Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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
up vote 8 down vote accepted

These are tabulated at the Online Encyclopedia of Integer Sequences. It appears to be known that there are infinitely many, and a link is given to a recent paper of Harman. Some high-powered math is involved.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.