- View Source--- In primenumbers@yahoogroups.com,

"bhelmes_1" <bhelmes@...> wrote:

> the distribution of primes

Since 1923, we have a had a very precise

> concerning the polynom f(x)=x^2+1

conjecture for the asymptotic density

of primes of the form x^2+1. See Shanks' review

http://www.ams.org/journals/mcom/1960-14-072/S0025-5718-1960-0120203-6/S0025-5718-1960-0120203-6.pdf

of the classic paper by G.H. Hardy and J.E. Littlewood:

"Some problems of 'Partitio numerorum'; III",

Acta Math. 44 (1923) pages 170.

The relevant Hardy-Littlewood constant,

1.3728134... is given, to 9 significant figures,

in Eq(3) of Shanks' paper.

More digits are easily obtainable from the methods in

"High precision computation of Hardy-Littlewood constants"

by Henri Cohen, available as a .dvi file from

http://www.math.u-bordeaux1.fr/~hecohen/

David