Low weight stats page.

[Kosmaj]

I see no reason why not. Has anybody worked on them? I have no idea, maybe Thomas or Curtis can tell you more. BTW, I see that the file contains more than 5000 Ks, how did you select exactly these 11 out of 5000?

And I just tried sieving k=15335906269828439. In the n=1-10k range no n survived sieving to 85M. In the n=10-200k range only 12 did!

[Citrix]

Originally Posted by Kosmaj

I see no reason why not. Has anybody worked on them? I have no idea, maybe Thomas or Curtis can tell you more. BTW, I see that the file contains more than 5000 Ks, how did you select exactly these 11 out of 5000?

And I just tried sieving k=15335906269828439. In the n=1-10k range no n survived sieving to 85M. In the n=10-200k range only 12 did!

I took all the ~5250 k's (to be more precise) and sieved them in the nmin=1 nmax=1M range upto pmax=10000. Then I selected all the k's with less than 128 candidates left. I have the number of candidates remaining for the rest of the k's, if anyone wants them.

Why I am working on these extremely low weight k's?

Looking at most of large megabit primes found in the top 5000 DB, they are either mersenne numbers or other numbers that can be tested really fast, like k<32 for proth and riesel. Then there are k's that have low weight.

Consider for example all the huge SOB primes. These SOB k have such low weight that they should not have found a prime in the n range they were searched for. Yet projects like rieselsieve, PSP and SOB continue to beat the odds and find new megabit primes.

So I think, that if we choose a bunch of k's and work of them, irrespective of weight, one of them would eventually beat the odds and spit out a prime. To test this hypothesis, I am reserving the lowest 11k's that I know of, to test them to a large n value.

The following k's had 0 values left under 1M. I think these are riesel number and not low wieght numbers, but I do not know how to prove it. Is there a way to decide on their identity?
1531543060309739
24495411634339871
27697189380823769
31153994867516291
61624064322011353
61670219307871063
79259968463949613


Thanks

[Kosmaj]

I checked k=1531543060309739 using the output of ksieve with p<2000 and found the covering set to be [3, 5, 7, 13, 17, 19, 73, 193, 257, 1153] and modulus=288. Here is the relevant part of the output:

3 | 1531543060309739*2^1-1  +2...
5 | 1531543060309739*2^2-1  +4...
7 | 1531543060309739*2^0-1  +3...
13 | 1531543060309739*2^4-1  +12...
17 | 1531543060309739*2^0-1  +8...
19 | 1531543060309739*2^2-1  +18...
73 | 1531543060309739*2^5-1  +9...
193 | 1531543060309739*2^44-1  +96...
257 | 1531543060309739*2^4-1  +16...
1153 | 1531543060309739*2^188-1  +288...

(I couldn't reduce it further.) The above primes can cover any slot between 1 and 288, therefore k=1531543060309739 is Riesel number. Most likely the same can be shown for other k's on your list.

[Citrix]

Originally Posted by Citrix

Can I reserve

1665624349782373
10075614324682349
12782924755172441
15335906269828439
23009979551311559
30729699810869707
41360993926068041
49050506465852977
49791527843569597
50670759245200691
72292129717621199
(11 k)

Complete to 1M, no primes, unreserving.
I think my hypothesis was wrong, the k's should have some substantial wieght else, no prime will be found.

Thanks.

[grobie]

Reserving k=41343149

[grobie]

Originally Posted by grobie

Reserving k=41343149

Tested to 475k (No Primes) Releasing this one.

[Templus]

k=10453199 tested until n=440000, no primes. Releasing

[grobie]

Status Update on k=256453:

Primes at:

n=607
n=41359
n=233779

Tested to 810k

Continuing to 1M

[VBCurtis]

Originally Posted by Citrix

Consider for example all the huge SOB primes. These SOB k have such low weight that they should not have found a prime in the n range they were searched for. Yet projects like rieselsieve, PSP and SOB continue to beat the odds and find new megabit primes.

So I think, that if we choose a bunch of k's and work of them, irrespective of weight, one of them would eventually beat the odds and spit out a prime. To test this hypothesis, I am reserving the lowest 11k's that I know of, to test them to a large n value.
Thanks

There's two issues here you missed. First, SOB has done a HUGE amount of work to find those primes-- take a glance at their production stats for an idea of just how much work. I don't know what makes you say they are beating the odds in finding those primes.

Second, the phrase "eventually beat the odds" makes no sense. If you search long enough, the odds say you WILL find a prime. You can hope to get lucky, which is really what the low-weight search is about; but saying weight has no relevance, or needs to be above a certain cutoff (which you concluded after striking out to 1M on 11 k-values, which was what, 250 tests?), is folly. I think you're confusing the depth of a search with the time taken TO search. Your original idea to test the very lowest-weight k's was fine, but to give up after a week and 11 candidates proved nothing. If you hope to find a 200k digit prime, it's going to take 3-6 Ghz-months on average, no matter how to try to do the search.

Hope this helps.
-curtis

[humanoverlord]

I would like to reserve the following k (I have indicated limits I have already tested them to and primes found):

k=131069 (to 290K), no additional primes beyond n=16 and 112 found by Joss
k=9705763 (to 635K), prime at n=49335

I have also done testing on some other low weight k's not listed (if yall are interested):

k=792729463 (to 330K), prime at n=4271, 24671
k=29330981023 (600K), no primes yet

I am not really interested in these latter two k's, so if you add them to the list, they can be considered available for reservation.



-Andrew

[Kosmaj]

Welcome to RPS!

I just updated our low weight stats page with your results, it's normally updated by Mike but I was just "in the office" updating our k<300 page so I did it this time.

BTW, maybe you have already noticed, we are currently processing 36 low weight Ks in our 3rd Drive, we are now at n=1,570,000. If you have some spare cpu cycles you are welcome to join. All candidates are sieved to 4.2T.

If you have any questions, please don't hesitate to ask.

Happy hunting!