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Pandigital prime

Problem 41 Published on Friday, 11th April 2003, 06:00 pm; Solved by 58477;
Difficulty rating: 5%

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?