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

franktaw at netscape.net franktaw at netscape.net
Thu Dec 17 22:21:46 CET 2009

Well, it should always terminate.  Unfortunately, PARI returns 0 for 
isprime(-p), where p is a positive prime (at least in my version), so 
there is no guarantee.

Franklin T. Adams-Watters

-----Original Message-----
From: 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.


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