Puzzle: doubly truncatable primes


Puzzle: doubly truncatable primes

Tom Marlow, from Saffron Walden in Essex, has been looking at the obscure subject of doubly truncatable primes. For example, taking the prime 1373 (and allowing 1 to be classed as a prime number) he finds that successively curtailing it first from the left and then from the right, produces the series 373 73 3, 137 13 and 1.

These six extra numbers are all prime, so Tom has designated 1373 as a seven-fold prime. Strangely enough, if these four digits are rearranged to give firstly 3137, and secondly 7331, then in both cases double truncation provides a series of primes. So these two new numbers are also seven-fold in character. These three four-digit primes seem to be the only ones of their size that have this property.

All this leads to Mr Marlow asking: "Which is the only five-digit prime that is double truncatable, ie to provide a nine-fold property?"

Click here for the solution

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This was first published in June 2008


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