    "        elif r in skip9set: i = i + 18\n",
    "            \n",
    "        n = i\n",
    "        odds = 0\n",
    "        \n",
    "       # special = 10971\n",
    "       # if i == special: print(\"{} made it past APRIORI, n = {}, odds = {}\".format(special,n,odds))\n",
    "    \n",
    "        while n != 1:  \n",
    "            \n",
    "            # generated by equivalencegenerator\n",
    "            res = (n % 256)\n",
    "            if res < 128:\n",
    "                if res < 64:\n",
    "                    if res < 32:\n",
    "                        if res < 16:\n",
    "                            if res < 8:\n",
    "                                if res < 4:\n",
    "                                    if res == 1: n = (81*n + 175) // 256; odds = odds + 3\n",
    "                                    else: n = (81*n + 269) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 5: n = (27*n + 121) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 347) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 12:\n",
    "                                    if res == 9: n = (243*n + 373) // 256; odds = odds + 4\n",
    "                                    else: n = (81*n + 133) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 13: n = (27*n + 161) // 256; odds = odds + 2\n",
    "                                    else: n = (81*n + 65) // 256; odds = odds + 3\n",
    "                        else:\n",
    "                            if res < 24:\n",
    "                                if res < 20:\n",
    "                                    if res == 17: n = (27*n + 53) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 503) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 21: n = (9*n + 67) // 256; odds = odds + 1\n",
    "                                    else: n = (81*n + 185) // 256; odds = odds + 3\n",
    "                            else:\n",
    "                                if res < 28:\n",
    "                                    if res == 25: n = (243*n + 581) // 256; odds = odds + 4\n",
    "                                    else: n = (2187*n + 2903) // 256; odds = odds + 6\n",
    "                                else:\n",
    "                                    if res == 29: n = (81*n + 211) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 697) // 256; odds = odds + 5\n",
    "                    else:\n",
    "                        if res < 48:\n",
    "                            if res < 40:\n",
    "                                if res < 36:\n",
    "                                    if res == 33: n = (81*n + 143) // 256; odds = odds + 3\n",
    "                                    else: n = (27*n + 79) // 256; odds = odds + 2\n",
    "                                else:\n",
    "                                    if res == 37: n = (81*n + 331) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 251) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 44:\n",
    "                                    if res == 41: n = (729*n + 1087) // 256; odds = odds + 5\n",
    "                                    else: n = (81*n + 101) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 45: n = (27*n + 65) // 256; odds = odds + 2\n",
    "                                    else: n = (729*n + 809) // 256; odds = odds + 5\n",
    "                        else:\n",
    "                            if res < 56:\n",
    "                                if res < 52:\n",
    "                                    if res == 49: n = (81*n + 383) // 256; odds = odds + 3\n",
    "                                    else: n = (81*n + 221) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 53: n = (9*n + 35) // 256; odds = odds + 1\n",
    "                                    else: n = (729*n + 1121) // 256; odds = odds + 5\n",
    "                            else:\n",
    "                                if res < 60:\n",
    "                                    if res == 57: n = (243*n + 485) // 256; odds = odds + 4\n",
    "                                    else: n = (81*n + 85) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 61: n = (81*n + 179) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 665) // 256; odds = odds + 5\n",
    "                else:\n",
    "                    if res < 96:\n",
    "                        if res < 80:\n",
    "                            if res < 72:\n",
    "                                if res < 68:\n",
    "                                    if res == 65: n = (27*n + 37) // 256; odds = odds + 2\n",
    "                                    else: n = (81*n + 205) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 69: n = (27*n + 185) // 256; odds = odds + 2\n",
    "                                    else: n = (729*n + 977) // 256; odds = odds + 5\n",
    "                            else:\n",
    "                                if res < 76:\n",
    "                                    if res == 73: n = (243*n + 437) // 256; odds = odds + 4\n",
    "                                    else: n = (27*n + 23) // 256; odds = odds + 2\n",
    "                                else:\n",
    "                                    if res == 77: n = (81*n + 419) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 259) // 256; odds = odds + 4\n",
    "                        else:\n",
    "                            if res < 88:\n",
    "                                if res < 84:\n",
    "                                    if res == 81: n = (243*n + 797) // 256; odds = odds + 4\n",
    "                                    else: n = (729*n + 1445) // 256; odds = odds + 5\n",
    "                                else:\n",
    "                                    if res == 85: n = (3*n + 1) // 256\n",
    "                                    else: n = (81*n + 121) // 256; odds = odds + 3\n",
    "                            else:\n",
    "                                if res < 92:\n",
    "                                    if res == 89: n = (81*n + 215) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 989) // 256; odds = odds + 5\n",
    "                                else:\n",
    "                                    if res == 93: n = (27*n + 49) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 211) // 256; odds = odds + 4\n",
    "                    else:\n",
    "                        if res < 112:\n",
    "                            if res < 104:\n",
    "                                if res < 100:\n",
    "                                    if res == 97: n = (243*n + 493) // 256; odds = odds + 4\n",
    "                                    else: n = (27*n + 143) // 256; odds = odds + 2\n",
    "                                else:\n",
    "                                    if res == 101: n = (27*n + 89) // 256; odds = odds + 2\n",
    "                                    else: n = (2187*n + 2579) // 256; odds = odds + 6\n",
    "                            else:\n",
    "                                if res < 108:\n",
    "                                    if res == 105: n = (243*n + 341) // 256; odds = odds + 4\n",
    "                                    else: n = (243*n + 367) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 109: n = (243*n + 905) // 256; odds = odds + 4\n",
    "                                    else: n = (729*n + 745) // 256; odds = odds + 5\n",
    "                        else:\n",
    "                            if res < 120:\n",
    "                                if res < 116:\n",
    "                                    if res == 113: n = (9*n + 7) // 256; odds = odds + 1\n",
    "                                    else: n = (81*n + 157) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 117: n = (27*n + 169) // 256; odds = odds + 2\n",
    "                                    else: n = (81*n + 89) // 256; odds = odds + 3\n",
