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C++ Program to Perform Fermat Primality Test
Fermat Primality test performs to check a given number is prime or not. Here is a C++ code of this algorithm.
Algorithm
Begin modulo(base, e, mod) a = 1 b = base while (e > 0) if (e mod 2 == 1) a = (a * b) % mod b = (b * b) % mod e = e / 2 return a % mod End Begin Fermat(ll m, int iterations) if (m == 1) return false done for (int i = 0; i < iterations; i++) ll x = rand() mod (m - 1) + 1 if (modulo(x, m - 1, m) != 1) return false done return true End
Example Code
#include <cstring>
#include <iostream>
#include <cstdlib>
#define ll long long
using namespace std;
ll modulo(ll base, ll e, ll mod) {
ll a = 1;
ll b = base;
while (e > 0) {
if (e % 2 == 1)
a = (a * b) % mod;
b = (b * b) % mod;
e = e / 2;
}
return a % mod;
}
bool Fermat(ll m, int iterations) {
if (m == 1) {
return false;
}
for (int i = 0; i < iterations; i++) {
ll x = rand() % (m - 1) + 1;
if (modulo(x, m - 1, m) != 1) {
return false;
}
}
return true;
}
int main() {
int iteration = 70;
ll num;
cout<<"Enter integer to test primality: ";
cin>>num;
if (Fermat(num, iteration))
cout<<num<<" is prime"<<endl;
else
cout<<num<<" is not prime"<<endl;
return 0;
}Output
Enter integer to test primality: 13 is prime
Updated on: 30-Jul-2019
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