This python library contains some useful functions to deal with prime numbers and whole numbers.

The file primelib.py or primliby.pyc will simply import by the import-statement. Important primelib.py or primelib.pyc must been in your project directory.

Example: (In your project)

import primelib

print primelib.isPrime(13)   # will print out 'True'
print primelib.primeFactorization(40)  # will print out [2,2,2,5]

OR

from primelib import *

print isPrime(...) 

More information about the functions.

help(function_name)

For example:

help(isPrime)

Overview about functions:

isPrime (number)

input: positive integer 'number' returns true if 'number' is prime otherwise false.

sieveEr (N)

input: positive integer 'N' > 2 returns a list of prime numbers from 2 up to N.

This function implements the algorithm called sieve of erathostenes.

getPrimeNumbers (N)

input: positive integer 'N' > 2 returns a list of prime numbers from 2 up to N (inclusive) This function is more efficient as function sieveEr(...)

primeFactorization (number)

input: positive integer 'number' returns a list of the prime number factors of 'number'

greatestPrimeFactor (number)

input: integer 'number' >= 0 returns the greatest prime number factor of 'number'

smallestPrimeFactor (number)

input: integer 'number' >= 0 returns the smallest prime number factor of 'number'

getPrime (n)

Gets the n-th prime-number.

input: positive integer 'n' >= 0 returns the n-th prime number, beginning at index 0

getPrimesBetween (pNumber1, pNumber2)

input: prime numbers 'pNumber1' and 'pNumber2' precondition: pNumber1 < pNumber2 returns a list of all prime numbers between 'pNumber1' (exclusiv) and 'pNumber2' (exclusiv)

isEven (number)

input: integer 'number' returns true if 'number' is even, otherwise false.

isOdd (number)

input: integer 'number' returns true if 'number' is odd, otherwise false.

gcd (number1, number2)

Greatest common divisor

input: two positive integer 'number1' and 'number2' returns the greatest common divisor of 'number1' and 'number2'

kgV (number1, number2)

Least common multiple

input: two positive integer 'number1' and 'number2' returns the least common multiple of 'number1' and 'number2'

getDivisors (number)

input: positive integer 'n' >= 1 returns all divisors of n (inclusive 1 and 'number')

isPerfectNumber (number)

input: positive integer 'number' > 1 returns true if 'number' is a perfect number otherwise false.

simplifyFraction (numerator, denominator)

input: two integer 'numerator' and 'denominator' assumes: 'denominator' != 0 returns: a tuple with simplify numerator and denominator.

factorial (n)

input: positive integer 'n' returns the factorial of 'n' (n!)

fib (n)

input: positive integer 'n' returns the n-th fibonacci term , indexing by 0

goldbach(number)

Goldbach's assumption

input: a even positive integer 'number' > 2 returns a list of two prime numbers whose sum is equal to 'number'