राबिन-मिलर प्रिमलिटी टेस्ट का उपयोग यह जांचने के लिए किया जाता है कि दी गई संख्या अभाज्य है या नहीं। यह फॉर्मेट प्रिमलिटी और सोलोवे-स्ट्रेसन टेस्ट के समान है। इस परीक्षण की खोज सबसे पहले रूसी गणितज्ञ एम. एम. आर्टजुहोव ने की थी।
एल्गोरिदम
Begin ll mulmod(ll a, ll b, ll m) ll x = 0,y = a mod m while (b > 0) if (b mod 2 == 1) compute x = (x + y) mod m y = (y * 2) mod m b = b/ 2 return x mod m. End Begin ll modulo(ll base, ll e, ll m) Initialize: ll x = 1 ll y = base while (e > 0) if (e mod 2 == 1) x = (x * y) mod m y = (y * y) mod m e = e / 2; return x mod m End Begin bool Miller(ll p, int iteration) if (p < 2) return false if (p != 2 and p mod 2==0) return false; Compute: ll s = p - 1 while (s mod 2 == 0) s = s/ 2; for i = 0 to iteration - 1 Do ll a = rand() mod (p - 1) + 1, temp = s ll mod = modulo(a, temp, p) while (temp != p - 1 and mod != 1 and mod != p - 1) mod = mulmod(mod, mod, p); temp *= 2; if (mod != p - 1 && temp % 2 == 0) return false else return true End
उदाहरण कोड
#include <iostream>
#include<stdlib.h>
#define ll long long
using namespace std;
ll mulmod(ll a, ll b, ll m)//It returns true if number is prime otherwise false {
ll x = 0,y = a % m;
while (b > 0) {
if (b % 2 == 1) {
x = (x + y) % m;
}
y = (y * 2) % m;
b /= 2;
}
return x % m;
}
ll modulo(ll base, ll e, ll m) {
ll x = 1;
ll y = base;
while (e > 0) {
if (e % 2 == 1)
x = (x * y) % m;
y = (y * y) % m;
e = e / 2;
}
return x % m;
}
bool Miller(ll p, int iteration) {
if (p < 2) {
return false;
}
if (p != 2 && p % 2==0) {
return false;
}
ll s = p - 1;
while (s % 2 == 0) {
s /= 2;
}
for (int i = 0; i < iteration; i++) {
ll a = rand() % (p - 1) + 1, temp = s;
ll mod = modulo(a, temp, p);
while (temp != p - 1 && mod != 1 && mod != p - 1) {
mod = mulmod(mod, mod, p);
temp *= 2;
}
if (mod != p - 1 && temp % 2 == 0) {
return false;
}
}
return true;
}
int main() {
int iteration = 10;
ll num;
cout<<"Enter integer to test primality: ";
cin>>num;
if (Miller(num, iteration))
cout<<num<<" is prime"<<endl;
else
cout<<num<<" is not prime"<<endl;
return 0;
} आउटपुट
Enter integer to test primality: 26 26 is not prime