# 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?
# Digit sum trick! number is divisible by 3 if and only if the digit sum of the number is divisible by 3
# simplifies problem to either 4 digit or 7 digit prime
# generate all primes beneath 7654321
# generate all possible 7 digit pandigital combinations
# largest 4 digit prime is 4231
from eulerhelpers import genprimes, isPandigital
from itertools import permutations
if __name__ == "__main__":
primes = genprimes(7654321)
x = 7654321
while True:
if isPandigital(x) and x in primes:
print x
break
x -= 1
if x <= 1000000:
break
from eulerhelpers import isPandigital #not as simple as saying 987654321 because n has to be greater than 1 #at n=2, it has to be 5 digit and 4 digit number #seed must be 5000 or below largest_pan = 123456789 for seed in range(9,10000): mult = 1 testpan = '' while len(testpan) < 9: testpan += str(seed*mult) if len(testpan) >= 9: if isPandigital(int(testpan)) and int(testpan) > largest_pan: largest_pan = int(testpan) mult+=1 print "largest pandigital is", largest_pan
