Primes on top-5000 site for low-weight k's
 

In my verification efforts looking for missing small primes on low-weight k's on our summary site, I did a search of the top-5000 site on ALL low-weight k's from k=10K to 1M, since some of those are 'kind of' small by today's standards. I found the below primes that are not shown on our site. Perhaps this will keep someone from searching ranges that have already been searched. The last time I checked, only one of the k's was reserved.

Prime / date found
236377*2^19693-1; 10/1998
278077*2^56913-1; 12/1998
370421*2^201442-1; 11/2000
464909*2^73740-1; 2/1999
487811*2^42478-1; 11/1998


In my verifications, in order to keep them from having a gap in searching, I have now completed searching all of the above k's up to n=100K and found no additional primes. So Karsten, in addition to adding the primes, you can show them all searched up to 100K with no gaps with the exception of k=370421. On k=370421, I'm searching up to the prime to completely fill the gap. That is still in process. I should be done with that in the new few days, long before you do another summary update. So hopefully none will have gaps at that time. I'll let you know the outcome of that search when I'm done with it.

Note that I am not reserving these k's. This is a verification effort only for small primes and the top-5000 site assisted in that effort. Hopefully I didn't step on any toes here.


Gary

[QUOTE=Cruelty;110709]Are you still working on it? If yes then, what about k=70079?
I see you are sieving [URL="http://www.mersenneforum.org/showpost.php?p=110378&postcount=182"]70079 and some others[/URL] too.
What about those?[/QUOTE]

I should have marked 3343, 3817, 4813 as unreserved. 70079 is now being LLR'ed.

284579 has now also been tested to 1000k with the following primes; 56, 4736. unreserving this one too.

[QUOTE]SB2, can you check and see where you started your testing on your k=239857, 248047, 306251, 320107, 334147, and 808477? I know you started where someone else left off at. It's just that I don't know where that point is.[/QUOTE]

As soon as I can make time, most likely this weekend.

[QUOTE=SB2;110751]I should have marked 3343, 3817, 4813 as unreserved. 70079 is now being LLR'ed.[/QUOTE] OK, then I wish to reserve 3343 from n=1M :smile:

reserved low weight k=613 from n=260k.
613*2^335655-1 is prime (llr at 340k)

Starting points in testing
 

[quote=SB2;110751]

As soon as I can make time, most likely this weekend.[/quote]


SB2, were you able to come up with those starting points in your testing for the 6 k's that I asked about?


Gary

SB2, me fill low gaps on 2 of your k's ?
 

SB2,

There are some gaps in testing at low values of n on 2 k's where the summary site shows that you have them reserved. But in looking at the thread here, I couldn't tell if you had intended to fill them or not. Being the 'official gap filler' here :smile:, I'd like a chance to fill those gaps if you are OK with it. Here are the particulars:

k=306251; gap from only known prime at n=22 up to n=300K

k=464353; gap below only known prime at n=371279


I would just test in the gapped range only. That would save you some LLR searching at low ranges.


Thanks,
Gary

[QUOTE=gd_barnes;110744]
(...)
Prime / date found
236377*2^19693-1; 10/1998
278077*2^56913-1; 12/1998
370421*2^201442-1; 11/2000
464909*2^73740-1; 2/1999
487811*2^42478-1; 11/1998
(...)
[/QUOTE]

hi Gary,
in your post #199 here you mentioned some low primes not in the summary.
i'm just including from TOP5000 id's from 200 to 400, means very first inserted in database. i found many other low primes of k<500000 so this all should be
Riesel numbers with their first prime! look here ([url]http://www.prothsearch.net/rieselprob.html[/url]) and see the text at 'On July 13, 2001, the value of f17 = 35 was established. (...)'
this means there are 35 k's < 509203 with their first prime between 131072 and 262144. other primes you listed could be values from f16, f15,...
so far i found 18 from these 35 k's: 25229, 81517, 105569, 105697, 132071, 132599, 144817, 217807, 285191, 307211, 321043, 331139, 370421, 392737, 393209, 408247, 466783, 485773.
k=466783 i tested in two days upto n=250k and there were only the one prime for n=245839!
to be sure i'm in contact with Wilfrid Keller who searched also these numbers.
(BTW he updated his page k<300 [url]http://www.prothsearch.net/riesel2.html[/url].)
hope i get some infos about all small Riesel numbers.
Karsten

