project_euler.problem_051.sol1

https://projecteuler.net/problem=51 Prime digit replacements Problem 51

By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.

By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.

Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.

Functions

digit_replacements(→ list[list[int]])	Returns all the possible families of digit replacements in a number which
prime_sieve(→ list[int])	Sieve of Erotosthenes
solution(→ int)	Returns the solution of the problem

Module Contents

project_euler.problem_051.sol1.digit_replacements(number: int) → list[list[int]]

Returns all the possible families of digit replacements in a number which contains at least one repeating digit

>>> digit_replacements(544)
[[500, 511, 522, 533, 544, 555, 566, 577, 588, 599]]

>>> digit_replacements(3112)
[[3002, 3112, 3222, 3332, 3442, 3552, 3662, 3772, 3882, 3992]]

project_euler.problem_051.sol1.prime_sieve(n: int) → list[int]

Sieve of Erotosthenes Function to return all the prime numbers up to a certain number https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

>>> prime_sieve(3)
[2]

>>> prime_sieve(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]

project_euler.problem_051.sol1.solution(family_length: int = 8) → int

Returns the solution of the problem

>>> solution(2)
229399

>>> solution(3)
221311