What is the least number $n$, such that $n^{2015}+2015$ is prime ?

According to my calculations, there is no prime for $n\le 6000$.

It is clear, that $n$ must be even, since $n^{2015}+2015$ must be odd.


The first one seems to be $n=9462$ (according to Mathematica), i.e. $$ 9462^{2015}+2015 $$ is prime. I have no good mathematical arguments for this, though.

The code I used to get this was:

 While[Not[PrimeQ[n^2015 + 2015]], Print[n]; n = n + 2]

It stoped at 9460. Just to be sure, I ran


and the response was True.

  • $\begingroup$ I trust mathematica. Thank you very much. $\endgroup$ – Peter Jan 3 '15 at 17:47
  • $\begingroup$ PARI/GP is very slow indeed. I am currently at $n=7398$. $\endgroup$ – Peter Jan 3 '15 at 17:49
  • $\begingroup$ Does primeq prove a number to be prime ? $\endgroup$ – Peter Jan 3 '15 at 17:50
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    $\begingroup$ Thank you for selecting the answer, I'm happy for it. I'm not sure it should be selected, though. What if someone comes up with a mathematical argument? $\endgroup$ – mickep Jan 3 '15 at 17:51
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    $\begingroup$ This chance is very, very low! Very little is known about the structure of such big primes! $\endgroup$ – Peter Jan 3 '15 at 17:52

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