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'