Choose your own K and work on finding a top-5000 prime!

[nuggetprime]

Greetings,
I've now access to a 24/7 quadcore machine for at least two months, so my res lack has found an end for now. I decided to reserve a lower and more lightweight k than 19217385 also, it's 1443.
Search is now at 235k, primes will follow soon.

Regards
nugget

[nuggetprime]

Primes upto 235k(from 10k):
12716
17183
22232
23930
24367
29674
37120
63208
68702
89252
222272

Regards,
nuggetprime

[nuggetprime]

Now at 300k. Sieving to 700k started.
One more prime found at n=268111.

-nugget

[kar_bon]

to nuggetprime/sps27:

please refer to http://www.rieselprime.org and on the left menu the pages for all k's.
the last update dates are not correct, please see the page itself!
in the near future i will update all these data-pages with all infos from this forum and Top-5000 primes.

for 1443 the range upto 35k was already searched!

to sps27:
to choose a k for testing look the k's listed on these pages.
a hint:
a k with a small Nash weight means: there are not so many candidates to test upto higher ranges (eg. about 1000 pairs to test upto n=1Million). but the chance to find a prime is low too.

a k with a high Nash-weight means: there're many pairs to test (eg. 50000 upto 1M) but the chance is higher to find a prime.

so play with some k's and choose one.

[nuggetprime]

@ kar_bon
yes, i didn't find the page first, but no problem , I wasted some cpu minutes,nothing more.

regards,
nugget

[sps27]

Well I'm working on k=35779

I'm at n=294k so far:

35779 37
35779 69
35779 79
35779 211
35779 265
35779 349
35779 411
35779 447
35779 489
35779 801
35779 2089
35779 2977
35779 3261
35779 3739
35779 3961
35779 4647
35779 6921
35779 19225
35779 23037
35779 26145
35779 29817
35779 39405
35779 41727
35779 60051
35779 76335
35779 106141
35779 268195

[VBCurtis]

sps-
The LLR software's method for testing k*2^n-1 (riesel numbers) takes somewhat longer for higher k values. A k-value in the 30,000 area might take 10-15% longer per test than a k near 1000 (this is guesswork, as I don't have data handy for a k near yours). The probability a given single test comes up prime is independent of the k-value, according to theory; it is affected by the depth of your sieve and the size of the exponent in the test.

Put these two observations together, and your chosen k will take some amount of time longer (perhaps 15%) to find each prime than an otherwise identically-performing k in the 1000-2000 range. This is why those lower k's are popular. When you tire of your current k, or run out of sieve, consider an untested (past 10,000) k value from the pages karbon referred to in the 1000-3000 area.

The good news about picking a k in the range you chose is that is it very very unlikely anyone has tested it before- that security may be worth the time-per-test penalty. It's fun to just jump in and try something on your own, too- 15% isn't very significant in the grand scheme of things, esp when trying new things out.
-Curtis

[lavalamp]

I still have quite a large number of results on my PC from a while ago. I was doing some investigating of prime density and searched quite a few ranges along the way.

I think that some may already be on 15k, but the majority are not.

[gd_barnes]

Originally Posted by sps27

Well I'm working on k=35779

I'm at n=294k so far:

35779 37
35779 69
35779 79
35779 211
35779 265
35779 349
35779 411
35779 447
35779 489
35779 801
35779 2089
35779 2977
35779 3261
35779 3739
35779 3961
35779 4647
35779 6921
35779 19225
35779 23037
35779 26145
35779 29817
35779 39405
35779 41727
35779 60051
35779 76335
35779 106141
35779 268195

n=7, i.e. 35779*2^7-1 is also prime

NewPGen erroneously removes small n-values when sieving. If using NewPGen for sieving, you have to manually test anything where 35779*2^n-1 is less than the depth of your sieve.

In this case, NewPGen assumed that 35779*2^7-1=4579711 has a factor of 4579711 and so removed it when the sieve depth got that high even though it is prime. I verified that was the only one missing up to your first listed prime at n=37.


Gary

[kar_bon]

to sps27:
your k is in the summary pages, the missing n too.

to lavalamp:
that's what i'm looking for.
i try to include all results with twins, if any, in the next update! thanks.

[gd_barnes]

Originally Posted by kar_bon

to sps27:
your k is in the summary pages, the missing n too.

to lavalamp:
that's what i'm looking for.
i try to include all results with twins, if any, in the next update! thanks.

Karsten, I don't see k=35779 in the summary pages. I am looking at rieselprime.org here. The last update is July 16th.

I also don't see it at rieselprime.de.


Gary