    "                            else:\n",
    "                                if res < 124:\n",
    "                                    if res == 121: n = (729*n + 1391) // 256; odds = odds + 5\n",
    "                                    else: n = (243*n + 319) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 125: n = (243*n + 601) // 256; odds = odds + 4\n",
    "                                    else: n = (2187*n + 2059) // 256; odds = odds + 6\n",
    "            else:\n",
    "                if res < 192:\n",
    "                    if res < 160:\n",
    "                        if res < 144:\n",
    "                            if res < 136:\n",
    "                                if res < 132:\n",
    "                                    if res == 129: n = (243*n + 653) // 256; odds = odds + 4\n",
    "                                    else: n = (27*n + 47) // 256; odds = odds + 2\n",
    "                                else:\n",
    "                                    if res == 133: n = (81*n + 491) // 256; odds = odds + 3\n",
    "                                    else: n = (81*n + 73) // 256; odds = odds + 3\n",
    "                            else:\n",
    "                                if res < 140:\n",
    "                                    if res == 137: n = (729*n + 1247) // 256; odds = odds + 5\n",
    "                                    else: n = (243*n + 527) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 141: n = (9*n + 11) // 256; odds = odds + 1\n",
    "                                    else: n = (243*n + 323) // 256; odds = odds + 4\n",
    "                        else:\n",
    "                            if res < 152:\n",
    "                                if res < 148:\n",
    "                                    if res == 145: n = (81*n + 287) // 256; odds = odds + 3\n",
    "                                    else: n = (81*n + 125) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 149: n = (27*n + 329) // 256; odds = odds + 2\n",
    "                                    else: n = (27*n + 19) // 256; odds = odds + 2\n",
    "                            else:\n",
    "                                if res < 156:\n",
    "                                    if res == 153: n = (81*n + 151) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 925) // 256; odds = odds + 5\n",
    "                                else:\n",
    "                                    if res == 157: n = (243*n + 761) // 256; odds = odds + 4\n",
    "                                    else: n = (2187*n + 2219) // 256; odds = odds + 6\n",
    "                    else:\n",
    "                        if res < 176:\n",
    "                            if res < 168:\n",
    "                                if res < 164:\n",
    "                                    if res == 161: n = (243*n + 557) // 256; odds = odds + 4\n",
    "                                    else: n = (81*n + 365) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 165: n = (243*n + 1121) // 256; odds = odds + 4\n",
    "                                    else: n = (729*n + 881) // 256; odds = odds + 5\n",
    "                            else:\n",
    "                                if res < 172:\n",
    "                                    if res == 169: n = (2187*n + 3389) // 256; odds = odds + 6\n",
    "                                    else: n = (243*n + 431) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 173: n = (81*n + 323) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 227) // 256; odds = odds + 4\n",
    "                        else:\n",
    "                            if res < 184:\n",
    "                                if res < 180:\n",
    "                                    if res == 177: n = (27*n + 85) // 256; odds = odds + 2\n",
    "                                    else: n = (27*n + 31) // 256; odds = odds + 2\n",
    "                                else:\n",
    "                                    if res == 181: n = (27*n + 233) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 331) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 188:\n",
    "                                    if res == 185: n = (81*n + 119) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 383) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 189: n = (243*n + 665) // 256; odds = odds + 4\n",
    "                                    else: n = (2187*n + 2123) // 256; odds = odds + 6\n",
    "                else:\n",
    "                    if res < 224:\n",
    "                        if res < 208:\n",
    "                            if res < 200:\n",
    "                                if res < 196:\n",
    "                                    if res == 193: n = (81*n + 239) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 743) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 197: n = (9*n + 19) // 256; odds = odds + 1\n",
    "                                    else: n = (243*n + 283) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 204:\n",
    "                                    if res == 201: n = (81*n + 103) // 256; odds = odds + 3\n",
    "                                    else: n = (81*n + 197) // 256; odds = odds + 3\n",
    "                                else:\n",
    "                                    if res == 205: n = (27*n + 97) // 256; odds = odds + 2\n",
    "                                    else: n = (729*n + 905) // 256; odds = odds + 5\n",
    "                        else:\n",
    "                            if res < 216:\n",
    "                                if res < 212:\n",
    "                                    if res == 209: n = (81*n + 223) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 439) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 213: n = (9*n + 131) // 256; odds = odds + 1\n",
    "                                    else: n = (243*n + 491) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 220:\n",
    "                                    if res == 217: n = (27*n + 29) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 287) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 221: n = (81*n + 275) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 761) // 256; odds = odds + 5\n",
    "                    else:\n",
    "                        if res < 240:\n",
    "                            if res < 232:\n",
    "                                if res < 228:\n",
    "                                    if res == 225: n = (729*n + 1607) // 256; odds = odds + 5\n",
    "                                    else: n = (9*n + 5) // 256; odds = odds + 1\n",
    "                                else:\n",
    "                                    if res == 229: n = (81*n + 395) // 256; odds = odds + 3\n",
    "                                    else: n = (729*n + 817) // 256; odds = odds + 5\n",
    "                            else:\n",
    "                                if res < 236:\n",
    "                                    if res == 233: n = (729*n + 1151) // 256; odds = odds + 5\n",
    "                                    else: n = (729*n + 1229) // 256; odds = odds + 5\n",
    "                                else:\n",
    "                                    if res == 237: n = (81*n + 259) // 256; odds = odds + 3\n",
    "                                    else: n = (2187*n + 2363) // 256; odds = odds + 6\n",
    "                        else:\n",
    "                            if res < 248:\n",
    "                                if res < 244:\n",
    "                                    if res == 241: n = (27*n + 149) // 256; odds = odds + 2\n",
    "                                    else: n = (243*n + 599) // 256; odds = odds + 4\n",
    "                                else:\n",
