#!/usr/bin/env python3

'''

Pandigital prime

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?

'''

from prime import primes

PANDIGITAL_SETS = {n: frozenset(str(i) for i in range(1, n + 1))

for n in range(1, 10)}

def is_pandigital(num):

string = str(num)

return set(string) == PANDIGITAL_SETS[len(string)]

# The largest possible pandigital number is 987,654,321. However no nine-digit

# pandigital number is prime, as the sum of the digits 1-9 is 45, so all such

# numbers can be divided by 9. The same applies to eight-digit pandigital

# numbers.

#

# So a sketch design presents itself: generate primes up to 7,654,321, then

# return the largest of these that is also pandigital.

if __name__ == '__main__':

print(next(prime for prime in reversed(list(primes.range(7654321)))

if is_pandigital(prime)))