p_1.py

import math


def pollard_P_1(n):
    z = []
    prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
             61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131,
             137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197,
             199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271,
             277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
             359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433,
             439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
             521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601,
             607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677,
             683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
             773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859,
             863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
             967, 971, 977, 983, 991, 997]

    def gcd(a, b):
        if b == 0:
            return a
        return gcd(b, a % b)

    def e(a, b):
        return pow(a, b, n)

    def mysqrt(n):
        x = n
        y = []
        while(x > 0):
            y.append(x % 100)
            x = x // 100
        y.reverse()
        a = 0
        x = 0
        for p in y:
            for b in range(9, -1, -1):
                if(((20*a+b)*b) <= (x*100+p)):
                    x = x*100+p - ((20*a+b)*b)
                    a = a*10+b
                    break
        return a

    B1 = mysqrt(n)
    for j in range(0, len(prime)):
        for i in range(1, int(math.log(B1)/math.log(prime[j]))+1):
            z.append(prime[j])

    for pp in prime:
        i = 0
        x = pp
        while(1):
            x = e(x, z[i])
            i = i+1
            y = gcd(n, x-1)
            if(y != 1):
                p = y
                q = n//y
                return p, q
            if(i >= len(z)):
                return 0, None