    "                                    if res == 245: n = (81*n + 635) // 256; odds = odds + 3\n",
    "                                    else: n = (243*n + 395) // 256; odds = odds + 4\n",
    "                            else:\n",
    "                                if res < 252:\n",
    "                                    if res == 249: n = (243*n + 421) // 256; odds = odds + 4\n",
    "                                    else: n = (729*n + 1085) // 256; odds = odds + 5\n",
    "                                else:\n",
    "                                    if res == 253: n = (729*n + 1931) // 256; odds = odds + 5\n",
    "                                    else: n = (6561*n + 6305) // 256; odds = odds + 7\n",
    "                                        \n",
    "            #if i == special: print(\"{} made it past LOOP, n = {}, mod128 = {}, odds = {}\".format(special,n,n%128,odds))\n",
    "                \n",
    "            if n != 1:\n",
    "                while not (n & 1):\n",
    "                    if ((n % 4) == 0):\n",
    "                        if ((n % 8) == 0):\n",
    "                            if ((n % 16) == 0):\n",
    "                                if ((n % 32) == 0):\n",
    "                                    if ((n % 64) == 0):\n",
    "                                        if ((n % 128) == 0):\n",
    "                                            if ((n % 256) == 0):\n",
    "                                                if ((n % 512) == 0):\n",
    "                                                    n = n // 512\n",
    "                                                else: n = n // 256\n",
    "                                            else: n = n // 128\n",
    "                                        else: n = n // 64\n",
    "                                    else: n = n // 32\n",
    "                                else: n = n // 16\n",
    "                            else: n = n // 8\n",
    "                        else: n = n // 4                                \n",
    "                    else: n = n // 2\n",
    "                odds = odds + 1\n",
    "            \n",
    "            #if i == special: print(\"{} made it past DIV BY 2, n = {}, odds = {}\".format(special,n,odds))\n",
    "                \n",
    "            if n < smalloddssize:               \n",
    "                if n < 4000:\n",
    "                    if n < 2000:\n",
    "                        if n < 1000: odds = odds + smallodds1[n]\n",
    "                        else: odds = odds + smallodds2[n]\n",
    "                    else:\n",
    "                        if n < 3000: odds = odds + smallodds3[n]\n",
    "                        else: odds = odds + smallodds4[n]\n",
    "                else:\n",
    "                    if n < 6000:\n",
    "                        if n < 5000: odds = odds + smallodds5[n]\n",
    "                        else: odds = odds + smallodds6[n]\n",
    "                    else:\n",
    "                        if n < 7000: odds = odds + smallodds7[n]\n",
    "                        else: odds = odds + smallodds8[n]\n",
    "                n = 1\n",
    "                #break\n",
    "            else:\n",
    "                newodds = currentrecordodds - odds\n",
    "                \n",
    "                # generated by laddergenerator\n",
    "                if n <= i1:\n",
    "                    if o1 <= newodds: n = 1\n",
    "                    elif n <= i2:\n",
    "                        if o2 <= newodds: n = 1\n",
    "                        elif n <= i3:\n",
    "                            if o3 <= newodds: n = 1\n",
    "                            elif n <= i4:\n",
    "                                if o4 <= newodds: n = 1\n",
    "                                elif n <= i5:\n",
    "                                    if o5 <= newodds: n = 1\n",
    "                                    elif n <= i6:\n",
    "                                        if o6 <= newodds: n = 1\n",
    "                                        elif n <= i7:\n",
    "                                            if o7 <= newodds: n = 1\n",
    "                                            elif n <= i8:\n",
    "                                                if o8 <= newodds: n = 1\n",
    "                                                elif n <= i9:\n",
    "                                                    if o9 <= newodds: n = 1\n",
    "                                                    elif n <= i10:\n",
    "                                                        if o10 <= newodds: n = 1\n",
    "                                                        elif n <= i11:\n",
    "                                                            if o11 <= newodds: n = 1\n",
    "                                                            elif n <= i12:\n",
    "                                                                if o12 <= newodds: n = 1\n",
    "                                                                elif n <= i13:\n",
    "                                                                    if o13 <= newodds: n = 1\n",
    "                                                                    elif n <= i14:\n",
    "                                                                        if o14 <= newodds: n = 1\n",
    "                                                                        elif n <= i15:\n",
    "                                                                            if o15 <= newodds: n = 1\n",
    "                                                                            else:\n",
    "                                                                                j = 16\n",
    "\n",
    "                                                                                while (j < ladderlength) and (n <= ladderinteger[j]):        \n",
    "                                                                                    if ladderodds[j] <= newodds:\n",
    "                                                                                        n = 1\n",
    "                                                                                        break\n",
    "                                                                                    j = j + 1\n",
    "\n",
    "        #if i == special: print(\"{} made it past LADDER, n = {}, odds = {}, recordodds = {}, currentladder = {}\".\n",
    "        #                       format(special,n,odds,currentrecordodds,ladderinteger[0]))\n",
    "            \n",
    "        # update ladder if a full count meets previous record\n",
    "        if currentrecordodds == odds:\n",
    "            ladderinteger[0] = i \n",
    "            \n",
    "           # if i == special: print(\"{} UPDATE LADDER, n = {}, odds = {}, recordodds = {}, currentladder = {}\".\n",
    "                 #                  format(special,n,odds,currentrecordodds,ladderinteger[0]))\n",
    "                \n",
    "        # log a new record reseting variables\n",
    "        elif currentrecordodds < odds:\n",
    "           # if printlines:\n",
    "           #     print(\"{} {} {}\".format(i,odds,datetime.now().timestamp()-lasttime))\n",
    "           #     lasttime = datetime.now().timestamp()\n",
    "            recordinteger.append(i)\n",
    "            recordodds.append(odds)\n",
    "            currentrecordodds = odds\n",
    "            ladderinteger.insert(0,i)\n",
    "            ladderodds.insert(0,odds)\n",
    "            ladderlength = ladderlength + 1\n",
    "            \n",
    "            # generated by laddergenerator\n",
    "            i1 = ladderinteger[1]\n",
    "            i2 = ladderinteger[2]\n",
    "            i3 = ladderinteger[3]\n",
    "            i4 = ladderinteger[4]\n",
    "            i5 = ladderinteger[5]\n",
