How to create a large prime number?

Question

I'd like to try to create a large prime number similar to what is created in OpenSSL but without extra libararies (ie. OpenSLL). Below this post there is a small sample code fromhttps://www.techiedelight.com/c-program-demonstrate-diffie-hellman-algorithm/. Let's say I've created a 128bit number. How would I modify the "compute" function to accommodate a 128bit number or larger?

#include <stdio.h>
 
// Function to compute `a^m mod n`
int compute(int a, int m, int n) {
    int r;
    int y = 1;
     while (m > 0)  {
        r = m % 2;
         // fast exponention
        if (r == 1) {
            y = (y*a) % n;
        }
        a = a*a % n;
        m = m / 2;
    }
     return y;
}
 
// C program to demonstrate the Diffie-Hellman algorithm
int main()
{
    int p = 23;        // modulus (prime number)
    int g = 5;        // base
    int a, b;    // `a` – Alice's secret key, `b` – Bob's secret key.
    int A, B;    // `A` – Alice's public key, `B` – Bob's public key
 
    // choose a secret integer for Alice's private key (only known to Alice)
    a = 6;        // or, use `rand()`
 
    // Calculate Alice's public key (Alice will send `A` to Bob)
    A = compute(g, a, p);
 
    // choose a secret integer for Bob's private key (only known to Bob)
    b = 15;        // or, use `rand()`
 
    // Calculate Bob's public key (Bob will send `B` to Alice)
    B = compute(g, b, p);
 
    // Alice and Bob Exchange their public key `A` and `B` with each other
 
    // Find secret key
    int keyA = compute(B, a, p);
    int keyB = compute(A, b, p);
 
    printf("Alice's secret key is %d\nBob's secret key is %d", keyA, keyB);
 
    return 0;
}