Try any numbers, but these numbers make the program crash 2468,
8902

conjecture.c

#include <stdio.h>

#include "sieve.h"

#include <string.h>

int getPrimes (int a[], int low, int high, int num, int lowIndex,

int HighIndex);

int getNextIndex (int a[], int index, int s);

extern int holder[];

/**

* assigns two variables to store primes, one the

* smallest prime (low prime) and another stores the highest

* prime that is less than num (high prime)

*/

int

main ()

{

findPrimes ();

int infinite = 1;

while (infinite)

{

int num; // the even number that can be represented by two primes

if (scanf ("%d", &num) == EOF)

break;

if (num % 2 != 0 || num < 3 || num > 100000)

{

fprintf (stderr, "%d is an invalid number\n", num);

continue;

}

int high = 0; // the low prime

int low = 0; // the high prime

int highIndex = 0;

int lowIndex = 0;

low = holder[lowIndex]; // initially low prime is first element (2)

int i = 0;

for (; i < N - 1; i++) // find the high prime

{

if (holder[i] != 0 && holder[i] < num)

high = holder[i];

highIndex = i;

}

getPrimes (holder, low, high, num, lowIndex, highIndex);

}

return 0;

}

/**

* given both the low and high prime, this function

* will increase the low prime and decrease the

* high prime until low prime + high prime = num

*/

int

getPrimes (int a[], int low, int high, int num, int lowIndex, int highIndex)

{

if (lowIndex > N - 1 || highIndex < 0)

{

printf ("No primes found\n");

return 1;

}

else if (high + low == num)

{

printf ("%d %d\n", low, high);

return 0;

}

else if (high + low < num) // get the next biggest low prime

{

lowIndex = getNextIndex (holder, lowIndex, 0);

low = holder[lowIndex];

return getPrimes (holder, low, high, num, lowIndex, highIndex);

}

else if (high + low > num) // get the next smallest high prime

{

highIndex = getNextIndex (holder, highIndex, 1);

high = holder[highIndex];

return getPrimes (holder, low, high, num, lowIndex, highIndex);

}

return 1;

}

/**

* returns the index of the next prime

* if s = 0 then search to the right of current index in the array

* if s = 1 then search to the left of current index in the array

*/

int

getNextIndex (int a[], int index, int s)

{

if (s == 0)

{

int i = index + 1;

for (; i < N - 1; i++)

{

if (a[i] != 0)

return i;

}

}

else

{

int i = index - 1;

for (; i >= 0; i--)

{

if (a[i] != 0)

return i;

}

}

return 1;

}

===========

sieve.c

#include <math.h>

#include <stdio.h>

#include "sieve.h"

int findPrimes ();

int holder[N];

/**

* findPrimes() stores all the primes

* from 2 to N in an array.

*/

int

findPrimes ()

{

int i = 0;

int j = 2;

for (; i < N - 1; i++) // delete first two elements

{ // and shift all elements two places to the left

holder[i] = j;

++j;

}

float fN = N;

float square = sqrt (fN);

int prime = 0;

int k = 0;

for (; k < N - 1; k++)

{ // loop finds next prime

if (holder[k] == 0)

continue;

prime = holder[k];

if (holder[k] > square) // no need if to continue

break; // if prime is > square of N

int p = k + 1;

for (; p < N - 1; p++)

{ // loop finds multiples of prime

if (holder[p] == 0) // then get next element

continue;

if (holder[p] % prime == 0)

{ // its a multiple

holder[p] = 0;

}

}

}

return 0;

}

===============

the header file

enum

{ N = 100000 };

extern int holder[];

int findPrimes ();