Finding Largest Twin Prime - c

Question

I am trying to create a c program which prompts for user input and then, finds the largest twin prime within that number. This program then loops continuously, prompting the user for an input again and again and finding the largest twin prime until the user enters -1, after which it terminates. I wrote down the basic code, but have yet been able to make it loop continuously when using certain numbers such as 20 and 65. I cannot figure out what is wrong with my code.
I seem to be having another problem as well. For 20, the values show (15,17) instead of (17,19). Obviously the logic is wrong somewhere but I am not sure exactly where either.
This is my code:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include<conio.h>
int prime(int x)
{
int i,numroot;
numroot=sqrt(x);
for(i=2;i<=numroot;i++)
if(x%i==0){
return(0);
}
return(1);
}
int main()
{
double N;
printf("This program prints out all the possible twin primes until a specific number which...\nyou can choose!");
printf("\nA note of caution: Although this program accepts decimals, the value entered must be between 5 and 10^9,inclusive of the 2 numbers.");
printf("\nKey in -1 to exit.");
printf("\nEnter N value upto which twin primes ought to be calculated until: ");
scanf("%lf",&N);
while (N!=-1) {
if (N<5 || N>pow(10,9)) {
printf("\nNumber not in the valid range was inputted. \nPlease reenter the value: ");
scanf("%lf",&N);
}
else {
int n;
n=floor(N);
int prime(int x);
int f,originalval;
originalval=N;
f=prime(n);
while(f==0){//Calculates for largest prime number below user input
n--;
f=prime(n);
}
int smallint=n-2;
while(prime(smallint)==1){
n--;
f=prime(n);
while(f==0){
n--;
f=prime(n);
}
int smallint=n-2;
}
printf("The largest twin prime pair not above %d is (%d,%d)",originalval,smallint,n);
printf("\nPlease re-enter the value:");
scanf("%lf",&N);
}
}
printf("\nProgram successfully terminated.");
return 0;
}

Answer 1

You are doing a research about prime numbers "upto" a given number N.
In this class of problems is more efficient (although more expensive in RAM space) to store information in tables of primes and composite numbers, like the Sieve of Eratosthenes.
Once you have filled the table with the information of which numbers are prime and composite, it's just a matter of iterate on the table to look for the twin primes, wherever they are.
However, although you inform to the user that all the twin primes will be shown, actually what your program does is trying to show only the lastest.
Please, have clear which is the goal of your program.
On the other hand, you are redefining the identifier smallint inside the innest loop, which is, for sure, a logical error.
In case you cannot use arrays to store the Sieve of Eratosthenes, then I show you here a method that is not hard to implement (but it's not, of course, the most efficient; however it will avoid a lot of redundant computations).
The twin primes (greater than 4) can be of two different forms:
6k-1, 6k+1
6k+1, 6k+5
So, I would jump in the sequence of numbers having the form 6k+1, 6k+5, for k = 0, 1, 2, 3, ..., so that I only would analyze the odd numbers in the sequence:
5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, ...
This can be obtained by adding 2, then 4, then 2, then 4, then 2, then 4...
So, one can take the first pair, let's say 5 and 7.
We divide both of them by the odd numbers of the form 6k+1 and 6k+5 less than the square root of the greatest of them (sqrt(7)).
If the less number (in this case 5) would be divisible by some number, we pick the following number in the list, which is 11, and divide it by all the numbers that were used so far to test if 7 is prime or not. From this point, we follow by dividing together, 7 and 11, by the remaining numbers up to sqrt(11), and so on.
Note that, for big numbers, 6k+1 and 6k+5 have very similar square roots.
If the opposite case happens, that is, that for the pair (5, 7), the biggest element of the couple (in this case: 7) is divisible by some other number, then we discard both of them (5 and 7) and pick the following two elementos of the list (in this example would be 11 and 13). So, we start the search from scratch (that is, by dividing by small numbers).
finally, if the loop ends without finding divisors for any element of the couple (which is indeed the case for 6 and 7), then we can inform that this couple is of twin primes.
(Or well we can keep silent).
Then, we discard the smallest element (in this case: 5) and retain the biggest element (in this case: 7).
Since we already know that 7 is prime, we only pick the following element of the list above (in this case, 11), and search for divisors of it, only.
I think that the method I have explained will avoid to you a lot of redundant computations.
Besides, it's necessary to keep the latest updated couple of twin primes found. I assume that is not necessary that I explain to you how to do that.

Answer 2

We should procure that both of numbers are prime. Between difference is 2. As you know first twin prime is (3,5). I haven't found a formula what I expected. So, I've used iteration for solution. If you look through the code, you can understand.
#include <stdio.h>
#include <math.h>
int twinPrime(int m);
int IsPrime(unsigned int number);
int main()
{
double N;
int floored;
int prime;
printf("This program prints out all the possible twin primes"
"until a specific number which...\nyou can choose!");
printf("\nA note of caution: Although this program accepts decimals, "
"the value entered must be between 5 and 10^9,inclusive of the 2 numbers.");
printf("\nKey in -1 to exit.");
printf("\nEnter N value upto which twin primes ought to be calculated until: ");
scanf("%lf",&N);
while (N != -1)
{
if (N < 5 || N > pow(10,9))
{
printf("\nNumber not in the valid range was inputted. \n"
"Please reenter the value: ");
scanf("%lf",&N);
}
else
{
floored = floor(N);
prime = twinPrime(floored);
printf("The largest twin prime pair not above %d is (%d,%d)",floored,prime - 2,prime);
printf("\nPlease re-enter the value:");
scanf("%lf",&N);
}
}
printf("\nProgram successfully terminated.");
return 0;
}
int twinPrime(int m)
{
int p = 3;
int q = 5;
for (; q < m - 1; q += 2)
{
if (IsPrime(q))
{
if (q - p == 2)
{
continue;
}
p = q;
}
}
return q;
}
int IsPrime(unsigned int number)
{
if (number <= 1) return 0; // zero and one are not prime
if ((number > 2) && ((number % 2) == 0)) return 0; //no even number is prime number (bar 2)
unsigned int i;
for (i=2; i*i<=number; i++)
{
if (number % i == 0) return 0;
}
return 1;
}