20121006, 14:14  #1 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
13167_{8} 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?

20130217, 03:12  #2 
"Matthew Anderson"
Dec 2010
Oregon, USA
7×89 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/home1 I have some new results that I have not included on the internet. 
20130217, 05:27  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10001111001000_{2} Posts 
This recent prime is relevant to your interest

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