## 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 sysimport mathclass 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 resultdef 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 100000There 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.