python - Segmentation fault in Prime Number generator -

i aware following isn't fastest way of generating list of primes posed myself problem , before googling wrote following program. works fine numbers < ~ 44,000 gives segmentation fault when ran on 2ghz core 2 duo macbook. not interested in alternative methods @ moment in why giving me seg fault.

the last prime able calculate 42751 before dies saying 'segmentation fault'.

from sys import argv, exit, setrecursionlimit  def isprime(no, halfno, x = 3):    # if counted through , numbers 3 x not factors prime   if x > halfno:     print no     return 1    # x factor?   if no % x == 0:     return 0   else:     isprime(no, halfno, x + 2)  path, limlow, limhigh = argv  limlow = int(limlow) limhigh = int(limhigh)  setrecursionlimit(limhigh)  # negitive numbers, 0 , 1 not primes answer invalid if limlow < 2:   exit('invalid input');  # if lower limit not prime increase 1 if limlow % 2 == 0:   limlow += 1  while (limlow <= limhigh):   isprime(limlow, limlow / 2)   limlow += 2 

you might getting stack overflow many recusive calls on stack. @ 42751 have 21375 depth function call stack. in such case, refining method might needed.

a handy little routine check primeness can written (pseudocode):

if n < 2 return false; if n == 2 or n == 3 return true; if n % 2 == 0 return false; if n % 3 == 0 return false; (i = 6; < sqrt(n); += 6) {   if (n % (i - 1) == 0) return false;   if (n % (i + 1) == 0) return false; } return true; 

this method works because of following:

1. if n less 2, can't prime
2. if n 2 or 3 must prime
3. if n not 2 or 3 divisible either, not prime
4. all prime numbers aside 2 , 3 can written in form 6k+1 or 6k-1. if number prime, not evenly divisible other prime number. need check until square root of n because more not divide evenly n.