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Pandigital prime sets

Problem 118

Published on Friday, 24th March 2006, 06:00 pm; Solved by 4267; Difficulty rating: 45%

Using all of the digits 1 through 9 and concatenating them freely to form decimal integers, different sets can be formed. Interestingly with the set {2,5,47,89,631}, all of the elements belonging to it are prime.

How many distinct sets containing each of the digits one through nine exactly once contain only prime elements?