# include <stdbool.h>
# include <stdlib.h>

# include "prime_pi.h"

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

bool is_prime3 ( int n )

/******************************************************************************/
/*
  Purpose:

    is_prime3() reports whether an integer is prime.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    28 December 2022

  Author:

    John Burkardt

  Input:

    int n: the value to be tested.

  Output:

    bool value: true if n is a prime.
*/
{
  int i;

  if ( n <= 1 )
  {
    return false;
  }

  if ( ( n == 2 ) || ( n == 3 ) )
  {
    return true;
  }

  if ( ( n % 2 == 0 ) || ( n % 3 == 0 ) )
  {
    return false;
  }

  for ( i = 5; i * i <= n; i = i + 6 )
  {
    if ( ( n % i == 0 ) || ( n % ( i + 2 ) == 0 ) )
    {
      return false;
    }
  }

  return true;
}
/******************************************************************************/

int prime_pi1 ( int n )

/******************************************************************************/
/*
  Purpose:

    prime_pi1() evaluates prime(n), the number of primes less than or equal to n.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    31 December 2022

  Author:

    John Burkardt

  Input:

    integer n: the value to be tested.

  Output:

    integer value: the value of pi(n).
*/
{
  int i;
  int value;

  value = 0;
  for ( i = 1; i <= n; i++ )
  {
    if ( is_prime3 ( i ) )
    {
      value = value + 1;
    }
  }

  return value;
}