Description
Given a big integer number, you are required to find out whether it's a prime number.
Input
The first line contains the number of test cases T (1 <= T <= 20 ), then the following T lines each contains an integer number N (2 <= N < 254).
Output
For each test case, if N is a prime number, output a line containing the word "Prime", otherwise, output a line containing the smallest prime factor of N.
Sample Input
2
5
10
Sample Output
Prime
2
Pollard Rho大数分解算法+Miller_Rabin判素数法模板
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 #include<cmath> 6 #include<ctime> 7 using namespace std; 8 typedef long long lol; 9 int prime[11]={2,3,5,7,11,13,17,19,23,29}; 10 lol ans,inf=1e18; 11 lol gcd(lol a,lol b) 12 { 13 if (!b) return a; 14 return gcd(b,a%b); 15 } 16 lol multi(lol x,lol y,lol Mod) 17 { 18 lol res=0; 19 x%=Mod; 20 while (y) 21 { 22 if (y&1) 23 { 24 res=(res+x)%Mod; 25 } 26 x=(x+x)%Mod; 27 y>>=1; 28 } 29 return res; 30 } 31 lol qpow(lol x,lol y,lol Mod) 32 { 33 lol res=1; 34 while (y) 35 { 36 if (y&1) 37 { 38 res=multi(res,x,Mod); 39 } 40 x=multi(x,x,Mod); 41 y>>=1; 42 } 43 return res; 44 } 45 bool Miller_Rabin(lol n) 46 {int i,j; 47 if (n==2) return 1; 48 if (n<2||n%2==0) return 0; 49 for (i=0;i<10;i++) 50 { 51 if (n==prime[i]) return 1; 52 if (n%prime[i]==0) return 0; 53 } 54 lol m=n-1,k=0; 55 while (m%2==0) 56 { 57 m>>=1; 58 k++; 59 } 60 for (i=0;i<10;i++) 61 { 62 lol a=rand()%(n-2)+2; 63 lol x=qpow(a,m,n); 64 lol y=0; 65 for (j=0;j<k;j++) 66 { 67 y=multi(x,x,n); 68 if (y==1&&x!=1&&x!=n-1) return 0; 69 x=y; 70 } 71 if (y!=1) return 0; 72 } 73 return 1; 74 } 75 lol pollard_rho(lol n,lol c) 76 { 77 lol i=1,k=2; 78 lol x=rand()%(n-1)+1,y=x; 79 while (1) 80 { 81 ++i; 82 x=(multi(x,x,n)+c)%n; 83 lol d=gcd((y-x+n)%n,n); 84 if (d>1&&d<n) return d; 85 if (y==x) return n; 86 if (i==k) 87 { 88 y=x; 89 k<<=1; 90 } 91 } 92 } 93 void find(lol n,lol c) 94 { 95 if (n==1) return; 96 if (Miller_Rabin(n)) 97 { 98 ans=min(ans,n); 99 return; 100 } 101 lol p=n; 102 lol k=c; 103 while (p==n) p=pollard_rho(p,c--); 104 find(p,k); 105 find(n/p,k); 106 } 107 int main() 108 {int T; 109 lol n; 110 cin>>T; 111 srand(time(0)); 112 while (T--) 113 { 114 cin>>n; 115 ans=inf; 116 if (Miller_Rabin(n)) printf("Prime "); 117 else 118 { 119 find(n,120); 120 printf("%lld ",ans); 121 } 122 } 123 }