Showing what's behind the curtain

The prime factorisation of binomial coefficients

Right triangles with integer coordinates

Finding Nim positions consisting of heap sizes n, 2n and 3n for n ≤ 2^{30} that result in a losing game.

Investigating a square digits number chain with a surprising property.

Investigating which primes will never divide a repunit containing 10**n digits.

Determining the first forty prime factors of a very large repunit.

Count how many numbers below a googol (10**100) are not “bouncy”

Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.

Find a set of five primes for which any two primes concatenate to produce another prime.

Common functions and helpful tools used to solve problems in Project Euler: Downloadable source: Euler.py source A set of routines used to help solve math problems. Euler.py is included as needed. The example below shows typical Python usage: from Euler import is_prime, is_perm Here is the contents of Euler.py from math import sqrt, ceil import […]