[seqfan] Re: A139414

[David Wilson]

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?