    "            i6 = ladderinteger[6]\n",
    "            i7 = ladderinteger[7]\n",
    "            i8 = ladderinteger[8]\n",
    "            i9 = ladderinteger[9]\n",
    "            i10 = ladderinteger[10]\n",
    "            i11 = ladderinteger[11]\n",
    "            i12 = ladderinteger[12]\n",
    "            i13 = ladderinteger[13]\n",
    "            i14 = ladderinteger[14]\n",
    "            i15 = ladderinteger[15]\n",
    "            o1 = ladderodds[1]\n",
    "            o2 = ladderodds[2]\n",
    "            o3 = ladderodds[3]\n",
    "            o4 = ladderodds[4]\n",
    "            o5 = ladderodds[5]\n",
    "            o6 = ladderodds[6]\n",
    "            o7 = ladderodds[7]\n",
    "            o8 = ladderodds[8]\n",
    "            o9 = ladderodds[9]\n",
    "            o10 = ladderodds[10]\n",
    "            o11 = ladderodds[11]\n",
    "            o12 = ladderodds[12]\n",
    "            o13 = ladderodds[13]\n",
    "            o14 = ladderodds[14]\n",
    "            o15 = ladderodds[15]\n",
    "\n",
    "        i = i + 2\n",
    "    print(\"s1: {}, s2: {}\".format(s1,s2))\n",
    "    return [starttime, datetime.now().timestamp(), start, end, ladderinteger, ladderodds, recordinteger, recordodds]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime  \n",
    "def SLengthRecordsEarlyMethod(end, \n",
    "                    start=2325, # generated by laddergenerator\n",
    "                    ladderinteger=[2323, 871, 703, 667, 313, 235, 171, 129, 97, 73, 55, 25, 9, 7, 3, 1], # generated by laddergenerator\n",
    "                    ladderodds=[66, 65, 62, 52, 47, 46, 45, 44, 43, 42, 41, 7, 6, 5, 2, 0], # generated by laddergenerator\n",
    "                    recordinteger=[1, 3, 7, 9, 25, 27, 73, 97, 129, 171, 231, 313, 327, 703, 871, 1161], # generated by laddergenerator\n",
    "                    recordodds=[0, 2, 5, 6, 7, 41, 42, 43, 44, 45, 46, 47, 52, 62, 65, 66], # generated by laddergenerator\n",
    "                    printlines = False):\n",
    "                     \n",
    "    starttime = datetime.now().timestamp()\n",
    "    lasttime = starttime\n",
    "    ladderlength = len(ladderinteger) - 1\n",
    "    currentrecordodds = ladderodds[0]\n",
    "    \n",
    "    # generated by laddergenerator\n",
    "    i1 = ladderinteger[1]\n",
    "    i2 = ladderinteger[2]\n",
    "    i3 = ladderinteger[3]\n",
    "    i4 = ladderinteger[4]\n",
    "    i5 = ladderinteger[5]\n",
    "    i6 = ladderinteger[6]\n",
    "    i7 = ladderinteger[7]\n",
    "    i8 = ladderinteger[8]\n",
    "    i9 = ladderinteger[9]\n",
    "    i10 = ladderinteger[10]\n",
    "    i11 = ladderinteger[11]\n",
    "    i12 = ladderinteger[12]\n",
    "    i13 = ladderinteger[13]\n",
    "    i14 = ladderinteger[14]\n",
    "    i15 = ladderinteger[15]\n",
    "    o1 = ladderodds[1]\n",
    "    o2 = ladderodds[2]\n",
    "    o3 = ladderodds[3]\n",
    "    o4 = ladderodds[4]\n",
    "    o5 = ladderodds[5]\n",
    "    o6 = ladderodds[6]\n",
    "    o7 = ladderodds[7]\n",
    "    o8 = ladderodds[8]\n",
    "    o9 = ladderodds[9]\n",
    "    o10 = ladderodds[10]\n",
    "    o11 = ladderodds[11]\n",
    "    o12 = ladderodds[12]\n",
    "    o13 = ladderodds[13]\n",
    "    o14 = ladderodds[14]\n",
    "    o15 = ladderodds[15]\n",
    "    \n",
    "    # generated by apriorigenerator\n",
    "    skipmodulus = 5184\n",
    "    skip1set = set([5, 13, 25, 31, 37, 41, 53, 61, 71, 77, 85, 95, 103, 109, 121, 125, 133, 143, 149, 157, 167, 175, 181, 185, 197, 205, 217, 221, 229, 233, 239, 247, 253, 265, 269, 277, 287, 293, 301, 311, 319, 325, 329, 341, 349, 359, 365, 373, 377, 383, 391, 397, 409, 415, 421, 431, 437, 445, 455, 463, 469, 473, 485, 493, 503, 509, 517, 521, 527, 541, 553, 557, 565, 581, 589, 601, 607, 613, 617, 629, 637, 647, 653, 661, 665, 671, 679, 685, 697, 701, 709, 719, 725, 733, 743, 751, 757, 761, 773, 781, 793, 797, 805, 809, 815, 823, 829, 841, 845, 853, 863, 869, 877, 887, 895, 901, 905, 917, 925, 935, 941, 949, 953, 959, 967, 973, 985, 989, 997, 1007, 1013, 1021, 1031, 1039, 1045, 1049, 1063, 1069, 1079, 1085, 1093, 1097, 1103, 1117, 1129, 1133, 1141, 1151, 1157, 1165, 1177, 1183, 1189, 1193, 1205, 1213, 1225, 1229, 1237, 1241, 1247, 1255, 1261, 1273, 1277, 1285, 1295, 1301, 1309, 1319, 1327, 1333, 1337, 1349, 1357, 1369, 1373, 1381, 1391, 1399, 1405, 1417, 1421, 1429, 1439, 1445, 1453, 1463, 1471, 1477, 1481, 1493, 1501, 1511, 1517, 1525, 1529, 1535, 1543, 1549, 1561, 1565, 1573, 1583, 1589, 1597, 1607, 1615, 1621, 1625, 1637, 1645, 1655, 1661, 1669, 1673, 1679, 1693, 1705, 1711, 1717, 1727, 1733, 1741, 1753, 1759, 1765, 1769, 1781, 1789, 1799, 1805, 1813, 1817, 1823, 1831, 1837, 1849, 1853, 1861, 1877, 1885, 1895, 1903, 1909, 1913, 1925, 1933, 1945, 1949, 1957, 1961, 1967, 1975, 1981, 1993, 1997, 2005, 2015, 2021, 2029, 2039, 2047, 2053, 2057, 2069, 2077, 2087, 2093, 2101, 2105, 2111, 2119, 2125, 2137, 2141, 2149, 2159, 2165, 2173, 2183, 2191, 2197, 2201, 2213, 2221, 2231, 2237, 2245, 2249, 2255, 2269, 2281, 2285, 2293, 2303, 2309, 2317, 2329, 2335, 2341, 2345, 2359, 2365, 2375, 2381, 2389, 2393, 2399, 2407, 2413, 2425, 2429, 2437, 2447, 2453, 2461, 2471, 2479, 2485, 2489, 2501, 2509, 2521, 2525, 2533, 2537, 2543, 2551, 2557, 2569, 2573, 2581, 2591, 2597, 2605, 2615, 2623, 2629, 2633, 2645, 2653, 2663, 2669, 2677, 2687, 2695, 2701, 2713, 2717, 2725, 2735, 2741, 2749, 2759, 2767, 2773, 2777, 2789, 2797, 2807, 2813, 2821, 2825, 2831, 2845, 2857, 2861, 2869, 2879, 2885, 2893, 2905, 2911, 2917, 2921, 2933, 2941, 2951, 2957, 2965, 2969, 2975, 2983, 2989, 3001, 3007, 3013, 3023, 3029, 3037, 3047, 3055, 3061, 3065, 3077, 3085, 3097, 3101, 3109, 3113, 3119, 3127, 3133, 3145, 3149, 3157, 3173, 3181, 3191, 3199, 3205, 3209, 3221, 3229, 3239, 3245, 3253, 3257, 3263, 3271, 3277, 3289, 3293, 3301, 3311, 3317, 3325, 3335, 3343, 3349, 3353, 3365, 3373, 3383, 3389, 3397, 3401, 3407, 3421, 3433, 3437, 3445, 3455, 3461, 3469, 3481, 3487, 3493, 3497, 3509, 3517, 3527, 3533, 3541, 3545, 3551, 3559, 3565, 3577, 3581, 3589, 3599, 3605, 3613, 3623, 3631, 3637, 3641, 3655, 3661, 3673, 3677, 3685, 3689, 3695, 3703, 3709, 3721, 3725, 3733, 3743, 3749, 3757, 3767, 3775, 3781, 3785, 3797, 3805, 3817, 3821, 3829, 3833, 3839, 3847, 3853, 3865, 3869, 3877, 3887, 3893, 3901, 3911, 3919, 3925, 3929, 3941, 3949, 3959, 3965, 3973, 3983, 3997, 4009, 4013, 4021, 4031, 4037, 4045, 4057, 4063, 4069, 4073, 4085, 4093, 4103, 4109, 4117, 4121, 4127, 4135, 4141, 4153, 4157, 4165, 4175, 4181, 4189, 4199, 4207, 4213, 4217, 4229, 4237, 4249, 4253, 4261, 4265, 4271, 4279, 4285, 4297, 4303, 4309, 4319, 4325, 4333, 4343, 4351, 4357, 4361, 4373, 4381, 4391, 4397, 4405, 4409, 4415, 4423, 4429, 4441, 4445, 4453, 4469, 4477, 4487, 4495, 4501, 4505, 4517, 4525, 4535, 4541, 4549, 4553, 4559, 4573, 4585, 4589, 4597, 4607, 4613, 4621, 4633, 4639, 4645, 4649, 4661, 4669, 4679, 4685, 4693, 4697, 4703, 4711, 4717, 4729, 4733, 4741, 4751, 4757, 4765, 4775, 4783, 4789, 4793, 4805, 4813, 4825, 4829, 4837, 4841, 4847, 4855, 4861, 4873, 4877, 4885, 4895, 4901, 4909, 4919, 4927, 4933, 4937, 4957, 4967, 4973, 4981, 4985, 4991, 4999, 5005, 5017, 5021, 5029, 5039, 5045, 5053, 5063, 5071, 5077, 5081, 5093, 5101, 5113, 5117, 5125, 5129, 5135, 5149, 5161, 5165, 5173, 5183])\n",
