Poj1811_prime test [Miller Rabin prime number test] [pollar rov integer decomposition]

Prime testtime limit: 6000 ms memory limit: 65536 ktotal submissions: 29193 accepted: 7392 case time limit: 4000 msdescription


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 <2 ^ 54 ).
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
Source

Poj monthly

T-group data. If n is the prime number of input N, "prime" is output; otherwise, the minimum prime factor of N is output.

Idea: Because the N scale is 2 ^ 54, it is impossible to judge the common gender. Use the miller Rabin prime number test.

If n is not a prime number, we need to perform prime factor decomposition on N. Because N is a large number, it is considered to be decomposed using the pollar rov integer.

# Include <stdio. h> # include <stdlib. h> # include <time. h> # include <math. h> # define max_val (POW (2.0, 60) // miller_rabbin prime test // _ int64 mod_mul (_ int64 x ,__ int64 y ,__ int64 Mo) // {// _ int64 t; // X % = Mo; // For (t = 0; y; X = (x <1) % Mo, y> = 1) // If (Y & 1) // t = (t + x) % Mo; // return T; // }__ int64 mod_mul (_ int64 x ,__ int64 y ,__ int64 Mo) {_ int64 T, T, A, B, C, D, E, F, g, H, V, ans; t = (_ int64) (SQRT (double (Mo) + 0.5); t = T * T-Mo; A = x/T; B = x % t; C = y/T; D = Y % t; E = A * C/T; F = A * C % t; V = (A * D + B * C) % Mo + E * t) % Mo; G = V/T; H = V % t; ans = (F + G) * T % Mo + B * D) % Mo + H * t) % Mo; while (ANS <0) ans + = Mo; return ans; }__ int64 mod_exp (_ int64 num ,__ int64 t ,__ int64 Mo) {_ int64 ret = 1, temp = num % Mo; for (; t> = 1, temp = mod_mul (temp, temp, Mo) if (T & 1) ret = mod_mul (Ret, temp, Mo ); return ret;} bool Miller _ Rabbin (_ int64 N) {If (n = 2) return true; If (n <2 |! (N & 1) return false; int T = 0; _ int64 A, X, Y, u = n-1; while (U & 1) = 0) {T ++; U >>=1 ;}for (INT I = 0; I <50; I ++) {A = rand () % (n-1) + 1; X = mod_exp (A, U, N); For (Int J = 0; j <t; j ++) {Y = mod_mul (x, x, N ); if (y = 1 & X! = 1 & X! = N-1) return false; X = y;} If (X! = 1) return false;} return true;} // pollarrov big integer factorization _ int64 minfactor ;__ int64 gcd (_ int64 A ,__ int64 B) {If (B = 0) return a; return gcd (B, A % B) ;}__ int64 pollarrov (_ int64 N, int c) {int I = 1; srand (Time (null); _ int64 x = rand () % N; _ int64 y = x; int K = 2; while (true) {I ++; X = (mod_exp (x, 2, n) + C) % N; _ int64 d = gcd (Y-X, N ); if (1 <D & D <n) return D; If (y = x) return N; if (I = k) {Y = X; K * = 2 ;}} void getsmallest (_ int64 N, int c) {If (n = 1) return; If (miller_rabbin (n )) {If (n <minfactor) minfactor = N; return;} _ int64 val = N; while (val = N) val = pollarrov (N, C --); getsmallest (Val, c); getsmallest (N/Val, c);} int main () {int t; _ int64 N; scanf ("% d ", & T); While (t --) {scanf ("% i64d", & N); minfactor = max_val; If (miller_rabbin (n )) printf ("prime \ n"); else {getsmallest (n, 200); printf ("% i64d \ n", minfactor) ;}} return 0 ;}

Poj1811_prime test [Miller Rabin prime number test] [pollar rov integer decomposition]