speed_test.py

from primes import is_prime
import time, argparse

order_2_primes = [101, 103, 107, 109, 113,
                    127, 131, 137, 139, 149]

order_3_primes = [1009, 1013, 1019, 1021, 1031, 
                    1033, 1039, 1049, 1051, 1061]

order_4_primes = [10007, 10009, 10037, 10039, 10061,
                    10067, 10069, 10079, 10091, 10093]

order_5_primes = [100003, 100019, 100043, 100049, 100057,
                    100069, 100103, 100109, 100129, 100151]

order_6_primes = [1000003, 1000033, 1000037, 1000039, 1000081,
                    1000099, 1000117, 1000121, 1000133, 1000151]

order_7_primes = [10000019, 10000079, 10000103, 10000121, 10000139,
                    10000141, 10000169, 10000189, 10000223, 10000229]

order_8_primes = [100000007, 100000037, 100000039, 100000049, 100000073,
                    100000081, 100000123, 100000127, 100000193, 100000213]

order_9_primes = [1000000007, 1000000009, 1000000021, 1000000033, 1000000087,
                    1000000093, 1000000097, 1000000103, 1000000123, 1000000181]


primes = {2: order_2_primes, 3: order_3_primes, 4: order_4_primes,
            5: order_5_primes, 6: order_6_primes, 7: order_7_primes,
            8: order_8_primes, 9: order_9_primes}

def time_execution_primes(order):
    prime_list = primes[order]
    total_time = 0
    iterations = len(prime_list)
    for prime in prime_list:
        start_time = time.time()
        is_prime(prime)
        total_time += (time.time() - start_time)
    return total_time/iterations, iterations

def known_prime_test(length):
    upper_bounds = {'short': 6, 'medium': 7, 'long': 8, 'superlong': 9, 'stupidlylong': 10}
    if length in upper_bounds:
        print("Testing {0} primes - length {1}".format(length, upper_bounds[length]))
        for order in range(2, upper_bounds[length]):
            result = time_execution_primes(order)
            print("Order {0}, average time: {1:f}s, number of iterations: {2}".format(order, *result))

def fermat_test(n=12):
    for x in range(n):
        print("2^(2^{0}) + 1 = 2^{1} + 1 = {2} is {3}".format(x, 2**x, 2**(2**x) + 1, 'prime' if is_prime(2**(2**x) + 1) else 'composite'))

parser = argparse.ArgumentParser(description='Test the Baillie-PSW implementation')
group = parser.add_mutually_exclusive_group()
group.add_argument('--short', help='Test primes up to order 5', action='store_true')
group.add_argument('--medium', help='Test primes up to order 6', action='store_true')
group.add_argument('--long', help='Test primes up to order 7', action='store_true')
group.add_argument('--superlong', help='Test primes up to order 8', action='store_true')
group.add_argument('--stupidlylong', help='Test primes up to order 9', action='store_true')
group.add_argument('--all', help='Test primes up to orders 5, 6, 7, 8 and 9', action='store_true')
group.add_argument('--fermat', help='Check the primality of the first n Fermat numbers', type=int, default=0)
args = parser.parse_args()

if args.short or args.all:
    known_prime_test('short')
if args.medium or args.all:
    known_prime_test('medium')
if args.long or args.all:
    known_prime_test('long')
if args.superlong or args.all:
    known_prime_test('superlong')
if args.stupidlylong or args.all:
    known_prime_test('stupidlylong')
if args.fermat:
    fermat_test(args.fermat)