    "    skip2set = set([3, 11, 23, 29, 35, 51, 59, 69, 83, 93, 101, 107, 119, 131, 141, 147, 155, 165, 173, 179, 195, 203, 215, 227, 237, 245, 251, 263, 275, 285, 291, 299, 309, 317, 323, 339, 347, 357, 371, 381, 389, 395, 407, 413, 419, 429, 435, 443, 453, 461, 467, 483, 491, 501, 515, 525, 539, 551, 563, 579, 587, 599, 605, 611, 627, 635, 645, 659, 669, 677, 683, 695, 707, 717, 723, 731, 741, 749, 755, 771, 779, 791, 803, 813, 821, 827, 839, 851, 861, 867, 875, 885, 893, 899, 915, 923, 933, 947, 957, 965, 971, 983, 995, 1005, 1011, 1019, 1029, 1037, 1043, 1061, 1067, 1077, 1091, 1101, 1115, 1127, 1139, 1149, 1155, 1163, 1175, 1181, 1187, 1203, 1211, 1223, 1235, 1245, 1253, 1259, 1271, 1283, 1293, 1299, 1307, 1317, 1325, 1331, 1347, 1355, 1367, 1379, 1389, 1397, 1403, 1415, 1427, 1437, 1443, 1451, 1461, 1469, 1475, 1491, 1499, 1509, 1523, 1533, 1541, 1547, 1559, 1571, 1581, 1587, 1595, 1605, 1613, 1619, 1635, 1643, 1653, 1667, 1677, 1691, 1703, 1709, 1715, 1725, 1731, 1739, 1751, 1757, 1763, 1779, 1787, 1797, 1811, 1821, 1829, 1835, 1847, 1859, 1875, 1883, 1893, 1901, 1907, 1923, 1931, 1943, 1955, 1965, 1973, 1979, 1991, 2003, 2013, 2019, 2027, 2037, 2045, 2051, 2067, 2075, 2085, 2099, 2109, 2117, 2123, 2135, 2147, 2157, 2163, 2171, 2181, 2189, 2195, 2211, 2219, 2229, 2243, 2253, 2267, 2279, 2291, 2301, 2307, 2315, 2327, 2333, 2339, 2357, 2363, 2373, 2387, 2397, 2405, 2411, 2423, 2435, 2445, 2451, 2459, 2469, 2477, 2483, 2499, 2507, 2519, 2531, 2541, 2549, 2555, 2567, 2579, 2589, 2595, 2603, 2613, 2621, 2627, 2643, 2651, 2661, 2675, 2685, 2693, 2699, 2711, 2723, 2733, 2739, 2747, 2757, 2765, 2771, 2787, 2795, 2805, 2819, 2829, 2843, 2855, 2867, 2877, 2883, 2891, 2903, 2909, 2915, 2931, 2939, 2949, 2963, 2973, 2981, 2987, 2999, 3005, 3011, 3021, 3027, 3035, 3045, 3053, 3059, 3075, 3083, 3095, 3107, 3117, 3125, 3131, 3143, 3155, 3171, 3179, 3189, 3197, 3203, 3219, 3227, 3237, 3251, 3261, 3269, 3275, 3287, 3299, 3309, 3315, 3323, 3333, 3341, 3347, 3363, 3371, 3381, 3395, 3405, 3419, 3431, 3443, 3453, 3459, 3467, 3479, 3485, 3491, 3507, 3515, 3525, 3539, 3549, 3557, 3563, 3575, 3587, 3597, 3603, 3611, 3621, 3629, 3635, 3653, 3659, 3671, 3683, 3693, 3701, 3707, 3719, 3731, 3741, 3747, 3755, 3765, 3773, 3779, 3795, 3803, 3815, 3827, 3837, 3845, 3851, 3863, 3875, 3885, 3891, 3899, 3909, 3917, 3923, 3939, 3947, 3957, 3971, 3981, 3995, 4007, 4019, 4029, 4035, 4043, 4055, 4061, 4067, 4083, 4091, 4101, 4115, 4125, 4133, 4139, 4151, 4163, 4173, 4179, 4187, 4197, 4205, 4211, 4227, 4235, 4247, 4259, 4269, 4277, 4283, 4295, 4301, 4307, 4317, 4323, 4331, 4341, 4349, 4355, 4371, 4379, 4389, 4403, 4413, 4421, 4427, 4439, 4451, 4467, 4475, 4485, 4493, 4499, 4515, 4523, 4533, 4547, 4557, 4571, 4583, 4595, 4605, 4611, 4619, 4631, 4637, 4643, 4659, 4667, 4677, 4691, 4701, 4709, 4715, 4727, 4739, 4749, 4755, 4763, 4773, 4781, 4787, 4803, 4811, 4823, 4835, 4845, 4853, 4859, 4871, 4883, 4893, 4899, 4907, 4917, 4925, 4931, 4955, 4965, 4979, 4989, 4997, 5003, 5015, 5027, 5037, 5043, 5051, 5061, 5069, 5075, 5091, 5099, 5111, 5123, 5133, 5147, 5159, 5171, 5181])\n",
    "    skip3set = set([21, 49, 67, 91, 99, 117, 139, 153, 163, 193, 213, 243, 261, 283, 307, 337, 345, 355, 387, 405, 427, 451, 481, 499, 537, 549, 577, 597, 625, 643, 675, 693, 715, 729, 739, 769, 789, 819, 837, 859, 883, 913, 921, 931, 963, 981, 1003, 1027, 1059, 1075, 1113, 1125, 1147, 1173, 1201, 1221, 1251, 1269, 1291, 1305, 1315, 1345, 1365, 1387, 1395, 1413, 1435, 1459, 1489, 1497, 1507, 1539, 1557, 1579, 1603, 1633, 1651, 1689, 1701, 1723, 1749, 1777, 1795, 1827, 1845, 1873, 1881, 1891, 1921, 1941, 1971, 1989, 2011, 2035, 2065, 2073, 2083, 2115, 2133, 2155, 2179, 2209, 2227, 2265, 2277, 2299, 2325, 2355, 2371, 2403, 2421, 2443, 2457, 2467, 2497, 2517, 2547, 2565, 2587, 2611, 2641, 2649, 2659, 2683, 2691, 2709, 2731, 2755, 2785, 2803, 2841, 2853, 2875, 2901, 2929, 2947, 2979, 2997, 3019, 3033, 3043, 3073, 3093, 3123, 3141, 3169, 3187, 3217, 3225, 3235, 3267, 3285, 3307, 3331, 3361, 3379, 3417, 3429, 3451, 3477, 3505, 3523, 3555, 3573, 3595, 3609, 3619, 3651, 3669, 3699, 3717, 3739, 3763, 3793, 3801, 3813, 3843, 3861, 3883, 3907, 3937, 3955, 3979, 3993, 4005, 4027, 4053, 4081, 4099, 4131, 4149, 4171, 4185, 4195, 4225, 4245, 4275, 4293, 4315, 4339, 4369, 4377, 4387, 4419, 4437, 4465, 4483, 4513, 4531, 4569, 4581, 4603, 4629, 4657, 4675, 4707, 4725, 4747, 4761, 4771, 4801, 4821, 4851, 4869, 4891, 4915, 4953, 4963, 4995, 5013, 5035, 5059, 5089, 5109, 5145, 5157, 5179])\n",
    "    skip4set = set([19, 47, 65, 89, 115, 137, 161, 191, 211, 259, 281, 305, 335, 353, 403, 425, 449, 479, 497, 535, 547, 575, 595, 623, 641, 691, 713, 737, 767, 787, 835, 857, 881, 911, 929, 979, 1001, 1025, 1057, 1073, 1111, 1123, 1145, 1171, 1199, 1219, 1267, 1289, 1313, 1343, 1363, 1385, 1411, 1433, 1457, 1487, 1505, 1555, 1577, 1601, 1631, 1649, 1687, 1699, 1721, 1747, 1775, 1793, 1843, 1871, 1889, 1919, 1939, 1987, 2009, 2033, 2063, 2081, 2131, 2153, 2177, 2207, 2225, 2263, 2275, 2297, 2323, 2353, 2369, 2419, 2441, 2465, 2495, 2515, 2563, 2585, 2609, 2639, 2657, 2681, 2707, 2729, 2753, 2783, 2801, 2839, 2851, 2873, 2899, 2927, 2945, 2995, 3017, 3041, 3071, 3091, 3139, 3167, 3185, 3215, 3233, 3283, 3305, 3329, 3359, 3377, 3415, 3427, 3449, 3475, 3503, 3521, 3571, 3593, 3617, 3649, 3667, 3715, 3737, 3761, 3791, 3811, 3859, 3881, 3905, 3935, 3953, 3977, 3991, 4003, 4025, 4051, 4079, 4097, 4147, 4169, 4193, 4223, 4243, 4291, 4313, 4337, 4367, 4385, 4435, 4463, 4481, 4511, 4529, 4567, 4579, 4601, 4627, 4655, 4673, 4723, 4745, 4769, 4799, 4819, 4867, 4889, 4913, 4951, 4961, 5011, 5033, 5057, 5087, 5107, 5143, 5155, 5177])\n",
    "    skip5set = set([17, 45, 113, 189, 209, 257, 333, 401, 477, 533, 545, 573, 593, 621, 689, 765, 785, 833, 909, 977, 1055, 1109, 1121, 1169, 1197, 1217, 1265, 1341, 1361, 1409, 1485, 1553, 1629, 1685, 1697, 1745, 1773, 1841, 1869, 1917, 1937, 1985, 2061, 2129, 2205, 2261, 2273, 2321, 2351, 2417, 2493, 2513, 2561, 2637, 2705, 2781, 2837, 2849, 2897, 2925, 2993, 3069, 3089, 3137, 3165, 3213, 3281, 3357, 3413, 3425, 3473, 3501, 3569, 3647, 3665, 3713, 3789, 3809, 3857, 3933, 3989, 4001, 4049, 4077, 4145, 4221, 4241, 4289, 4365, 4433, 4461, 4509, 4565, 4577, 4625, 4653, 4721, 4797, 4817, 4865, 4949, 5009, 5085, 5105, 5141, 5153])\n",
    "    skip6set = set([531, 571, 1053, 1107, 1683, 1867, 2259, 2349, 2835, 3163, 3411, 3645, 3987, 4459, 4563, 4947, 5139])\n",
    "    skip7set = set([569, 1865, 3161, 4457, 4945])\n",
    "    skip8set = set([4943])\n",
    "    skip9set = set([4941])  \n",
    "    \n",
    "    i = start\n",
    "    mask1 = 1\n",
    "    while i < end:\n",
    "       \n",
    "        # generated by apriorigenerator\n",
    "        r = (i % skipmodulus)\n",
    "        if r in skip1set: i = i + 2\n",
    "        elif r in skip2set: i = i + 4\n",
    "        elif r in skip3set: i = i + 6\n",
    "        elif r in skip4set: i = i + 8\n",
    "        elif r in skip5set: i = i + 10\n",
    "        elif r in skip6set: i = i + 12\n",
    "        elif r in skip7set: i = i + 14\n",
    "        elif r in skip8set: i = i + 16\n",
    "        elif r in skip9set: i = i + 18\n",
    "\n",
    "        n = i\n",
    "        odds = 0\n",
    "        while n != 1:\n",
    "            n = 3*n + 1    \n",
    "            # loop to minimize number of divisions\n",
    "            if (n % 4) == 0:\n",
    "                if (n % 8) == 0:\n",
    "                    n = n // 8\n",
    "                    if (n % 2) == 0:\n",
    "                        if (n % 4) == 0:\n",
    "                            n = n // 4\n",
    "                            while (n % 2) == 0:\n",
    "                                if (n % 4) == 0:\n",
    "                                    n = n // 4\n",
    "                                else:\n",
    "                                    n = n // 2\n",
    "                        else:\n",
    "                            n = n // 2\n",
    "                else:\n",
    "                    n = n // 4\n",
    "            else:\n",
    "                n = n // 2\n",
    "            odds = odds + 1\n",
    "            newodds = currentrecordodds - odds\n",
    "            \n",
    "            # generated by laddergenerator\n",
    "            if n <= i1:\n",
    "                if o1 <= newodds: n = 1\n",
    "                elif n <= i2:\n",
    "                    if o2 <= newodds: n = 1\n",
    "                    elif n <= i3:\n",
    "                        if o3 <= newodds: n = 1\n",
