[seqfan] Re: A139414
dwilson at gambitcomm.com
Fri Jan 30 01:14:36 CET 2009
Harry J. Smith wrote:
> 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
> 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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