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.

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

1 Answer 1


Actually, it has a name and it's quaintly called an "emirp". (The word "prime" in reverse.) The link given is to the Online Encyclopaedia of Integers' list,

$13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167,\dots$

While there are an infinite number of primes, I believe it is an open problem if there is an infinite number of emirps.

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 $\arcsin(x)$.

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    $\begingroup$ Confusingly, in French it's the other way around; the "réciproque" of $\sin(x)$ is $\arcsin(x)$, and "l'invers" of $\sin(x)$ is $\csc(x)$. $\endgroup$
    – Lee Sleek
    May 20, 2013 at 17:53
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    $\begingroup$ Ah, some things get lost in translation, do they? :) $\endgroup$ May 20, 2013 at 17:56

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