    "                        elif n <= i4:\n",
    "                            if o4 <= newodds: n = 1\n",
    "                            elif n <= i5:\n",
    "                                if o5 <= newodds: n = 1\n",
    "                                elif n <= i6:\n",
    "                                    if o6 <= newodds: n = 1\n",
    "                                    elif n <= i7:\n",
    "                                        if o7 <= newodds: n = 1\n",
    "                                        elif n <= i8:\n",
    "                                            if o8 <= newodds: n = 1\n",
    "                                            elif n <= i9:\n",
    "                                                if o9 <= newodds: n = 1\n",
    "                                                elif n <= i10:\n",
    "                                                    if o10 <= newodds: n = 1\n",
    "                                                    elif n <= i11:\n",
    "                                                        if o11 <= newodds: n = 1\n",
    "                                                        elif n <= i12:\n",
    "                                                            if o12 <= newodds: n = 1\n",
    "                                                            elif n <= i13:\n",
    "                                                                if o13 <= newodds: n = 1\n",
    "                                                                elif n <= i14:\n",
    "                                                                    if o14 <= newodds: n = 1\n",
    "                                                                    elif n <= i15:\n",
    "                                                                        if o15 <= newodds: n = 1\n",
    "                                                                        else:\n",
    "                                                                            j = 16\n",
    "\n",
    "                                                                            while (j < ladderlength) and (n <= ladderinteger[j]):        \n",
    "                                                                                if ladderodds[j] <= newodds:\n",
    "                                                                                    n = 1\n",
    "                                                                                    break\n",
    "                                                                                j = j + 1\n",
    "        # update ladder if a full count meets previous record\n",
    "        if currentrecordodds == odds:\n",
    "            ladderinteger[0] = i \n",
    "        # log a new record reseting variables\n",
    "        elif currentrecordodds < odds:\n",
    "            if printlines:\n",
    "                print(\"{} {} {}\".format(i,odds,datetime.now().timestamp()-lasttime))\n",
    "                lasttime = datetime.now().timestamp()\n",
    "            recordinteger.append(i)\n",
    "            recordodds.append(odds)\n",
    "            currentrecordodds = odds\n",
    "            ladderinteger.insert(0,i)\n",
    "            ladderodds.insert(0,odds)\n",
    "            ladderlength = ladderlength + 1\n",
    "            \n",
    "            # generated by laddergenerator\n",
    "            i1 = ladderinteger[1]\n",
    "            i2 = ladderinteger[2]\n",
    "            i3 = ladderinteger[3]\n",
    "            i4 = ladderinteger[4]\n",
    "            i5 = ladderinteger[5]\n",
    "            i6 = ladderinteger[6]\n",
    "            i7 = ladderinteger[7]\n",
    "            i8 = ladderinteger[8]\n",
    "            i9 = ladderinteger[9]\n",
    "            i10 = ladderinteger[10]\n",
    "            i11 = ladderinteger[11]\n",
    "            i12 = ladderinteger[12]\n",
    "            i13 = ladderinteger[13]\n",
    "            i14 = ladderinteger[14]\n",
    "            i15 = ladderinteger[15]\n",
    "            o1 = ladderodds[1]\n",
    "            o2 = ladderodds[2]\n",
    "            o3 = ladderodds[3]\n",
    "            o4 = ladderodds[4]\n",
    "            o5 = ladderodds[5]\n",
    "            o6 = ladderodds[6]\n",
    "            o7 = ladderodds[7]\n",
    "            o8 = ladderodds[8]\n",
    "            o9 = ladderodds[9]\n",
    "            o10 = ladderodds[10]\n",
    "            o11 = ladderodds[11]\n",
    "            o12 = ladderodds[12]\n",
    "            o13 = ladderodds[13]\n",
    "            o14 = ladderodds[14]\n",
    "            o15 = ladderodds[15]\n",
    "\n",
    "        i = i + 2\n",
    "    return [starttime, datetime.now().timestamp(), start, end, ladderinteger, ladderodds, recordinteger, recordodds]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sep 03, 2020 22:01:02 Seconds 7.4878480434417725 Odd Ints Per Second 667732.7679451433\n",
      "-------------\n",
      "Ladders [8400511, 6649279, 5649499, 3732423, 3542887, 3064033, 2298025, 1723519, 1564063, 1117065, 837799, 626331, 511935, 410011, 230631, 216367, 156159, 142587, 106239, 77031, 52527, 35655, 34239, 26623, 23529, 17647, 13255, 10971, 6171, 3711, 2919, 2463, 2323, 871, 703, 667, 313, 235, 171, 129, 97, 73, 55, 25, 9, 7, 3, 1] [256, 248, 228, 222, 217, 209, 208, 207, 197, 196, 195, 189, 174, 166, 164, 142, 141, 138, 130, 129, 125, 119, 114, 113, 103, 102, 101, 98, 96, 87, 79, 76, 66, 65, 62, 52, 47, 46, 45, 44, 43, 42, 41, 7, 6, 5, 2, 0]\n",
      "-------------\n",
      "Records [313, 327, 703, 871, 1161, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, 26623, 34239, 35655, 52527, 77031, 106239, 142587, 156159, 216367, 230631, 410011, 511935, 626331, 837799, 1117065, 1501353, 1723519, 2298025, 3064033, 3542887, 3732423, 5649499, 6649279, 8400511] [47, 52, 62, 65, 66, 76, 79, 87, 96, 98, 101, 102, 103, 113, 114, 119, 125, 129, 130, 138, 141, 142, 164, 166, 174, 189, 195, 196, 197, 207, 208, 209, 217, 222, 228, 248, 256]\n",
      "-------------\n",
      "Ladder integers agree with expection.\n",
      "Ladder odds agree with expection.\n",
      "Record integers agree with expection.\n",
      "Record delays agree with expection.\n"
     ]
    }
   ],
   "source": [
    "reportSLengthRecords(SLengthRecords(10000000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is code to profile a call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cProfile\n",
    "import re\n",
    "import pstats\n",
    "from pstats import SortKey\n",
    "cProfile.run('SLengthRecords(10000000)', 'restats')\n",
    "p = pstats.Stats('restats')\n",
    "p.strip_dirs().sort_stats(-1).print_stats()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is code to display a report from the output of SLengthRecords."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime  \n",
    "def reportSLengthRecords(datafromrun):\n",
    "    starttime = datafromrun[0]\n",
    "    endtime = datafromrun[1]\n",
    "    startint = datafromrun[2]\n",
    "    endint = datafromrun[3]\n",
    "    ladderinteger = datafromrun[4]\n",
    "    ladderodds = datafromrun[5]\n",
    "    recordinteger = datafromrun[6]\n",
    "    recordodds = datafromrun[7]\n",
    "    elapsedtime = endtime - starttime\n",
    "    oddspersecond = (endint - startint)/(2*elapsedtime) \n",
    "    spacer = \"-------------\"\n",
    "    print(\"{} Seconds {} Odd Ints Per Second {}\".\\\n",
    "          format(datetime.now().strftime(\"%b %d, %Y %H:%M:%S\"),elapsedtime,oddspersecond))\n",
    "    print(\"{}\".format(spacer))\n",
    "    print(\"Ladders\")\n",
    "    print(\"INTEGERS  {}\".format(ladderinteger))\n",
    "    print(\"ODD STEPS {}\".format(ladderodds))\n",
    "    print(\"{}\".format(spacer))\n",
    "    print(\"Records\")\n",
    "    print(\"INTEGERS  {}\".format(recordinteger))\n",
