Free open-source library from Christian Bender

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)

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Overview about functions:

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isPrime (number)

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

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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. 

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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(...)


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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'

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getPrime (n)

Gets the n-th prime-number. 

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

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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) 

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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.

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gcd (number1, number2)

Greatest common divisor

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

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kgV (number1, number2)

Least common multiple

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

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NEW-FUNCTION

getDivisors (number)

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

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NEW-FUNCTIONS

isPerfectNumber (number)

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

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NEW-FUNCTION

simplifyFraction (numerator, denominator)

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

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NEW-FUNCTION

factorial (n)

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


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NEW-FUNCTION

fib (n)

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


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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'