# Prime with digits reversed is prime?

Well, just another idea came up into my mind and i have no idea how to solve it :D Is there infinitely many prime numbers, which are not repunits and their inverse is also prime? (For example, inverse of 31 is 13 which is also prime. i didn't have any other name to describe the function!) P.S:I now know they are called Emirps.

• are reverse ordered prime numbers, e.g., $31\rightarrow 13$, which are still prime, are infinitely many? May 20, 2013 at 15:59
• Do you allow palindromic primes? It is conjectured, but not proven, that there are infinitely many repunit primes (eg 11). May 20, 2013 at 16:13
• look at en.wikipedia.org/wiki/Emirp May 20, 2013 at 16:41
• and for repunit I suggest en.wikipedia.org/wiki/Repunit May 20, 2013 at 16:51
• well i bet i should say that they are not repunits.
– CODE
May 20, 2013 at 17:19

$13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167,\dots$
P.S. Regarding terminology, given $x$, then its "multiplicative inverse" (or "reciprocal") is $1/x$. For functions, for ex, given $\sin(x)$, then its "inverse function" is $\arcsin(x)$.
• Confusingly, in French it's the other way around; the "réciproque" of $\sin(x)$ is $\arcsin(x)$, and "l'invers" of $\sin(x)$ is $\csc(x)$. May 20, 2013 at 17:53