    "    print(\"ODD STEPS {}\".format(recordodds))\n",
    "    print(\"{}\".format(spacer))\n",
    "    \n",
    "    expectedladderinteger = [670617279, 268549803, 226588897, 169941673, 127456255, 36791535, 15733191, 14934241, \n",
    "                            11200681, 8400511, 6649279, 5649499, 3732423, 3542887, 3064033, 2298025, 1723519, 1564063, \n",
    "                            1126015, 837799, 626331, 511935, 410011, 230631, 216367, 156159, 142587, 106239, 77031, \n",
    "                            52527, 35655, 35497, 26623, 23529, 17673, 13255, 10971, 6171, 3711, 2919, 2463, 2323, 871, \n",
    "                            703, 667, 313, 235, 171, 129, 97, 73, 55, 25, 9, 7, 3, 1] \n",
    "    expectedrecordinteger = [1, 3, 7, 9, 25, 27, 73, 97, 129, 171, 231, 313, 327, 703, 871, 1161, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, 26623, \n",
    "                            34239, 35655, 52527, 77031, 106239, 142587, 156159, 216367, 230631, 410011, 511935, 626331,\n",
    "                            837799, 1117065, 1501353, 1723519, 2298025, 3064033, 3542887, 3732423, 5649499, 6649279, \n",
    "                            8400511, 11200681, 14934241, 15733191, 36791535, 63728127, 169941673, 226588897, \n",
    "                            268549803, 670617279]\n",
    "    expectedrecordodds = [0, 2, 5, 6, 7, 41, 42, 43, 44, 45, 46, 47, 52, 62, 65, 66, 76, 79, 87, 96, 98, 101, 102, 103, 113, 114, 119, 125, 129, 130, 138, 141,\n",
    "                        142, 164, 166, 174, 189, 195, 196, 197, 207, 208, 209, 217, 222, 228, 248, 256, 257, 258, 263,\n",
    "                        278, 357, 358, 359, 362, 370]\n",
    "\n",
    "    lastindex = len(recordinteger)\n",
    "    ladderindex = len(expectedladderinteger) - len(ladderinteger)\n",
    "    if expectedladderinteger[ladderindex:] == ladderinteger:\n",
    "        print(\"Ladder integers PASS.\")\n",
    "    else:\n",
    "        print(\"Ladder integers DO NOT PASS.\")\n",
    "        print(\"Received: {}\".format(ladderinteger))\n",
    "        print(\"Expected: {}\".format(expectedladderinteger[ladderindex:]))\n",
    "        print(\" \")\n",
    "        D = [(ladderinteger[i],expectedladderinteger[ladderindex:][i]) for i in range(len(ladderinteger)) if ladderinteger[i] != expectedladderinteger[ladderindex:][i]]\n",
    "        print(\"(Received,Expected) : {}\".format(D))\n",
    "        print(\"{}\".format(spacer))\n",
    "    if expectedrecordinteger[:lastindex] == recordinteger:\n",
    "        print(\"Record integers PASS.\")\n",
    "    else:\n",
    "        print(\"Record integers DO NOT PASS.\")\n",
    "        print(\"Received: {}\".format(recordinteger))\n",
    "        print(\"Expected: {}\".format(expectedrecordinteger[:lastindex]))\n",
    "        print(\" \")\n",
    "        D = [(recordinteger[i],expectedrecordinteger[:lastindex][i]) for i in range(len(recordinteger)) if recordinteger[i] != expectedrecordinteger[:lastindex][i]]\n",
    "        print(\"(Received,Expected) : {}\".format(D))\n",
    "        print(\"{}\".format(spacer))\n",
    "    if expectedrecordodds[:lastindex] == recordodds:\n",
    "        print(\"Record delays   PASS.\")\n",
    "    else:\n",
    "        print(\"Record delays   DO NOT PASS.\")\n",
    "        print(\"Received: {}\".format(recordodds))\n",
    "        print(\"Expected: {}\".format(expectedrecordodds[:lastindex]))\n",
    "        print(\" \")\n",
    "        D = [(recordodds[i],expectedrecordodds[:lastindex][i]) for i in range(len(recordodds)) if recordodds[i] != expectedrecordodds[:lastindex][i]]\n",
    "        print(\"(Received,Expected) : {}\".format(D))\n",
    "        print(\"{}\".format(spacer))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This procedure presents properties of a particular integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def trajectory(n):\n",
    "    C = [n]\n",
    "    maximum = [0,n]\n",
    "    start = n\n",
    "    glide = []\n",
    "    i = 0\n",
    "    even = 0\n",
    "    odd = 0\n",
    "    while n % 2 == 0:\n",
    "       n = n // 2\n",
    "       C.append(n)\n",
    "       even = even + 1\n",
    "       i = i + 1\n",
    "       if glide == []:\n",
    "            glide = [i,n]\n",
    "    T = [n]                       # sequence\n",
    "    S = [n]\n",
    "    Splus = [[n,n%8]]\n",
    "    while n > 1:   # cycles add multiple loops to 1 before stopping\n",
    "        if n % 2 == 1:\n",
    "            n = (3*n + 1)                 # Collatz function\n",
    "            C.append(n)\n",
    "            i = i + 1\n",
    "            if n > maximum[1]:\n",
    "                maximum = [i,n]\n",
    "            odd = odd + 1\n",
    "            n = n // 2\n",
    "            i = i + 1\n",
    "            if n < start:\n",
    "                if glide == []:\n",
    "                    glide = [i,n]\n",
    "            T.append(n)\n",
    "            C.append(n)\n",
    "            even = even + 1\n",
    "        while n % 2 == 0:           # if n is even keep dividing by 2\n",
    "            n = n // 2              # divide by 2\n",
    "            i = i + 1\n",
    "            if n < start:\n",
    "                if glide == []:\n",
    "                    glide = [i,n]\n",
    "            T.append(n)         # count that the division occurred\n",
    "            C.append(n)\n",
    "            even = even + 1\n",
    "        S.append(n)\n",
    "        Splus.append([n,n%8])  \n",
    "        # add the new n to the list\n",
    "    print(\"C  {}\".format(C))\n",
    "    print(\" \")\n",
    "    print(\"T  {}\".format(T))\n",
    "    print(\" \")\n",
    "    print(\"S  {}\".format(S))\n",
    "    print(\" \")\n",
    "    print(\"Splus {}\".format(Splus))\n",
    "    print(\"Delay        {}\".format(odd + even))\n",
    "    print(\"Glide        {}\".format(glide))\n",
    "    print(\"Maximum      {}\".format(maximum))\n",
    "    print(\"Odd          {}\".format(odd))\n",
    "    print(\"Even         {}\".format(even))\n",
    "    strength = 5*odd - 3*even\n",
    "    print(\"Strength     {}\".format(strength))\n",
    "    print(\"Level        {}\".format(math.floor(-strength/8)))\n",
    "    residue = math.pow(2,even)/(math.pow(3,odd)*start)\n",
    "    residue2 = 2^even - 3^odd*start\n",
    "    residue3 = 1 - (math.pow(3,odd)*start)/math.pow(2,even)\n",
    "    #print(\"Residue      {} = {}/{} = {}\".format(residue,factor(residue.numerator()),factor(residue.denominator()),RR(residue)))\n",
    "    #print(\"Residue2     {} = {}\".format(residue2,factor(residue2)))\n",
    "    #print(\"Residue3     {} = {}/{} = {}\".format(residue3,factor(residue3.numerator()),factor(residue3.denominator()),RR(residue3)))\n",
    "    #gamma = even/ln(start)\n",
    "    #print(\"Gamma        {} = {}\".format(gamma,RR(gamma)))\n",
    "    completeness = odd/even\n",
    "    #maxcompleteness = ln(start)/even\n",
    "    #lntwothree = ln(2)/ln(3)\n",
    "    #print(\"Completeness {}: {} < {} < {}\".format(completeness,RR(maxcompleteness),RR(completeness),RR(lntwothree)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C  [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1]\n",
      " \n",
      "T  [27, 41, 62, 31, 47, 71, 107, 161, 242, 121, 182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 1822, 911, 1367, 2051, 3077, 4616, 2308, 1154, 577, 866, 433, 650, 325, 488, 244, 122, 61, 92, 46, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1]\n",
      " \n",
      "S  [27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1]\n",
      " \n",
      "Splus [[27, 3], [41, 1], [31, 7], [47, 7], [71, 7], [107, 3], [161, 1], [121, 1], [91, 3], [137, 1], [103, 7], [155, 3], [233, 1], [175, 7], [263, 7], [395, 3], [593, 1], [445, 5], [167, 7], [251, 3], [377, 1], [283, 3], [425, 1], [319, 7], [479, 7], [719, 7], [1079, 7], [1619, 3], [2429, 5], [911, 7], [1367, 7], [2051, 3], [3077, 5], [577, 1], [433, 1], [325, 5], [61, 5], [23, 7], [35, 3], [53, 5], [5, 5], [1, 1]]\n",
