Write a program in java to test GoldBach's conjecture for numbers between 900000 and 900100 and optimize running time.

**Subject Computer Science Java Programming**

Write a program in java to test GoldBach's conjecture for numbers between 900000 and 900100 and optimize running time.

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static boolean IsPrime(int n) // n is between 6 and 40000000

{

int i = 5;

boolean prime = true;

if ((n > 3) && (((n % 2) == 0) || ((n % 3) == 0))) // check if it is dividable with 2 or 3, if yes it is not a prime

{

prime = false;

}

while ((prime) && ((i * i) <= n)) // Check candidates to squareroot of n, if there is a divisor at least one is less than the squareroot

{

/*

The candidates for prime numbers are 6k +- 1, k is a whole positive number

6k, 6k + 2 and 6k + 4 are dividable by 2

6k + 3 is dividable by 3

So only 6k +1 and 6k +5 (same as 6k -1 of next k) can be primes

i starts from 5, which is for k = 1 6k -1

Then i and i + 2, which is 6k + 1 is checked if they divide n with mod 0, if yes, n is not prime

i is increased by 6, same as k is incremented by 1

*/

prime = (((n % i) != 0) && ((n % (i + 2)) != 0));

i += 6;

}

return prime;

}...

{

int i = 5;

boolean prime = true;

if ((n > 3) && (((n % 2) == 0) || ((n % 3) == 0))) // check if it is dividable with 2 or 3, if yes it is not a prime

{

prime = false;

}

while ((prime) && ((i * i) <= n)) // Check candidates to squareroot of n, if there is a divisor at least one is less than the squareroot

{

/*

The candidates for prime numbers are 6k +- 1, k is a whole positive number

6k, 6k + 2 and 6k + 4 are dividable by 2

6k + 3 is dividable by 3

So only 6k +1 and 6k +5 (same as 6k -1 of next k) can be primes

i starts from 5, which is for k = 1 6k -1

Then i and i + 2, which is 6k + 1 is checked if they divide n with mod 0, if yes, n is not prime

i is increased by 6, same as k is incremented by 1

*/

prime = (((n % i) != 0) && ((n % (i + 2)) != 0));

i += 6;

}

return prime;

}...

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