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

Rick Shepherd rlshepherd2 at gmail.com
Thu Dec 17 22:00:58 CET 2009

```Anyone who updates A089727, please also add a cross-reference to "A171751
(corresponding k)",
which I'll be submitting within the hour.  Also, of course it proves nothing
but I can state
that Michael Porter's PARI program does terminate as-is while calculating at
least the first 20000000
terms of A089727.  If I understand the preceding conversation correctly,
although it's a reasonable
conjecture (assuming GRH) that A089727(n) exists for all n as stated,
shouldn't "(or 0 if no such
prime exists)" be added (for now) to ensure its being well-defined?

[A089726, the sister-sequence that I believe Rainer Rosenthal intended
below, doesn't have this
potential non-well-defined problem (by Dirichlet's Theorem).]

An aside:  Older versions of PARI seem not to like the opening bracket in
A089727(n) = {local(k);k=n;while(!isprime(n*k+1),k--);n*k+1}
after the first "=", but (at least some versions) have no trouble with
{A089727(n) = local(k);k=n;while(!isprime(n*k+1),k--);n*k+1}, which is
why I post PARI programs like this.  Please let me know ASAP if
newer PARI versions require the first syntax.

Thanks and regards,
Rick

On Thu, Dec 17, 2009 at 3:29 PM, Rainer Rosenthal <r.rosenthal at web.de>wrote:

> Jonathan Post schrieb:
> > Xylouris, updating Heath-Brown's result on Linnik's constant, proved
> > in 2009 that prime(k) << k^5.2.
>
> Thanks a lot. Wouldn't it be nice to have some points of this discussion
> mentioned as
> a comment for this nice sequence
> http://www.research.att.com/~njas/sequences/A089727 ?
> And how about some theory for its sister-sequence A089727?
>
> Best regards,
> Rainer Rosenthal
> r.rosenthal at web.de
>
>
>
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>

```