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 :)

$ ./myprimes.py 100000
There are 8392 primes between 100000 and 200000: 100003, 100019, 100043 ...