[seqfan] Re: Primes of the form kn+1

Robert Gerbicz robert.gerbicz at gmail.com
Thu Dec 17 19:00:07 CET 2009


2009/12/17 Michael Porter <ic_designer at verizon.net>

> Is it true that for every positive integer n, there is a prime of the form
> kn+1 with 1<=k<=n?
>
> I submitted the following PARI program for sequence A089727:
> A089727(n) = {local(k);k=n;while(!isprime(n*k+1),k--);n*k+1}
> and then I started wondering if the while loop would always terminate.
>
> Thanks,
> Michael
>
>
>
>
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>

That's very probably because the expected smallest k for which k*n+1 is
prime (in average) is about eulerphi(n)*log(n)/n.



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