# [seqfan] Re: A139414

Harry J. Smith hjsmithh at sbcglobal.net
Fri Jan 30 01:30:52 CET 2009

```Yes to question one:

A005846  Primes of form n^2 + n + 41.

41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281,
313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601, 1847, 1933, 2111,
2203, 2297, 2393, 2591, 2693, 2797 (list; graph; listen)

But the offset is listed as 1,1. It should be 0,1.

It has a link to a b-file, but the link is broken. So only 49 primes are
given in the list.

-Harry

> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On
> Behalf Of David Wilson
> Sent: Thursday, January 29, 2009 4:15 PM
> To: Sequence Fanatics
> Subject: [seqfan] Re: A139414
>
> Harry J. Smith wrote:
> > Neil:
> >
> > The process of generating primes using polynomials have been in the
> > mathematics literature since Euler.
> >
> > Here are some notes from http://math453fall2008.wikidot.com/lecture-2
> >
> > Generating Primes Through Polynomials
> > We asked earlier if there was any formula we could use to generate prime
> > numbers, something which would make discovering new prime numbers as
simple
> > as plug-and-chug.
> >
> > A long time ago the amazing mathematician Leonard Euler showed that the
> > polynomial
> >
> > 	n^2  + n + 41         (6)
> >
> > generates distinct prime values for all integral inputs between 0 and
39.
> > This was an amazing discovery, and even today the record for producing
> > consecutive primes by a polynomial sits at just 57 (in 2005, the record
was
> > just 43!). So one might ask: is there a polynomial out there which only
> > takes prime values? Sadly, the answer is know. However..
> >
> Now here we go.
>
> Do we have those 57 primes in the OEIS?
>
> And what's the current record for primes in AP, and do we have those?
>
>
>
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```