Java program for Brun’s Constant
Twin Primes are the prime numbers with a difference of 2, e.g., (3, 5),
(5, 7), (11, 13), (17, 19) ... etc. The sum of reciprocals of the twin primes up
to a limit, converges to sum known as Brun’s Constant. Example :
Say for Inputted number 13 and its twin primes are (3, 5), (5, 7), (11,
13) and its sum of reciprocals is
(1/3 + 1/5) + (1/5 + 1/7) +
(1/11 + 1/13) = 1.044022644022644
Write a program to create Primes which include methods:
Booleans isPrime(int n) Checks whether n is prime or not
Void twinPrimesBrunConstant – Which checks twin prime and also calculate
brun’s constant.
Solution
import java.util.Scanner;
/**
* class BrunsConstant
* Input 2 nos. and check whether
they make up Brun’s Constant or not, Brun’s Constant is sum of
* reciprocal of Twin Prime Nos.
e.g (1/3) + (1/5) is a Brun’s Constant
*/
public class BrunsConstant
{
static double sum=0.0;
static int i, f;
// Check the number prime or
not
public static boolean
isPrime(int n)
{
f=1;
for (i = 2 ; i < n ;
i++)
{
if(n % i == 0)
{
f=0;
break;
}
}
if(f == 1)
return true;
else
return false;
}
// Here checked the two
number twin prime or not
// and also calculate brun's constant.
public static void
twinPrimesBrunConstant(int number )
{
System.out.println("Twin prime");
System.out.println("==========");
for (int i = 2; i <
number ; i++)
{
int num1 = i;
int num2 = i + 2;
if (isPrime(num1)
&& isPrime(num2))
{
System.out.println(num1 + " " + num2);
sum = sum +
(double)1/num1 + (double)1/num2;
}
}
}
public static void
main(String[] args)
{
int no;
Scanner scanner = new
Scanner(System.in);
System.out.print("Enter a number: ");
no = scanner.nextInt();
twinPrimesBrunConstant(no);
System.out.println("Brun's
Constant:" + sum);
}
}
Advanced Java: Learn Java Advanced Features
Output
Enter a number: 13
Twin prime
==========
3 5
5 7
11 13
Brun's Constant:1.044022644022644
Enter a number: 50
Twin prime
==========
3 5
5 7
11 13
17 19
29 31
41 43
Brun's Constant:1.2698646333745234
