# Flirtatious Primes

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?

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I'm interested in seeing whether or not it depends on the base. It's clearly infinite for unary. :P –  tskuzzy Jun 28 '12 at 5:50
Mersenne primes are flirtatious in binary. –  Blue Jun 28 '12 at 6:02
Down-voted because answer can easily be found by calculating a few terms and searching OEIS. See Gerry Myerson answer below. –  Fred Kline Jun 28 '12 at 8:46
@FredDanielKline: Not everyone knows about OEIS (yet). Asking a question like this one is a way to find out about it. –  Blue Jun 28 '12 at 8:52
@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. –  user12014 Jul 9 '12 at 5:01