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

===================================================================
MathPages at  -->  http://www.seanet.com/~ksbrown/
===================================================================

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From: scv <scv2@aol.com>
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)