如何更快地找到第n个质数？

Question

I just started to learn how to program and I was trying to make a program to find the nth prime number. And I did it. But it takes a very long time for large number. Is there a way to make it faster? Here's the code I used(it's really basic):

def prime_finder(nth1):
   s = 1
   n = 0
   while n < nth1:
       s += 1
       for x in range(2,s):
          if s % x == 0:
             break
       else:
          n += 1

   return s

print prime_finder(31337)

Answer 1

You could speed it up by instead of iterating range(2,s) to find a factor, try range(2,int(math.sqrt(s))) If a number doesn't divide anything less than its square root, it must be prime.

Remember to import math

as well.