sol1.py

"""
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.
"""

from __future__ importannotations

fromcollectionsimportCounter


defprime_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]
 """
is_prime= [True] *n
is_prime[0] =False
is_prime[1] =False
is_prime[2] =True

foriinrange(3, int(n**0.5+1), 2):
index=i*2
whileindex<n:
is_prime[index] =False
index=index+i

primes= [2]

foriinrange(3, n, 2):
ifis_prime[i]:
primes.append(i)

returnprimes


defdigit_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]]
 """
number_str=str(number)
replacements= []
digits= ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"]

forduplicateinCounter(number_str) -Counter(set(number_str)):
family= [int(number_str.replace(duplicate, digit)) fordigitindigits]
replacements.append(family)

returnreplacements


defsolution(family_length: int=8) ->int:
"""
 Returns the solution of the problem

 >>> solution(2)
 229399

 >>> solution(3)
 221311
 """
numbers_checked=set()

# Filter primes with less than 3 replaceable digits
primes= {
xforxinset(prime_sieve(1_000_000)) iflen(str(x)) -len(set(str(x))) >=3
 }

forprimeinprimes:
ifprimeinnumbers_checked:
continue

replacements=digit_replacements(prime)

forfamilyinreplacements:
numbers_checked.update(family)
primes_in_family=primes.intersection(family)

iflen(primes_in_family) !=family_length:
continue

returnmin(primes_in_family)

return-1


if__name__=="__main__":
print(solution())