only list I am on that defaults to individual responses, rather than

group responses.)

A different take on data analysis.

If you plot sum of inverses versus product((p-1)/(p-2)) you get an

almost perfect linear fit, with correlation coefficient r=1-(3*10^-

5). For n=50 data points that's a pretty good fit.

Adam

--- In primenumbers@yahoogroups.com, "Mark Underwood" <marku606@y...>

wrote:>

the

> I just surveyed the gold mine of data which Adam presented below,

> quality of which went over and above what I was hoping for. And

even

> more that that I am elated that it so strongly corresponds with

what

> I was heuristically hanging my hat on. I was expecting somewhat

grouped

> tighter results but I am still very happy with these results which

> confirm my heuristics to a great degree of confidence. I have

> Adam's data to show how it falls into the pattern.

inverse

>

> To five significant digits (rounded),

>

> Primes separated by 2^n, that is 2, 4, 8, 16, 32, and 64 have

> sums of .017153, .017049, .017045, .016999, .016973 and .016981

54,

> respectively. That is about .0170. Call this B' for Brun

> modified.

>

> Primes separated by (2^n) x (3^m), that is 6, 12, 18, 24, 36, 48,

> 72 and 96 have inverse sums

of .033958, .034063, .034055, .034087, .034211, .034002, .034026, .03

>

> 3998, and .034012 respectively. That is about .0340. The

expected

> result is B' x (3-1)/(3-2) = .0340

1)/

>

> Primes separated by (2^n) x (5^m), that is 10, 20, 40, 50, 80, and

> 100 have inverse sums

> of .022674, .022699, .022724, .022635, .022733, and .022683

> respectively. That is about .0227. The expected result is B' x (5-

> (5-2) = .0227

have

>

> Primes separated by (2^n) x (7^m), that is 14, 28, 56, and 98 have

> inverse sums of .020386, .020450, .020338 and 020352 respectively.

> That is about .0204. The expected result is B' x ((7-1)/(7-2)

> = .0204.

>

> Primes separated by (2^n) x (11^m), that is 22, 44 and 88 have

> inverse sums of .018834, .018879 and .018920 respectively. That is

> about .0189. The expected result is B' x (11-1)/(11-2) = .0189.

>

> Primes separated by (2^n) x (13^m), that is 26 and 52 have inverse

> sums of .018643 and .018612 respectively. That is about .0186. The

> expected result is B' x (13-1)/(13-2) = .0185.

>

> And so on.

>

> Primes separated by (2^n) x (3^m) x (5^r), that is 30, 60 and 90

> inverse sums of .045331, .045362 and .045378 respectively. That is

inverse

> about .0453. The expected result is B' x (3-1)/(3-2) x (5-1)/(5-2)

> = .0453.

>

> Primes separated by (2^n) x (3^m) x (7^r), that is 42 and 84 have

> inverse sums of .040838 and .040786. That is about .0408. The

> expected result is B' x (3-1)/(3-2) x (7-1)/(7-2) = .0408

>

> Primes separated by (2^n) x (5^m) x (7^r), that is 70 has an

> sum of about 0273. The expected result is B' x (5-1)/(5-2) x (7-1)/

(7-

> 2) = .272

the

>

> Good enough for me! Thanks Adam!

>

> Mark

>

>

>

>

> --- In primenumbers@yahoogroups.com, "Adam" <a_math_guy@y...> wrote:

> > Hmmm, I posted some data (somewhere) but it isn't showing up on

> > list. Did I send it to somebody's email, instead of the list?

If

> > so, please post for me. Anyway, it defintely looked like there

sum

> were

> > patterns (wait, I might have saved the data)......here ya' go,

> of

output

> > (1/p) for p>10^6 and p<20 million when (p+k) is also prime,

> is

> > (k,sum):

> >

> >

> > 2, .01715295754

> > 4, .01704852064

> > 6, .03395755937

> > 8, .01704518900

> > 10, .02267391029

> > 12, .03406331599

> > 14, .02038594306

> > 16, .01699946972

> > 18, .03405521233

> > 20, .02269903011

> > 22, .01883421188

> > 24, .03408741833

> > 26, .01864293196

> > 28, .02044996718

> > 30, .04533148052

> > 32, .01697346702

> > 34, .01813592253

> > 36, .03421070761

> > 38, .01801860557

> > 40, .02272393752

> > 42, .04083825580

> > 44, .01887947490

> > 46, .01780359233

> > 48, .03400242989

> > 50, .02263451790

> > 52, .01861219959

> > 54, .03402561886

> > 56, .02033752356

> > 58, .01760087352

> > 60, .04536210827

> > 62, .01762533361

> > 64, .01698090345

> > 66, .03778604223

> > 68, .01808951646

> > 70, .02731960955

> > 72, .03398823253

> > 74, .01746662755

> > 76, .01806215382

> > 78, .03717973980

> > 80, .02273260129

> > 82, .01748673074

> > 84, .04078555194

> > 86, .01747334842

> > 88, .01892019678

> > 90, .04537844859

> > 92, .01780730452

> > 94, .01745072896

> > 96, .03401206908

> > 98, .02035243350

> > 100, .02268286529

> >

> > Adam

> >