From: rgep@pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: generating primes and the special number 163
Date: 19 Feb 1996 11:43:58 GMT
In article <4g5qt3$koq@reader2.ix.netcom.com>,
inertia@ix.netcom.com(Maxon J Buscher ) writes:
|> The quadratic n^2 + n + 41 = p generates primes for n = 0 through
|> 39.
|> The discriminant of f(x) = x^2 + x + 41 is -163. And further:
|> e^(pi*sqrt(163)) = 262 537 412 640 768 744.000 000 000 000.
|> This is very close to being an integer and that is the reason the
|> above equation can generate primes. I don't understand why - I read
|> about it
|> in Mathematics -The New Golden Age (Keith Devlin, Pelican Books 1988).
I thoroughly recommend
Author: Cox, David A.
Title: Primes of the form x(2) + ny(2): Fermat, class field theory,
and complex multiplication/ David A. Cox
New York; Chichester: Wiley, c1989
xi,351 p; 25cm
Notes: "A Wiley-Interscience publication."
Subjects: Numbers, Prime
Richard Pinch; Queens' College, Cambridge
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From: ksbrown@ksbrown.seanet.com (Kevin Brown)
Newsgroups: sci.math
Subject: Re: generating primes and the special number 163
Date: Tue, 20 Feb 1996 02:03:36 GMT
[above post quoted, now deleted -- djr]
Another excellent book that discusses prime-producing quadratic
polynomials, class numbers of quadratic orders, and many other
interesting topics is
Quadratics
by Richard A. Mollin
CRC Press, 1996
ISBN: 0-8493-3983-9
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MathPages at --> http://www.seanet.com/~ksbrown/
===================================================================
==============================================================================
From: scv
Newsgroups: sci.math
Subject: Re: generating primes and the special number 163
Date: 19 Feb 1996 03:19:41 GMT
inertia@ix.netcom.com(Maxon J Buscher ) wrote:
> The quadratic n^2 + n + 41 = p generates primes for n =
>0 through 39.
>2) Can this equation be bettered? Has anyone tried it?
n^2 - 79x + 1601 gives primes for n = 0,1,...,79.
- scv (scott)