# C++ Program to Perform Fermat Primality Test

C++Server Side ProgrammingProgramming

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
Published on 15-Mar-2019 10:53:12
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