判断大素数
// 18位素数:154590409516822759 // 19位素数:2305843009213693951 (梅森素数) // 19位素数:4384957924686954497 LL prime[6] = {2, 3, 5, 233, 331}; LL qmul(LL x, LL y, LL mod) { // 乘法防止溢出, 如果p * p不爆LL的话可以直接乘; O(1)乘法或者转化成二进制加法 return (x * y - (long long)(x / (long double)mod * y + 1e-3) *mod + mod) % mod; /* LL ret = 0; while(y) { if(y & 1) ret = (ret + x) % mod; x = x * 2 % mod; y >>= 1; } return ret; */ } LL qpow(LL a, LL n, LL mod) { LL ret = 1; while(n) { if(n & 1) ret = qmul(ret, a, mod); a = qmul(a, a, mod); n >>= 1; } return ret; } bool Miller_Rabin(LL p) { if(p < 2) return 0; if(p != 2 && p % 2 == 0) return 0; LL s = p - 1; while(! (s & 1)) s >>= 1; for(int i = 0; i < 5; ++i) { if(p == prime[i]) return 1; LL t = s, m = qpow(prime[i], s, p); while(t != p - 1 && m != 1 && m != p - 1) { m = qmul(m, m, p); t <<= 1; } if(m != p - 1 && !(t & 1)) return 0; } return 1; }