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Prime Ponderings

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 Puzzle ID: #19862 Fun: (2.71) Difficulty: (2.78) Category: Math Submitted By: snaps

What are the largest and smallest 5-digit numbers that satisfy the following conditions?

1. Each digit of the number is a prime digit.
2. Each successive pair of digits forms a 2-digit number that is NOT a prime number.
3. Each of the prime digits must appear at least once in the 5-digit number.

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 jimrcook Dec 16, 2004 Very nice one. I'd probably have solved it better if I hadn't misread criterion 3. I thought it said each must appear only once, and decided you must have counted 1 as a prime digit. There's no solution to that one. Sigh. Once I got over that, I saw the answer. (user deleted) Jan 02, 2005 Great puzzle. I enjoyed it. cloud_strife Jan 19, 2005 "Of that list, 33 is the only number that contains a 3 as the second digit and so for criterion 3 to be satisfied, 3 can only appear at the start of the 5-digit numbers" hey, i don't get this part of the answer.. can u explain it more clearly? thanks brianz May 11, 2005 Good one. Very fun. solidtanker Jun 24, 2005 Enjoyable. I love prime numbers, they are a great mystery! Sunrose Sep 11, 2005 I enjoyed this math teaser Good Job javaguru Jan 28, 2009 It was easier to list the numbers that can,t be formed (23, 37, 53, 73) than the ones that can. This made the requirement of starting with a 3 clear and the rest was easy. spikethru4 Feb 10, 2011 @jimrcook - I made the same mistake, but if you include 1 as a 'prime digit' the smallest is 32157 and the largest 35721. eddandi Feb 16, 2011 1 is a prime number and is not included in this. why? javaguru Mar 09, 2011 By definition, 1 is not a prime number.