PROJECT EULER SOLUTION # 146

Solution to problem number 146 of Project Euler.

Question # 146

The smallest positive integer n for which the numbers n²+1, n²+3, n²+7, n²+9, n²+13, and n²+27 are consecutive primes is 10. The sum of all such integers n below one-million is 1242490.

What is the sum of all such integers n below 150 million?

Solution # 146

/*******************************************************************************/

#include<stdio.h>

int is_prime(long long int);

long long int next_prime(long long int);

int fun(long long int);

int main()

{

      long long int i,sum=0;

      for(i=2;i<150000000;i+=2)

      {

            //printf("i = %lld  sum = %lld\n",i,sum);

            if(fun(i))

            {

                  sum+=i;

                  printf("sum = %lld\t\ti = %lld\n",sum,i);

            }

      }

      printf("sum = %lld\n",sum);

      return 0;

}

int is_prime(long long int n)

{

      long long int i;

      if(n%2==0)

            return 0;

      for(i=3;i*i<=n;i+=2)

            if(n%i==0)

                  return 0;

      return 1;

}

long long int next_prime(long long int n)

{

      long long int i;

      for(i=n+2;;i+=2)

      {

            if(is_prime(i))

                  return i;

      }

      return 0;

}

int fun(long long int n)

{

      if(primecheck(n))

            if(next_prime(n*n+1)==n*n+3 && next_prime(n*n+3)==n*n+7 && next_prime(n*n+7)==n*n+9 && next_prime(n*n+9)==n*n+13 && next_prime(n*n+13)==n*n+27)

                  return 1;

      return 0;

}

int primecheck(long long int n)

{

      long long int i;

      if((n*n+1)%2==0)

            return 0;

      for(i=3;i*i<=(n*n+27);i+=2)

      {

            if((n*n+1)%i==0)

                  return 0;

            if((n*n+3)%i==0)

                  return 0;

            if((n*n+7)%i==0)

                        return 0;

                if((n*n+9)%i==0)

                        return 0;

            if((n*n+13)%i==0)

                        return 0;

                if((n*n+27)%i==0)

                        return 0;

      }

      return 1;

}

/*******************************************************************************/