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?
"""
import math
from itertools import permutations 


def all_primes(upper_bound):
  primes = [2]
  for i in range(3, upper_bound):
    j = 0
    while j < len(primes) and primes[j] <= int(i ** 0.5):
      if i % primes[j] == 0:
        break
      j += 1
    else:
      primes.append(i)
  return primes

def is_prime(x, primes):
  sqrt = int(x ** 0.5) + 1
  for prime in primes:
    if x % prime == 0:
      return False
    if prime == primes[-1]:
      return False
    if prime > sqrt:
      return True
  return True



def is_prime(num, pri):
  #for i in  primes:
  if num % 2 == 0:
    return False

  for i in range(3, math.ceil(math.sqrt(num))+ 1, 2):
    if num % i == 0:
      return False
  return True    


#primes =  [2]
p = permutations("1234567")
for i in list(p)[::-1]:
  x  = "".join(i)
  if is_prime(int(x)):
    print(x)
    break