# coding: utf-8 # Your code here! # coding: utf-8 # Your code here! import random class millerrabin: # factor n into a power of 2 times an odd number def pow2_factor(n): power = 0 while n % 2 == 0: n //= 2 power += 1 return power, n """ Rabin-Miller primality test returning False implies that n is guarenteed composite returning True means that n is probably prime with a 4 ** -k chance of being wrong """ def is_prime(n, k): if n==1: return False if n==2: return True if n==3: return True if n==4: return False r, d = millerrabin.pow2_factor(n - 1) """ returns true if a is a valid 'witness' for n a valid witness increases chances of n being prime an invalid witness guarentees n is composite """ def valid_witness(a): x = pow(a, d, n) if x == 1 or x == n - 1: return False for _ in range(r - 1): x = pow(x, 2, n) if x == 1: return True if x == n - 1: return False return True for _ in range(k): if valid_witness(random.randrange(2, n - 2)): return False return True for i in range(int(input())): x = int(input()) print(x, int(millerrabin.is_prime(x,50)))