Problem41.py

"""
@author: mc-es

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?

Answer: 7652413
"""

from itertools import permutations
import math


def isPrime(n):
 if n <= 1:
 return False
 if n == 2:
 return True
 if n % 2 == 0:
 return False
 for i in range(3, int(math.sqrt(n)) + 1, 2):
 if n % i == 0:
 return False
 return True


def largestPandigitalPrime():
 for n in range(9, 0, -1):
 digits = "".join(str(i) for i in range(1, n + 1))
 pandigitalNumbers = sorted(
 ["".join(p) for p in permutations(digits)], reverse=True
 )
 for numStr in pandigitalNumbers:
 num = int(numStr)
 if isPrime(num):
 return num
 return None


print(largestPandigitalPrime())