C Program to Implement Rabin-Miller Primality Test to Check if a Number is Prime

This C program implements the Rabin-Miller Primality Test to check if a given number is Prime. The Miller–Rabin primality test or Rabin–Miller primality test is a primality test: an algorithm which determines whether a given number is prime, similar to the Fermat primality test and the Solovay–Strassen primality test.

Here is the source code of the C program to check if a given number is prime or not. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include <stdio.h>
```
```
#include <string.h>
```
```
#include <stdlib.h>
```
```
/* 
```

 * calculates (a * b) % c taking into account that a * b might overflow

```
 */
```

long long mulmod(long long a, long long b, long long mod)

```
{
```
```
    long long x = 0,y = a % mod;
```
```
    while (b > 0)
```
```
    {
```
```
        if (b % 2 == 1)
```
```
        {    
```
```
            x = (x + y) % mod;
```
```
        }
```
```
        y = (y * 2) % mod;
```
```
        b /= 2;
```
```
    }
```
```
    return x % mod;
```
```
}
```
```
/* 
```
```
 * modular exponentiation
```
```
 */
```

long long modulo(long long base, long long exponent, long long mod)

```
{
```
```
    long long x = 1;
```
```
    long long y = base;
```
```
    while (exponent > 0)
```
```
    {
```
```
        if (exponent % 2 == 1)
```
```
            x = (x * y) % mod;
```
```
        y = (y * y) % mod;
```
```
        exponent = exponent / 2;
```
```
    }
```
```
    return x % mod;
```
```
}
```
```
 
```
```
/*
```

 * Miller-Rabin Primality test, iteration signifies the accuracy

```
 */
```
```
int Miller(long long p,int iteration)
```
```
{
```
```
 
```
```
    int i;
```
```
    long long s;
```
```
    if (p < 2)
```
```
    {
```
```
        return 0;
```
```
    }
```
```
    if (p != 2 && p % 2==0)
```
```
    {
```
```
        return 0;
```
```
    }
```
```
     s = p - 1;
```
```
    while (s % 2 == 0)
```
```
    {
```
```
        s /= 2;
```
```
    }
```
```
    for (i = 0; i < iteration; i++)
```
```
    {
```

        long long a = rand() % (p - 1) + 1, temp = s;

        long long 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 0;
```
```
        }
```
```
    }
```
```
    return 1;
```
```
}
```
```
//Main
```
```
int main()
```
```
{
```
```
    int iteration = 5;
```
```
    long long num;
```

    printf("Enter integer to test primality: ");

```
    scanf("%lld", &num);
```
```
    if ( Miller( num, iteration))
```

        printf("\n%lld is prime\n", num);

```
    else
```

        printf("\n%lld is not prime\n", num);

```
    return 0;
```
```
}
```

$ gcc bubblesort.c -o bubblesort
$ ./bubblesort
 
Enter integer to test Primality: 89
89 is prime

Sanfoundry Global Education & Learning Series – 1000 C Programs.

Here’s the list of Best Books in C Programming, Data Structures and Algorithms.

« Prev - C Program to Implement Sieve of Eratosthenes to Generate Prime Numbers

» Next - C Program to Find GCD of Two Numbers

Related Posts:

Recommended Articles: