{"id":26,"date":"2013-08-13T19:35:00","date_gmt":"2013-08-13T19:35:00","guid":{"rendered":"https:\/\/www.root42.de\/blog\/?p=26"},"modified":"2013-08-13T19:35:00","modified_gmt":"2013-08-13T19:35:00","slug":"there-are-approximately-nlnn-primes-between-n-and-2n","status":"publish","type":"post","link":"https:\/\/www.root42.de\/blog\/?p=26","title":{"rendered":"There are approximately N\/ln(N) primes between N and 2N"},"content":{"rendered":"

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


#!\/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()
<\/pre>\n
 And it seems to work, but check WolframAlpha<\/a> if you don’t trust me \ud83d\ude42  <\/p>\n

$ .\/myprimes.py 100000
There are 8392 primes between 100000 and 200000: 100003, 100019, 100043 ...
<\/pre>\n","protected":false},"excerpt":{"rendered":"
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, … Continue reading “There are approximately N\/ln(N) primes between N and 2N”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[7,26,15],"tags":[],"_links":{"self":[{"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=\/wp\/v2\/posts\/26"}],"collection":[{"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26"}],"version-history":[{"count":0,"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=\/wp\/v2\/posts\/26\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.root42.de\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}