primelib

[christianbender]

This python library contains some useful functions to deal with
prime numbers and whole numbers. The ideas came by the problems sets from ProjectEuler.

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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'

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greatestPrimeFactor (number)

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

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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.

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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'