Just saw this very nice video by @numberphile, and thought I whip up a small Python program to demonstrate the prime number theorem:

#!/usr/bin/env python

#

# "Chebyshev said it, and I say it again: There's always a prime between n and 2n."

#

import sys

import math

class PrimeFinder:

def __init__( self, n ):

self.n = n

def isNPrime( self, N ):

for x in range( 2, int( math.sqrt( N ) ) + 1 ):

if N % x == 0:

return False

return True

def computeAllPrimesBetweenNAndTwoN( self ):

result = []

for N in range( self.n, 2 * self.n + 1 ):

if self.isNPrime( N ):

result = result + [ N ]

return result

def main():

if len( sys.argv ) != 2:

print "Prints all prime numbers between N and 2N"

print "Usage: %s N" % sys.argv[ 0 ]

print "Where N is some positive, natural number."

sys.exit( 0 )

N = int( sys.argv[ 1 ] )

primeFinder = PrimeFinder( N )

allPrimes = primeFinder.computeAllPrimesBetweenNAndTwoN()

print "There are %u primes between %u and %u: %s" % (

len( allPrimes ), N, 2 * N, str( allPrimes )[ 1 : -1 ]

)

if __name__ == "__main__":

main()

And it seems to work, but check WolframAlpha if you don’t trust me đŸ™‚

$ ./myprimes.py 100000

There are 8392 primes between 100000 and 200000: 100003, 100019, 100043 ...