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Old 2012-10-06, 14:14   #1
Just call me Henry
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Sep 2007
Cambridge (GMT/BST)

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Default Primes on quadric irreducible polynomials

I saw this webpage 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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Old 2013-02-17, 03:12   #2
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"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
I have some new results that I have not included on the internet.
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Old 2013-02-17, 05:27   #3
Batalov's Avatar
Mar 2008

100011110010002 Posts

This recent prime is relevant to your interest
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