Here's a possibly interesting prime puzzle. Call a prime $p$ flirtatious if the sum of its digits is also prime. Are there finitely many flirtatious primes, or infinitely many?
Flirtatious Primes
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elementary-number-theory
prime-numbers
puzzle
recreational-mathematics
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5I'm interested in seeing whether or not it depends on the base. It's clearly infinite for unary. :P – 2012-06-28
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8Mersenne primes are flirtatious in binary. – 2012-06-28
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0Down-voted because answer can easily be found by calculating a few terms and searching OEIS. See Gerry Myerson answer below. – 2012-06-28
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3@FredDanielKline: Not everyone knows about OEIS (yet). Asking a question like this one is a way to find out about it. – 2012-06-28
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2@FredDanielKline This is also a nice way for other members of the forum, such as myself, to come across an interesting problem they might otherwise not have heard about. – 2012-07-09