A twice prime number is defined as a prime number whose digits are also prime. For example: $23$ is prime. It is made up of the digit $2$, which is prime, and the digit $3$, which is also prime. Therefore, $23$ is twice prime. Counter example: $19$ is prime, but $1$ nor $9$ is prime and therefore $19$ is not twice prime.

Does twice prime only consist of two prime digits? Or can we have a three digit prime which can qualify as twice prime?

  • $\begingroup$ $113,137,173$ are some of them $\endgroup$ – user35508 Jun 25 '17 at 13:35
  • $\begingroup$ Next questions: are there infinitely many twice primes? And also, does this concept already exist under a different guise? Finally, I feel uncomfortable that this is a concept rooted in our decimal number system. $\endgroup$ – Colm Bhandal Jun 25 '17 at 13:37
  • $\begingroup$ @user35508 $1$ is not considered a prime number- I believe that's what is alluded to above. $\endgroup$ – Colm Bhandal Jun 25 '17 at 13:38
  • $\begingroup$ @ColmBhandal ... It is also made up like $11$ and $3$ $\endgroup$ – user35508 Jun 25 '17 at 13:39
  • $\begingroup$ @user35508 Very good point. But my interpretation of the OPs question is that "digit" means single decimal digit. We must await clarification from the OP...? $\endgroup$ – Colm Bhandal Jun 25 '17 at 13:40

$$ 233, 257, 2377, 23327,\ldots. $$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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