Low-weight k verification status
 

[quote=kar_bon;111450]hi Gary,
in your post #199 here you mentioned some low primes not in the summary.
i'm just including from TOP5000 id's from 200 to 400, means very first inserted in database. i found many other low primes of k<500000 so this all should be
Riesel numbers with their first prime! look here ([URL]http://www.prothsearch.net/rieselprob.html[/URL]) and see the text at 'On July 13, 2001, the value of f17 = 35 was established. (...)'
this means there are 35 k's < 509203 with their first prime between 131072 and 262144. other primes you listed could be values from f16, f15,...
so far i found 18 from these 35 k's: 25229, 81517, 105569, 105697, 132071, 132599, 144817, 217807, 285191, 307211, 321043, 331139, 370421, 392737, 393209, 408247, 466783, 485773.
k=466783 i tested in two days upto n=250k and there were only the one prime for n=245839!
to be sure i'm in contact with Wilfrid Keller who searched also these numbers.
(BTW he updated his page k<300 [URL]http://www.prothsearch.net/riesel2.html[/URL].)
hope i get some infos about all small Riesel numbers.
Karsten[/quote]


Karsten,

3 days ago, I completed an extensive search on 57 low-weight k's shown on our summary site for 200K < k < 1M up to n=100K. I found primes on all k's that are not being searched by Riesel sieve that are less than the 1st true Riesel number at k=509203. That was my main objective of this effort.

I was already aware of the primes shown in the Riesel Sieve effort but I wanted to test them up to at least n=100K or to their first known prime. In some cases, there were multiple primes whereas they only showed the first found prime, for obvious reasons. On most of the ones where we didn't previously post a prime, it's because we hadn't tested them here yet. But on 6 total k's, I found 'truly missing' primes. That is they are shown as tested quite high on our summary site but did not have small primes listed.

I was not so successful finding primes for 509203 < k < 1M and obviously those aren't being tested by Riesel Sieve. There turned out to be 10 k's in that range where I couldn't find a prime up to n=100K so I seached all of those up to n=300K with little success...I only found a prime on ONE of them! So even after all of this testing, there will still be 9 low-weight k's for 509203 < k < 1M that will have no primes found up to n=300K. Most were unreserved but on the couple that were, I confirmed that no primes had been found by anyone else in this thread. So...we have some 'really composite' k's in that range that may be 'more composite' than many of the k's currently being searched by Riesel Sieve, but still not provable as a true Riesel number.

I'm sure there's some overlap in your effort and mine but both are definitely necessary efforts to get everything correct and listed. I'll find some things that you won't and you'll find some things that I won't and where there's overlap, we'll be confirming one another's testing and research.

I'm holding off posting my large list waiting a response from SB2 to my two questions above before posting them all. I'm trying not to step on toes here. There seems to be some inconsistency on whether they are reserved or not by him. On ones that he has only sieved or partially sieved but not yet LLR'd, some are shown as reserved and some aren't. I really hope to get a response from him to my questions in the next few days. Once I do, I may do some additional gap-filling (see below) and then post my entire list. At that point, we should have major fill ins on k's with no current primes shown as well as several gaps filled.

On a final note, in order to speed this 'clean up' process along, you may be able to answer the 2 questions that I have for SB2 as follows:

1. Is there a way for you to look back and see where SB2 may have started his testing on k=239857, 248047, 306251, 320107, 334147, and 808477? If you have an old archived copy of a prior summary site, you may be able to tell. If he started at n > 100K on one or more of them, then I may want to do some additional verification.

2. Can you see if he really has k=464353 reserved? It seems obvious that he still has k=306251 reserved. His last status 2-3 weeks ago says he's "Done to 550k no new primes..testing on hold". But on k=464353, I cound not find where that one was ever officially reserved even though it's shown as reserved on the summary site. The last we saw on that one is that he was sieveing it way back on March 18th, 2007 but there has never been in testing and no further status reports on it. I'd really like to knock out the gap on these two as the final part of this effort.



