Miller_Rabin素数判断，rho

 1 const int Safe=3;
 2 int gcd(int a,int b){return !b?a:gcd(b,a%b);}
 3 int mul(int a,int b,int p){
 4     int tmp=(a*b-(int)((double)a/p*b+1e-8)*p);
 5     return tmp<0?tmp+p:tmp;
 6 }
 7 int pow(int a,int b,int p){
 8     int ans=1;a%=p;
 9     for(int i=b;i;i>>=1,a=mul(a,a,p))
10         if(i&1)ans=mul(ans,a,p);
11     return ans;
12 }
13 bool check(int a,int n,int r,int s){
14     int ans=pow(a,r,n),p=ans;
15     for(int i=1;i<=s;i++){
16         ans=mul(ans,ans,n);
17         if(ans==1&&p!=1&&p!=n-1) return true;
18         p=ans;
19     } if(ans!=1)return true;return false;
20 }
21 bool MR(int n){
22     if(n<=1) return false;
23     if(n==2) return true;
24     if(!(n&1)) return false;
25     int r=n-1,s=0;
26     while(!(r&1)) r>>=1,s++;
27     for(int i=0;i<Safe;i++)
28         if(check(rand()%(n-1)+1,n,r,s)) return false;
29     return true;
30 }

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <algorithm>
 4 #include <cstring>
 5 #include <cmath>
 6 #define ll long long 
 7 #define inf 1000000000
 8 #define Safe 5
 9 using namespace std;
10 ll gcd(ll a, ll b){
11     return b == 0 ? a : gcd(b, a % b);
12 }
13 ll n, x, mx;
14 ll mul(ll a, ll b, ll p){
15     ll tmp = (a * b - (ll)((long double)a / p * b + 1e-8) * p);
16     return tmp < 0 ? tmp + p : tmp;
17 }
18 ll pow(ll a, ll b, ll p){
19     ll ans = 1; a %= p;
20     for(ll i = b; i; i >>= 1, a = mul(a, a, p))
21         if(i & 1) ans = mul(ans, a, p);
22     return ans;
23 }
24 bool check(ll a, ll n, ll r, ll s){
25     ll ans = pow(a, r, n), p = ans;
26     for(int i = 1; i <= s; i ++){
27         ans = mul(ans, ans, n);
28         if(ans == 1 && p != 1 && p != n - 1) return true;
29         p = ans;
30     }
31     if(ans != 1)return true;
32     return false;
33 }
34 bool MR(ll n){
35     if(n <= 1) return false;
36     if(n == 2) return true;
37     if(n % 2 == 0) return false;
38     ll r = n - 1, s = 0;
39     while(r % 2 == 0) r /= 2, s ++;
40     for(int i = 0; i < Safe; i ++)
41         if(check(rand() % (n - 1) + 1, n, r, s)) return false;
42     return true;
43 }
44 ll rho(ll n, ll c){
45     ll k = 2, x = rand() % n, y = x, p = 1;
46     for(ll i = 1; p == 1; i ++){
47         x = (mul(x, x, n) + c) % n;
48         p = y > x ? y - x : x - y;
49         p=gcd(n, p);
50         if(i == k) y = x, k += k;
51     }
52     return p;
53 }
54 void solve(ll n){
55     if(n == 1) return;
56     if(MR(n)) { mx = max(n, mx); return; }
57     ll t = n;
58     while(t == n) t = rho(n, rand() % (n - 1) + 1);
59     solve(t); solve(n / t);
60 }
61 void read(ll &x){
62     x = 0; ll sig = 1; char ch = getchar();
63     while(!isdigit(ch)) { if(ch == ‘-‘) sig = -1; ch = getchar(); }
64     while(isdigit(ch)) x = 10 * x + ch - ‘0‘, ch = getchar();
65     x *= sig; return ;
66 }
67 ll cnt = 0;
68 void init(){
69     read(n);
70     cnt = 0;
71     return ;
72 }
73 void work(){
74     while(n --){
75         read(x);
76         if(MR(x)) cnt ++;
77         mx = 0; solve(x);
78         if(mx == x) puts("Prime");
79         else printf("%lld\n", mx);
80     }
81     return ;
82 }
83 void print(){
84     printf("%lld\n", cnt); 
85     return ;
86 }
87 int main(){
88     init();
89     work();
90     print();
91     return 0;
92 }