Re: small Collection of Primes
- --- In firstname.lastname@example.org,
"bhelmes_1" <bhelmes@...> wrote:
> the distribution of primesSince 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
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