riemann-matiyasevich-aaronson.nql

/* sent to me via e-mail from Yuri Matiyasevich and Scott Aaronson */

global x;
global lcm;
global l;
global num;
global denom;
global i;
global a;
global b;
global c;
global d;

proc main() {
    /* x = 0; */
    lcm = 1;
    while (true) {
        x = x + 1;
        l = lcm;
        while (lcm != (lcm / l) * l || lcm != (lcm / x) * x) {
            lcm = lcm + 1;
        }
        if (x > 253) {
            num = 0;
            denom = 1;
            i = 1;
            while (i <= lcm) {
                num = num * i + denom;
                denom = denom * i;
                i = i + 1;
            }
            a = num - denom * x;
            a = a * a;
            b = denom * denom;
            c = 0;
            d = 1;
            i = 1;
            while (i <= x) {
                c = c * i + d;
                d = d * i;
                i = i + 1;
            }
            c = c * c;
            c = c * c * x;
            d = d * d;
            d = d * d;
            if (a * d > b * c) {
                return;
            }
        }
    }
}