Finding the nth prime number using Python

Question

When I run this code, even for just counting to the 10th prime number (instead of 1000) I get a skewed/jacked output--all \"not prime\" titles for my is_composite variable,

Answer 1

This code below generates a list of primes upto 1 million. Using that list, you can test for primes < 1 Trillion in a reasonably fast way. This runs in a pretty fast time for 10-12 digit primes.

import math
from itertools import islice
# number of primes below the square root of x
# works well when x is large (x > 20 and much larger)
numchecks = lambda x: int((math.sqrt(x))/(math.log(math.sqrt(x)) - 1.084)) + 1

primes = [2,3,5]
primes = primes + [x for x in range(7, 48, 2) if all((x%y for y in islice( primes, 1, int(math.sqrt(x)) )))]
primes = primes + [x for x in range(49, 2400, 2) if all((x%y for y in islice( primes, 1, numchecks(x) )))]
primes = primes + [x for x in range(2401, 1000000, 2) if all((x%y for y in islice( primes, 1, numchecks(x) )))]

You can increase the number of saved primes by extending the process above, but the program will take a long time (but one time only process).

In your code, you can test if 'test_num' is prime using the following...

test_num = 23527631
if test_num<100:
    checks = int(math.sqrt(test_num))
else:
    checks = numchecks(test_num)

isPrime = all(test_num%x for x in islice(primes, 0, checks))
print 'The number is', 'prime' if isPrime else 'not prime'
print 'Tested in', checks, 'divisions'