These links are helpful:
Miller-Rabin Algorithm:
Modular Arithmetic:
Source (C++):
#include <iostream> #include <cstring> #include <cstdlib> #include <stdio.h> #define ull unsigned long long using namespace std; /* * calculates (a * b) % c taking into account that a * b might overflow */ ull mulmod(ull a, ull b, ull mod) { ull x = 0,y = a % mod; while (b > 0) { if (b % 2 == 1) { x = (x + y) % mod; } y = (y * 2) % mod; b /= 2; } return x % mod; } /* * modular exponentiation */ ull modulo(ull base, ull exponent, ull mod) { ull x = 1; ull y = base; while (exponent > 0) { if (exponent % 2 == 1)x = mulmod(x, y, mod); y = mulmod(y, y, mod); exponent = exponent / 2; } return x % mod; } /* * Miller-Rabin primality test, iteration signifies the accuracy */ bool MillerRabin(ull p,int iteration) { if (p < 2) { return false; } if (p != 2 && p % 2==0) { return false; } ull s = p - 1; while (s % 2 == 0) { s /= 2; } for (int i = 0; i < iteration; i++) { ull a = rand() % (p - 1) + 1, temp = s; ull mod = modulo(a, temp, p); if(mod==1 || mod == p-1)continue; while (temp != p - 1 && mod != 1 && mod != p - 1) { mod = mulmod(mod, mod, p); temp *= 2; } if (mod != p - 1)return false; } return true; } int main() { int tests = 5; ull num; scanf("%llu", &num); if (MillerRabin(num, tests))printf("YES\n"); else printf("NO\n"); }
