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A library of number theory related functions inspired by Project Euler.

Project Description

eulerlib is a library of recreational mathematics and number theory related functions inspired by Project Euler. Available functions include:

  • Prime number generation
  • Divisor functions (sigma functions)
  • Euler’s totient function
  • Greatest Common Divisor (GCD) using Euclid’s algorithm
  • Least Common Multiple (LCM)
  • Integer square root
  • Fibonacci numbers
  • Pandigital numbers
  • Palindrome numbers
  • Pythagorean triples

Functions from this library can be used to solve recreational mathematics and programming problems such as problems in Project Euler.


eulerlib is avalaible through Python Package Index (PyPI) using pip.

>>> pip install --upgrade eulerlib

To uninstall using pip.

>>> pip uninstall eulerlib


In Python console you can import functions/classes from eulerlib as needed.

>>> from eulerlib import primes
>>> p10 = primes(10)
>>> print(p10)
[2, 3, 5, 7]

The Divisors class implements functions related to prime factorization, sigma functions etc.

>>> from eulerlib import Divisors
>>> mydiv = Divisors(10000)
>>> div84 = mydiv.divisors(84) #divisors of 84
>>> print(div84)
[1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84]
>>> pf840 = mydiv.prime_factors(840) # prime factors of 840
>>> print(pf840)
[(2, 3), (3, 1), (5, 1), (7, 1)]

Example: Solved Project Euler problem 3.

from eulerlib import is_square, primes
#get approximate square root of number since
#largest prime factor < sq. root
(is_sq, sqroot) = is_square(600851475143L)
#get a list of primes less than the approx. square root.
test_primes = primes(sqroot + 1L)
#test the primes from the list to find the largest factor
len_p = len(test_primes)
for i in range(1,len_p+1):
    j = 0 - i
    test_fact = test_primes[j]
    if 600851475143L%test_fact == 0:
answer = test_fact #Set the answer

See complete documentation.

Modules Functions to generate lists of primes.
  • Euler’s divisor functions (sigma funtions)
  • Euler’s totient function (phi function)
  • Prime factors of a number
  • Divisors of a number
  • Greatest Common Divisor (GCD)
  • Least Common Multiple (LCM)
  • Digital root and digital sum of a number Functions related to the Fibonacci sequence. Functions related to Pythagorean triples.

Miscellaneous functions:

  • Pandigital numbers
  • Conversion from decimal to base n (2-36)
  • Number to lists and vice versa
  • Palindrome numbers


Source code repositories (GitHub, BitBucket) are available. Bug reports and suggestions are most welcome.


eulerlib is licensed under Apache License 2.0.

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