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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?

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  • $\begingroup$ $113,137,173$ 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
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$$ 233, 257, 2377, 23327,\ldots. $$

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