# Prime numbers like 113

The number 113 is prime. The sum, product and all permutations of it's digits are prime. Are there any other such prime numbers?

• $2,3,5,7, 11$ for example :) – Amateur Apr 6 '14 at 22:52
• $131$ and $311$ are obvious examples – Henry Apr 6 '14 at 22:57
• If there are more examples, they consist of an even number of the digit '1', plus exactly one '3' or '7'. As the number of digits gets larger, the chances that all of the permutations are prime decreases, but I don't have a proof right now that more of your 'special' primes don't exist. – user7530 Apr 6 '14 at 23:04

• $31111$, $311111111$, $13111111111$, $71111$, $7111111$ and $71111111111$ are not prime but this hardly proves the case for longer possibilities – Henry Apr 7 '14 at 7:26