      "Delay        111\n",
      "Glide        [96, 23]\n",
      "Maximum      [77, 9232]\n",
      "Odd          41\n",
      "Even         70\n",
      "Strength     -5\n",
      "Level        0\n"
     ]
    }
   ],
   "source": [
    "trajectory(27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equivalencegenerator(powerof2,showdetails=False):\n",
    "    spacer = \"-----------------------------------------\"\n",
    "    source = \"# generated by equivalencegenerator\"\n",
    "    offset = 3\n",
    "    groupsize = 4\n",
    "    groups = powerof2 // groupsize\n",
    "    twos = [powerof2]\n",
    "    temp = powerof2\n",
    "\n",
    "    while temp > groupsize:\n",
    "        temp = temp // 2\n",
    "        twos.append(temp)\n",
    "    \n",
    "    print(\"{}{}\".format(\"\\t\"*offset,source))\n",
    "    print(\"{}res = (n % {})\".format(\"\\t\"*offset,powerof2))\n",
    "    j = 1\n",
    "    \n",
    "    for i in range (1,powerof2,2):\n",
    "        R = i\n",
    "        C = powerof2\n",
    "        R2 = i\n",
    "        C2 = powerof2\n",
    "        odds = 0\n",
    "        r = 0\n",
    "        c = 1\n",
    "        g = 1\n",
    "        \n",
    "        if showdetails:\n",
    "            print(\"({}m + {}) = ({}*n + {})/{}   : odds = {}\".format(C,R,c,r,g,odds))\n",
    "        \n",
    "        while (((C % 2) == 0) and ((R % 2) == 1)):\n",
    "            C = 3*C\n",
    "            R = 3*R + 1\n",
    "            C2 = 3*C2\n",
    "            R2 = 3*R2 + g\n",
    "            c = 3*c\n",
    "            r = 3*r + g\n",
    "            while ((C % 2) == 0) and ((R % 2) == 0):\n",
    "                g = 2*g\n",
    "                R = R//2\n",
    "                C = C//2\n",
    "\n",
    "            if ((C % 2) == 0) and ((R % 2) == 1):\n",
    "                odds = odds + 1\n",
    "            if showdetails:\n",
    "                print(\"({}m + {})/{} = {}m + {} = ({}*n + {})/{}   : odds = {}\".format(C2,R2,g,C,R,c,r,g,odds))\n",
    "                \n",
    "        for t in range(0,len(twos)-1):\n",
    "            spacing = offset + t\n",
    "            if (i % twos[t]) == 1:\n",
    "                print(\"{}if res < {}:\".format(\"\\t\"*spacing,i - 1 + (twos[t] // 2)))\n",
    "            elif (i % twos[t]) == (1 + (twos[t] // 2)) and (twos[t] != 4):\n",
    "                print(\"{}else:\".format(\"\\t\"*spacing))   \n",
    "                \n",
    "        spacing = offset + len(twos) - 1\n",
    "        if (i % 4) == 1:\n",
    "            if odds > 0:  \n",
    "                print(\"{}if res == {}: n = ({}*n + {}) // {}; odds = odds + {}\".format(\"\\t\"*spacing,i,c,r,g,odds))\n",
    "            else:\n",
    "                print(\"{}if res == {}: n = ({}*n + {}) // {}\".format(\"\\t\"*spacing,i,c,r,g))\n",
    "        else:\n",
    "            if odds > 0:  \n",
    "                print(\"{}else: n = ({}*n + {}) // {}; odds = odds + {}\".format(\"\\t\"*spacing,c,r,g,odds))\n",
    "            else:\n",
    "                print(\"{}else: n = ({}*n + {}) // {}\".format(\"\\t\"*spacing,c,r,g))\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def apriorigenerator(modulus):\n",
    "    a = []\n",
    "    skip = []\n",
    "    count = 0\n",
    "    i = 1\n",
    "    while i < modulus:\n",
    "        p = AttemptProof(modulus, i)\n",
    "        if p[0] not in ['U','P']:\n",
    "            a.append(i)\n",
    "        i = i + 2\n",
    "    i = modulus - 1\n",
    "    while i > 0:\n",
    "        if i in a:\n",
    "            if count == len(skip):\n",
    "                skip.append([])\n",
    "            skip[count].insert(0,i)\n",
    "            count = count + 1\n",
    "        else:\n",
    "            count = 0\n",
    "        i = i - 2\n",
    "    skip.insert(0,a)\n",
    "    genstring = \"# generated by apriorigenerator\"\n",
    "    spacer = \"----------\"\n",
    "    print(\"\\t{}\".format(genstring))\n",
    "    print(\"\\tskipmodulus = {}\".format(modulus))\n",
    "    for i in range(1,len(skip)):\n",
    "        print(\"\\tskip{}set = set({})\".format(i,skip[i]))    \n",
    "    print(spacer)\n",
    "    print(\"\\t\\t{}\".format(genstring))\n",
    "    print(\"\\t\\tr = (i % skipmodulus)\")\n",
    "    for i in range(1,len(skip)):\n",
    "        if i == 1:\n",
    "            print(\"\\t\\tif r in skip{}set: i = i + {}\".format(i,2*i))\n",
    "        else:\n",
    "            print(\"\\t\\telif r in skip{}set: i = i + {}\".format(i,2*i))\n",
    "        i = i + 1\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def laddergenerator(quantity):\n",
    "    ladderinteger = [8400511, 6649279, 5649499, 3732423, 3542887, 3064033, 2298025, 1723519, 1564063, 1117065, \n",
    "                      837799, 626331, 511935, 410011, 230631, 216367, 156159, 142587, 106239, 77031, 52527, \n",
    "                      35655, 34239, 26623, 23529, 17647, 13255, 10971, 6171, 3711, 2919, 2463, 2323, 871, 703, \n",
    "                      667, 313, 235, 171, 129, 97, 73, 55, 25, 9, 7, 3, 1]\n",
    "    ladderodds = [256, 248, 228, 222, 217, 209, 208, 207, 197, 196, 195, 189, 174, 166, 164, 142, 141, 138, 130, \n",
    "                  129, 125, 119, 114, 113, 103, 102, 101, 98, 96, 87, 79, 76, 66, 65, 62, 52, 47, 46, 45, 44, \n",
    "                  43, 42, 41, 7, 6, 5, 2, 0]\n",
    "    recordinteger = [1, 3, 7, 9, 25, 27, 73, 97, 129, 171, 231, 313, 327, 703, 871, 1161, 2463, 2919, 3711, \n",
    "                     6171, 10971, 13255, 17647, 23529, 26623, 34239, 35655, 52527, 77031, 106239, 142587, 156159, \n",
    "                     216367, 230631, 410011, 511935, 626331, 837799, 1117065, 1501353, 1723519, 2298025, 3064033, \n",
    "                     3542887, 3732423, 5649499, 6649279, 8400511, 11200681, 14934241, 15733191, 36791535, 63728127, \n",
    "                     169941673, 226588897, 268549803, 670617279]\n",
    "    recordodds = [0, 2, 5, 6, 7, 41, 42, 43, 44, 45, 46, 47, 52, 62, 65, 66, 76, 79, 87, 96, 98, 101, 102, 103, 113, \n",
    "                  114, 119, 125, 129, 130, 138, 141, 142, 164, 166, 174, 189, 195, 196, 197, 207, 208, 209, 217, 222, \n",
    "                  228, 248, 256, 257, 258, 263, 278, 357, 358, 359, 362, 370]\n",
    "    recordintegers = []\n",
    "    source = \"# generated by laddergenerator with input \" + str(quantity)\n",
    "#    print(\"\\t\\tstart={}, {}\".format(ladderinteger[-quantity-1]+2,source))\n",
    "#    print(\"\\t\\tladderinteger={}, {}\".format(ladderinteger[-quantity-1:],source))\n",
    "    #print(\"ladderodds={}, {}\".format(ladderodds[-quantity-1:],source))\n",
    "#    print(\"\\t\\trecordinteger={}, {}\".format(recordinteger[:quantity+1],source))\n",
    "#    print(\"\\t\\trecordodds={}, {}\".format(recordodds[:quantity+1:],source))\n",
    " #   print(\"-------------\")\n",
    "    print(\"\\t\"+source)\n",
    "    for i in range (1,quantity+1):\n",
    "        print(\"\\ti{} = ladderinteger[{}]\".format(i,i))\n",
    "    for i in range (1,quantity+1):\n",
    "        print(\"\\to{} = ladderodds[{}]\".format(i,i))\n",
    "    print(\"-------------\")\n",
    "    print(source)\n",
    "    for i in range (1,quantity+1):\n",
    "        if i == 1:\n",
    "            print(\"{}if n <= i{}:\".format(\"\\t\"*i,i))\n",
    "        else:\n",
    "            print(\"{}elif n <= i{}:\".format(\"\\t\"*i,i))\n",
    "        print(\"{}if o{} <= newodds: n = 1\".format(\"\\t\"*(i+1),i))\n",
    "    print(\"{}else:\".format(\"\\t\"*i))\n",
    "    print(\"{}j = {}\".format(\"\\t\"*(i+1),quantity+1))\n",
    "    print()\n",
    "    "
   ]
  }
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