import math from collections import defaultdict def Miller_Rabin_Primality_Test(N): if N==1: return False NN=N-1 NN=NN//(NN&-NN) if N<4759123141: lst=[2,7,61] elif N<341550071728321: lst=[2,3,5,7,11,13,17] else: lst=[2,3,5,7,11,13,17,19,23,29,31,37] if N in lst: return True for a in lst: n=NN p=pow(a,n,N) if p==1: continue while p!=N-1: p=p*p%N if p==1 or n==N-1: return False n<<=1 return True def Pollard_Rho(N): if N==1: return None if Miller_Rabin_Primality_Test(N): return None m=1<