#coding: utf-8 ''' mbinary ####################################################################### # File : factorize.py # Author: mbinary # Mail: zhuheqin1@gmail.com # Blog: https://mbinary.xyz # Github: https://github.com/mbinary # Created Time: 2018-12-16 09:36 # Description: factorization, using pollard's rho algorithm and miller-rabin primality test ####################################################################### ''' from random import randint from isPrime import isPrime from gcd import gcd def factor(n): '''pollard's rho algorithm''' if n<1:raise Exception('[Error]: {} is less than 1'.format(n)) if n==1: return [] if isPrime(n):return [n] fact=1 cycle_size=2 x = x_fixed = 2 c = randint(1,n) while fact==1: for i in range(cycle_size): if fact>1:break x=(x*x+c)%n if x==x_fixed: c = randint(1,n) continue fact = gcd(x-x_fixed,n) cycle_size *=2 x_fixed = x return factor(fact)+factor(n//fact) def fact(n): f=2 ret = [] while f*f<=n: while not n%f: ret.append(f) n//f f+=1 if n>1:ret.append(n) return ret if __name__=='__main__': while 1: n = int(input('n: ')) print(factor(n))