Primes on quadric irreducible polynomials

henryzz · 2012-10-06, 14:14

I saw this webpage http://109.90.219.147/devalco/basic_polynoms/ and thought that people might be interested in finding polynomials with higher prime density. He has found some rules on what makes a good poly. Can we find some more?

MattcAnderson · 2013-02-17, 03:12

One quadratic polynomial that merits consideration is
h(n) = n^2 + n + 41
It has the property that h(n) is prime for n=0..39.
Note that h(40) = 40(40 + 1) + 41.
Also, h(n) never has a factor smaller than 40 when n is an integer. I have a proof of this fact.
I put some more results on the web at
https://sites.google.com/site/mattc1anderson/home-1
I have some new results that I have not included on the internet.

Batalov · 2013-02-17, 05:27

This recent prime is relevant to your interest

2012-10-06, 14:14	#1
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 37·163 Posts	Primes on quadric irreducible polynomials I saw this webpage http://109.90.219.147/devalco/basic_polynoms/ and thought that people might be interested in finding polynomials with higher prime density. He has found some rules on what makes a good poly. Can we find some more?

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2013-02-17, 03:12	#2
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 4A8₁₆ Posts	One quadratic polynomial that merits consideration is h(n) = n^2 + n + 41 It has the property that h(n) is prime for n=0..39. Note that h(40) = 40(40 + 1) + 41. Also, h(n) never has a factor smaller than 40 when n is an integer. I have a proof of this fact. I put some more results on the web at https://sites.google.com/site/mattc1anderson/home-1 I have some new results that I have not included on the internet.

2013-02-17, 05:27	#3
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×7×479 Posts	This recent prime is relevant to your interest