Thanks a bunch,
Gary


-edit-
Additional comment:
Note that I did not do any research or testing on any k's that were not already shown on our summary site so it looks like our efforts are mostly separate from one another. There were already so many k's shown on our site in that range that I didn't want to take on any additional effort at the time. It looks like in your effort, you have discovered many new k's with primes to list from Riesel Sieve. On some of their earlier searches where the prime is relatively low, I suspect that some of them may not be very low weight.

57 low-weights for k=200K-1M missing & addl primes
 

Karsten,

I've held off waiting on a response from SB2 for long enough now. I posted 3 messages in this thread and sent him a PM over a month ago asking for additional information, all with no response. So it's time for me to post this large verification effort that I did on low-weight k's. It will give everyone a lot of good information.

See the attached list for missing and additional low-weight primes to post. There were 6 'truly missing' primes. What this does is that it gives us at least one prime for every k < 509203 that is listed on our summary site and is not being searched by Riesel-sieve. That and double-checking for low primes were my main objectives of the effort.

All needed details are in the attachment but here is a synopsis of my thinking when doing testing:
1. All low-weight k's for 200K < k < 1M were tested up to n=100K with a few exceptions that already had several primes.
2. If no primes were found for a k in #1, then it was tested up to n=300K.
3. If prior testing had already been done for 100K < n < 375K, then I double-checked the entire testing range and tested a little further.

A secondary objective of the effort was to find very composite k's > 509203 that would be interesting for others to search for larger primes. I found 9 k's with Nash weight > 0 where 509203 < k < 1M had no primes up to at least n=300K. I call these "quasi Riesel #'s". :wink: For everyone's prime-searching pleasure, I'll list them right here. :smile:

low-weight k's for 509203 < k < 1M with Nash weight > 0 that have no primes for n <= 300K:
612509
671413
685183
686711
700057
780427
844559
963643
981493

5 of the 9 k's above are unreserved and the other 4 are showing reserved by SB2, but I don't think anyone really knows for sure. 3 of those 4 show 'sieved to 2000K ready to test' over 6 weeks ago but what does that really mean? Is he going to post the sieve file for others to test or is he going to test them himself? The other one shows "I have stated sieving" over 5 MONTHS ago! But no follow-up was ever given.

If anyone can get a hold of SB2, please let him know that we badly need a status update from him.

The attachment is in an Excel spreadsheet. Let me know if you have any problems reading it.


Gary

Status update: k=56251213 now at n=2.06M and still looking.

Low-weight primes for k=8M-12M up to n=100K
 

[COLOR=black][FONT=Verdana]I decided to give one of my cores a 'break' last night from top-5000 searches and have it do some prime searches for all low-weight k's shown on our site from k=8M to 12M up to n=100K. Below is what I found.[/FONT][/COLOR]

[quote]
[COLOR=black][FONT=Verdana]k: n[/FONT][/COLOR]
9096613: 47, 50951
9705763: 49335
9770317: 2205
10013593: 3847
10108837: 33657
10247561: 730
10284899: 868, 2596
10296007: 24305
10346561: 32714
10598947: 3025
10639619: 24
10906603: 23, 2471
10932097: 35045
10943321: 374, 2390
11311003: 3
11553221: 170, 54026
11639819: 12, 5124
11846279: 72
[/quote]

[COLOR=black][FONT=Verdana]4 of these primes had already been found and posted but I'm listing them all for completeness here.[/FONT][/COLOR]

[FONT=Verdana][COLOR=black]3 of the primes were 'missing'. That is the k had been previously searched past the range of the prime but they had not been posted.[/COLOR][/FONT]

[FONT=Verdana][COLOR=black]If anyone is interested in searching some barren k's, here is a list of them in this range that still have no primes up to n=100K as searched by me or higher as previously searched by others:[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]8376239[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]8922449[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]10453199[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]10463923[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]10544249[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]10671431[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]10813783[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11223059[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11319193[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11468609[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11658187[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11716993[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11741347[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11847299[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11932211[/COLOR][/FONT]
[FONT=Verdana][COLOR=black]11955659[/COLOR][/FONT]


[FONT=Verdana][COLOR=black]Gary[/COLOR][/FONT]