Twin Prime Numbers in C

Twin prime numbers consist of prime number pairs separated by a gap of 2.

They are relatively rare but are fascinating for their proximity to each other in the number line.

Properties:

Twin primes are pairs of prime numbers.

The difference between each twin prime pair is always 2.

Both numbers in a twin prime pair are prime numbers.

Program 1:

// Program for Twin Prime Number in C
#include<stdio.h> 

// Function to check if a number is prime
int isPrime(int n) {
    if (n <= 1) {
        return 0; 
    }
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            return 0; // n is not prime if it has a divisor other than 1 and itself
        }
    }
    return 1; // n is prime
}

int main() {
    int start, end;

    printf("Enter the range to find twin prime numbers (start end): ");
    scanf("%d %d", &start, &end);

    printf("Twin prime numbers in c range %d to %d are:\n", start, end);

    for (int i = start; i <= end - 2; i++) {
        if (isPrime(i) && isPrime(i + 2)) {
            printf("(%d, %d)\n", i, i + 2);
        }
    }

    return 0;
}

Output:

Enter the range to find twin prime numbers (start end): 1
100
Twin prime numbers in c range 1 to 100 are:
(3, 5)
(5, 7)
(11, 13)
(17, 19)
(29, 31)
(41, 43)
(59, 61)
(71, 73)

Program 2:

#include<stdio.h> 

// Function to check if a number is prime
int isPrime(int n) {
    if (n <= 1) {
        return 0; 
    }
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            return 0; // n is not prime if it has a divisor other than 1 and itself
        }
    }
    return 1; // n is prime
}

int main() {
    int count = 0, n = 2, start, end;

    printf("Enter the digit of twin prime pairs to display: ");
    scanf("%d", &count);

    printf("First %d twin prime pairs are:\n", count);

    while (count > 0) {
        if (isPrime(n) && isPrime(n + 2)) {
            printf("(%d, %d)\n", n, n + 2);
            count--;
        }
        n++;
    }

    return 0;
}

Output:

Enter the digit of twin prime pairs to display: 2
First 2 twin prime pairs are:
(3, 5)
(5, 7)

Both programs utilize the isPrime function to check if a number is prime.

Program 1 takes a range from the user and finds twin primes within that range.

Program 2 takes a count from the user and displays the specified number of twin prime pairs starting from the smallest twin prime.