米勒罗宾素数检测

Posted 2022-07-13 meanttobe

 1 #include<iostream>
 2 #include<cstdio>
 3 using namespace std;
 4 typedef long long ll;
 5 // 18位素数：154590409516822759
 6 // 19位素数：2305843009213693951 (梅森素数)
 7 // 19位素数：4384957924686954497
 8 ll prime[6] = 2, 3, 5, 233, 331;
 9 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
10 
11 
12     return (x * y - (long long)(x / (long double)mod * y + 1e-3) *mod + mod) % mod;
13     /*
14     ll ret = 0;
15     while(y) 
16         if(y & 1)
17             ret = (ret + x) % mod;
18         x = x * 2 % mod;
19         y >>= 1;
20     
21     return ret;
22     */
23 
24 ll qpow(ll a, ll n, ll mod) 
25     ll ret = 1;
26     while(n) 
27         if(n & 1) ret = qmul(ret, a, mod);
28         a = qmul(a, a, mod);
29         n >>= 1;
30     
31     return ret;
32 
33 bool Miller_Rabin(ll p) 
34     if(p < 2) return 0;
35     if(p != 2 && p % 2 == 0) return 0;
36     ll s = p - 1;
37     while(! (s & 1)) s >>= 1;
38     for(int i = 0; i < 5; ++i) 
39         if(p == prime[i]) return 1;
40         ll t = s, m = qpow(prime[i], s, p);
41         while(t != p - 1 && m != 1 && m != p - 1) 
42             m = qmul(m, m, p);
43             t <<= 1;
44         
45         if(m != p - 1 && !(t & 1)) return 0;
46     
47     return 1;
48 
49 int main()
50 
51     ll n;
52     while(cin>>n)
53     
54         if(Miller_Rabin(n))
55             cout<<true<<endl;
56         else cout<<false<<endl;
57     
58     return 0;
59