Python/project_euler/problem_041/sol1.py
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"""
Pandigital prime
Problem 41: https://projecteuler.net/problem=41
We shall say that an n-digit number is pandigital if it makes use of all the digits
1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
So we will check only 7 digit pandigital numbers to obtain the largest possible
pandigital prime.
"""
from __future__ import annotations
import math
from itertools import permutations
def is_prime(number: int) -> bool:
"""Checks to see if a number is a prime in O(sqrt(n)).
A number is prime if it has exactly two factors: 1 and itself.
>>> is_prime(0)
False
>>> is_prime(1)
False
>>> is_prime(2)
True
>>> is_prime(3)
True
>>> is_prime(27)
False
>>> is_prime(87)
False
>>> is_prime(563)
True
>>> is_prime(2999)
True
>>> is_prime(67483)
False
"""
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True
def solution(n: int = 7) -> int:
"""
Returns the maximum pandigital prime number of length n.
If there are none, then it will return 0.
>>> solution(2)
0
>>> solution(4)
4231
>>> solution(7)
7652413
"""
pandigital_str = "".join(str(i) for i in range(1, n + 1))
perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
pandigitals = [num for num in perm_list if is_prime(num)]
return max(pandigitals) if pandigitals else 0
if __name__ == "__main__":
print(f"{solution() = }")