In an email dated Mon, 28 11 2005 2:19:43 pm GMT, "newjack56" <

mrnsigepalum@...> writes:

>As a follow up to my earlier post on prime frequencies (sorry, don't

>have it with me at the momoment) I was trying to find a way in

>determining n as prime with it ending either in 1, 3, 7, or 9. Chris

>pointed me into a direction on the internet (thank you) and I found

>some amazing results. I found this table from a project Andrew

>Granville and Greg Martin worked on.

>

>x 1 3 7 9

>100 5 7 6 7

>200 10 12 12 10

>500 22 24 24 23

>.

>.

>.

>500,000 10,386 10,382 10,403 10,365

>1,000,000 19,617 19,665 19,621 19,593

>

>The lead trades off between 3 and 7. Also, the number of primes of x

>following the formula 3n+2 had the strongest and most dominate course.

From my NMBRTHRY post

http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0403&L=NMBRTHRY&P=R1117&I=-3
here is another data point for your table:

x 1 3 7 9

10^13 86516370000 86516427946 86516367790 86516371101

where 3 is in the lead, but only by an incredibly small relative margin.

This is line with theory, which says that asymptotically the 4 fractions are equal.

So I don't think anything useful can come out of this line of investigation.

-Mike Oakes