There are approximately N/ln(N) primes between N and 2N

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 ...

How to read input from a bunch of commands in bash

You can use the <( … ) subshell syntax to read from a bunch of commands, that you whip up on the fly:

cat < <( echo "foo"; sleep 2; echo "bar" )

You can use this for example for accessing IMAP servers, which need a short delay during login.