--- In

primenumbers@yahoogroups.com,

Chroma <chromatella@...> wrote:

> Small supplement your results

> Pk -> n = 0..10^k

>

> {rank/P4,{a, P2, P4, P5, P6}}

> {1,{247757,71,5028,39759,324001}}

> {2,{595937,61,4978,39293,322141}}

....

> {16,{15102077,46,4631,38561,318251}}

Thanks, Marian. Note that what was in 16th place when

ranked by P4 is now in third place when ranked by P6.

Most of us believe (yet cannot prove) that the asymptotic density

is given by Conjecture F of "Partitio Numerorum, III"

by Hardy and Littlewood, in Acta Mathematica, December 1923,

Volume 44, Issue 1, pp 1-70.

Henri Cohen computed, for example

HL(x^2+x+41) = 3.319773177471421665323556857649887966468554585653...

It would be interesting to compute the constants

HL(x^2+x+a), for a = 247757, 595937, 15102077.

David