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 ============================================================================== 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/ =================================================================== ============================================================================== 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)