Goldbach\'s Conjecture I am being asked to take two user input limits and print

Question

Goldbach's Conjecture

I am being asked to take two user input limits and print out the prime numbers that sum to that number.

Example:

Enter lower limit: 4

Enter upper limit: 12

(4 = 2 + 2), (6 = 3 + 3), (8 = 3 + 5), (10 = 3 + 7 = 5 + 5), (12 = 5 + 7)

The maximum number of pairs = 2

My code works except that it considers 15 as a prime number and thus throws off my max pairs.

Can I get a fix on it?

Code:

def is_prime(n):
limit = int (n ** 0.5) + 1
div = 2
while (div < limit):
if (n % div == 0):
return False
div = div + 1
return True

def main():

#Input limits
low = eval (input("Enter lower limit: "))
  
high = eval (input("Enter upper limit: "))

#Check limits

while (low % 2 != 0) or (low < 4) or (high % 2 != 0) or (low > high):
low = eval (input("Enter lower limit: "))
  
high = eval (input("Enter upper limit: "))

num = low
maxpairs = 0
#Print pairs

for i in range (num, high + 2, 2):
x = 2
half = i / 2
pairs = 0
print (i, end = " ")
while (x <= half):
if (is_prime (x)):
x = x   
y = i - x   
if (is_prime (y)):
pairs += 1
print ("=", x, "+", y, end = " ")
if (maxpairs < pairs):
maxpairs = pairs
x = x + 1

print ()

  
print ("The maximum number of pairs = ", maxpairs)
  
main()

Explanation / Answer

#include<stdio.h>

#include<math.h>

int primecheck(long int x);

main()

{

  long int a,b,c;

  int i,j,k;

  label: printf("Enter the number: ");

  scanf("%ld",&a);

  if ((a%2)==1)

  {

    printf(" That's an odd number you dumbo! Goldbach's Conjecture involves an even number! ");

    goto label;

  }

  for (b=2;b<a;++b)

  {

    for (c=2;c<a;++c)

    {

     j=primecheck(b),k=primecheck(c);

     if ((j==0) && (k==0) && (b+c==a) && (b<=c))

     printf(" %4ld + %4ld = %4ld",b,c,a);

  }

  }

  printf(" ");

}

int primecheck(long int x)

{

long int i=2;

while (i<x)

{

if ((x%i)==0)

break;

++i;

}

if (i==x)

return(0);

else

return(1);

}

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