Twin Prime Numbers in C

This topic will discuss twin primes and how we can print twin primes in the C programming language. A twin prime is a pair of prime numbers representing the difference of two prime numbers always 2 and is therefore called a twin prime. In simple words, if the difference between two prime numbers is 2 and there is exactly one composite number between them, then the number is called twin prime numbers.

For example, (59, 61) and (71, 73) are twin prime pairs, and the difference between these numbers is 61 - 59 = 2, and 73 - 71 = 2.

Properties of the twin prime number

(2, 3) are not considered twin primes because there is no composite number between them, and neither is the difference of two prime numbers (2, 3) is equal to 2.
(3, 5) is a pair of twin primes because the difference of two primes (5 - 3 = 2) is 2 and hence (3, 5) is a twin prime.
Every twin other than (3, 5) is in the form of a prime number (6n - 1, 6n + 1), where n defines the natural number.
5 is the only prime number in which the difference between both positive and negative primes is 5. So, 5 appears in two prime pairs (3, 5) and (5, 7).
If we add two pairs of twin prime numbers, the result of twin primes will be divisible by 12, except for (3, 5) pairs of twin prime numbers.

Program to print twin primes from 2 to n using user defined function

Create a program in C programming language to generate twin prime number between 2 to n.

Program1.c

#include <stdio.h>
#include <conio.h>
int main ()
{
	// declare variables
	int i, num, count = 0;
	printf (" Enter the last number: ");
	scanf (" %d", &num); // get the last number
	
	for (i = 2; i <= num; i++)
	{
		if (twinprime (i) && twinprime (i+2))
		{
			printf (" \n The twin prime number is: (%d, %d) ", i, i+2);
			count++; // counter increment by 1
		}
	}
	printf (" \n \n Total number of twin prime pairs: %d", count);
	return 0;
}
// function definition 
int twinprime( int n)
{
	int i = 2;
	// use for loop to find the twin prime
	for (i = 2; i <= n/2; i++)
	{
		// if n is completely divisible by 1 without leaving any remainder, it returns 0
		if (n%i == 0)
			return 0;
	}
	// otherwise it returns 1
	if (i > n / 2)
		return 1;
}

Output

Enter the last number: 100
 The twin prime number is: (3, 5)
 The twin prime number is: (5, 7)
 The twin prime number is: (11, 13)
 The twin prime number is: (17, 19)
 The twin prime number is: (29, 31)
 The twin prime number is: (41, 43)
 The twin prime number is: (59, 61)
 The twin prime number is: (71, 73)
 Total number of twin prime pairs: 8

In the above program, a for loop that iterates over the numbers between the specified range of 2 to 100. After that, we create a twinprime() as a user-defined function called inside the for loop to check the primes of the 'i' and 'i+2' index. And if the condition is met, it prints the total pair of twin prime and the twin prime numbers.

Program to print twin primes using the Sieve of Eratosthenes algorithm

The Sieve of Eratosthenes is an approach to get a list of all prime numbers that are less than or equal to a given number (n). It iterates the prime number up to n consecutive number and checks that both the i^th and (i + 2) numbers are prime, and then it prints the prime number; otherwise, it moves to the next number to get the twin primes. Here, (3, 5), (5, 7), (11, 13) are examples of the Sieve of Eratosthenes algorithm.

Let's consider an example to get the twin primes using the Sieve of Eratosthenes algorithm.

Program2.c

#include <stdio.h>
#include <string.h>
int main()
{
	// declare an integer variable
	int num;
	printf (" Enter the last number to get twin prime numbers: ");
	scanf (" %d", &num); 	
	// call twinprime() function
	twinprime( num); // pass num as an argument
	return 0;
}
void twinprime (int n)
{
	int j;
	/* here we create a unsigned char array 'prime[]' and initialize all its entries as true. */
	unsigned char prime[n + 1]; // declaration of the unsigned char prime[] array	
	memset (prime, 1, sizeof(prime));	
	// use for loop to iterate over a certain range
	for ( j = 2; (j * j) <= n; j++)
	{
		// if the condition of prime[j] remains true, it is a prime
		if (prime [j] == 1)
		{
			int i = 0;
			// update the multiples of j
			for (i = (j * 2); i <= n; i += j)	
				prime[i] = 0;
		}
	  } 	  
	  // now check for twin prime numbers and print the twin primes	  
	  for ( j = 2; j <= (n - 2); j++)
	  {
	  	if (prime[j] && prime[j + 2])
	  		printf (" \n The twin prime numbers: (%d, %d) ", j, j +2);	   	
	   } 
}	

Output

Enter the last number to get twin prime numbers: 200
 The twin prime numbers: (3, 5)
 The twin prime numbers: (5, 7)
 The twin prime numbers: (11, 13)
 The twin prime numbers: (17, 19)
 The twin prime numbers: (29, 31)
 The twin prime numbers: (41, 43)
 The twin prime numbers: (59, 61)
 The twin prime numbers: (71, 73)
 The twin prime numbers: (101, 103)
 The twin prime numbers: (107, 109)
 The twin prime numbers: (137, 139)
 The twin prime numbers: (149, 151)
 The twin prime numbers: (179, 181)
 The twin prime numbers: (191, 193)
 The twin prime numbers: (197, 199)

Program to check whether a given number is a twin prime or not

Let us consider an example of whether a given number is twin prime or not in the C programming language.

Program3.c

#include <stdio.h>
#include <string.h>
// function definition of the checktwin()
void checktwin(num1, num2)
{
	// declare integer variables
	int i;	
	// declare and initialize isprime
	unsigned char isprime = 1;	
	// use for loop to check the prime number for the first number 
	for ( i = 2; i <= (num1 / 2); i++ )
	{
		// if num1 is completely divisible by i, the if block is executed
		if (num1 % i == 0)
		{
			isprime = 0;
			break;
		}			
	}
	/* here isprime is called and abs() function get the absolute result of num1 and num2 */
	if (isprime && abs(num1 - num2) == 2)
	{
		// declare isprime2 as unsigned char and initialize as 1 that represents true.
		unsigned char isprime2 = 1;		
		// use for loop to check the second number is a prime number
		for ( i = 2; i <= num2 / 2; i++)
		{
			// it checks num2 is completely divisible by i and return 0
			if (num2 % i == 0)
			{
				// isprime2 initialize by 0
				isprime2 = 0;
				break;
			}
		}
		// check the isprime2 condition
		if (isprime2)
		{
			printf (" %d and %d are twin prime", num1, num2);
		}
		else
			printf (" %d and %d are not twin prime", num1, num2);	
	}
	else
		printf (" %d and %d are not twin prime number", num1, num2);
}
int main()
{
	int num1, num2;	
	printf (" Enter the first number: ");
	scanf ("%d", &num1); // get first number	
	printf (" Enter the second number: ");
	scanf (" %d", &num2); // get second number	
	checktwin(num1, num2); /* call the checktwin() function and pass num1 and num2 as parameters. */
	return 0;
}

Output

Enter the first number: 71
 Enter the second number: 73
 71 and 73 are twin prime

2nd execution:

Enter the first number: 15
 Enter the second number: 17
 15 and 17 are not twin prime

In the above program, we take two numbers from the user to check whether the given number is twin prime or not. Here we take 5 and 7 as the prime number, and the function returns 5 and 7 are twin prime. Similarly, we take the numbers 15 and 17, and the function returns numbers, not twin primes.

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