[seqfan] Re: A139414
Harry J. Smith
hjsmithh at sbcglobal.net
Thu Jan 29 23:57:14 CET 2009
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
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..
I think the 4 polynomials in sequence A139414 are unique in how many primes
they generate Sequence A155814 is just a nice companion.
p1(n) =4*x^2 - 146*x + 1373,
p2(n)= 4*x^2 - 144*x + 1459,
p3(n)= 4*x^2 - 142*x + 1301,
p4(n)= 4*x^2 - 140*x + 1877.
I know you cannot please everybody, but I will miss the sequence on
Have you seen A090101 Numbers n such that n and the 6 successive integers
if substituted for x in polynomial 5x^2+5x+1.
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
> Behalf Of N. J. A. Sloane
> Sent: Thursday, January 29, 2009 1:31 PM
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] Re: A139414
> I agree with those comments! A139414 and its child
> A155814 are too artificial and will be deleted
> Seqfan Mailing list - http://list.seqfan.eu/
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