Low weight stats page.

[SB2]

k=334331 LLR tested to n=1M. --> releasing.

334331 78
334331 294
334331 7998

[humanoverlord]

k=56251213 now at n=1.96M... still no primes.

[kar_bon]

k (Range) (n's left) (sieved to) (llr'ed to)
9787 (1M) 1324 241G 577K
20141 (5M) 16025 361G 1M
27253 (5M) 15305 463G 1M
31511 (5M) 13137 70G 1M
50227 (1M) 930 640G 775K
57943 (1M) 640 488G 755K
99311355 (1-285k) 21232 327G 148k
99311355 (285k-1M) 110233 347G 295k
352744289 (5M) 4602 282G 1M
353437897 (5M) 4026 600G 1M
353880067 (5M) 1826 1.4T 1.625M
475977645 (1M) 91879 3.36T 381k
372321161 (5M) 1554 506G 1.143M no primes
8922449 (5M) 3629 129G 405k no primes

[kar_bon]

llr completed to n=1M: no new primes. (5 for this k mentioned before)
releasing this k.

[gd_barnes]

I have tested 31 low-weight k's from k=10K to 200K up to n=100K that are shown on the summary page. This was a verification effort and not a gap-filling effort, although I did partially fill a gap on a couple of them. I have found that there are missing small primes on 9 of them.

Because of the complexity of the different situations on the k's, I won't go into a lot of detail in a message here. Attached are the details of the problems found and some k's that need to be unreserved. On 4 of the k's that had their first prime higher than n=100K, I tested to a little higher than their first prime.

The bottom line is that for every one of the k's that I tested that did not already have a prime listed, I found at least one and sometimes several primes. Of course I did not test Riesel k's as I'm sure that all of those have been double-checked by that effort at all ranges of n.

The main problem that I found is that very small primes are being missed on low-weight k's.

This was originally in a spreadsheet that I cut-and-pasted into a Notepad document, so you may need to maximize it on your screen to see it clearly.


Gary

[SB2]

Much delayed status report;

3343 - Done to 1000k no new primes
3817 - Done to 1000k no new primes
4813 - Done to 1000k no new primes
5077 - Done to 900k 490629, 881829..testing in progress
6119 - Done to 1035k 678080, 1011416..testing in progress
7331 - Done to 477k no new primes..testing in progress
9179 - sieving to 1000k ..in progress
9613 - Done to 630k 464439..testing in progress
9913 - Done to 736k no new primes..testing in progress
10949 - Done to 879k no new primes..testing in progress
11519 - sieving to 1000k ..in progress
12791 - Done to 683k no new primes..testing in progress
17077 - Done to 762k no new primes..testing in progress
19919 - Done to 417k no new primes..testing in progress
21547 - sieving to 1000k ..in progress
21673 - Sieved to 1000k ..Ready for testing
22183 - Sieved to 1000k ..Ready for testing
24067 - Sieved to 1000k ..Ready for testing
24671 - Sieved to 1000k ..Ready for testing
25229 - Sieved to 1000k ..Ready for testing
30727 - Sieved to 1000k ..Ready for testing
43541 - Sieved to 1000k ..Ready for testing
48973 - Sieved to 1000k ..Ready for testing
65279 - sieving to 1000k ..in progress
70079 - sieving to 1000k ..in progress
106303 - sieving to 1000k ..in progress
114613 - sieving to 1000k ..in progress
117037 - sieving to 1000k ..in progress
236337 - Sieved to 2000k ..Ready to test
239857 - Done to 500k no new primes..testing on hold
248047 - done to 512k no new primes..testing on hold
278713 - Done to 1000k no new primes
284579 - Done to 916k 56, 4736..testing in progress
294907 - Sieved to 2000k ..Ready to test
306251 - Done to 550k no new primes..testing on hold
313979 - Sieved to 2000k ..Ready to test
320107 - Done to 592k no new primes..testing on hold
334147 - Done to 600k no new primes..testing on hold
334331 - Done to 1000k 78, 294, 7998
685183 - Sieved to 2000k ..Ready to test
686711 - Sieved to 2000k ..Ready to test
700477 - sieving to 1000k ..in progress
808477 - Done to 856k no new primes..testing in progress
842711 - Sieved to 2000k ..Ready to Test
844559 - Sieved to 2000k ..Ready to test
10284899 - Sieved to 1000k ..Ready to test
10247561 - Done to 727k no new primes..testing in progress
10346561 - Done to 1000k 32714, <released>
37616317 - Sieved to 1000k ..Ready to test
36231101 - Done to 1000k 469002, <released>

47 - Done to 586k no new primes..testing in progress
53 - Done to 582k 582078,..testing in progress
11025 - Done to 399k 372717..testing in progress

[gd_barnes]

As you may know, I have done a lot of gap-filling and some double-checking on this site.

A couple of weeks ago, I noticed the unusual number of low-weight k's that have no primes listed, many that were unreserved, and were not being searched by RieselSieve, so I knew they must have a prime. So last week, I undertook an effort to test 31 low-weight k's from k=10K to 200K from n=0 to 100K that had 2 or less primes, regardless of their current status; i.e. whether they were reserved or not, whether they were being worked on here or not, etc. I only excluded RieselSieve project k's from the effort. I found 9 of them that had unlisted primes, 8 of which whose first primes was n < 1K. 4 of those were explainable because they were either clearly never tested for n < 100K, were never tested for n > 30K, or because they had been reserved by someone who has been inactive for well over a year and had never reported any activity on them. But the other 5 of them appeared that they should have been listed.

This resulted in at least one prime being found for all listed low-weight k's between k=10K and 200K. I posted the missing primes in the 'small primes found' forum yesterday.

I suspect two problems that may have caused this: (1) Most of you may already be aware of this but I should mention it anyway in case someone is not...When using NewPGen for sieving, it will erroneously remove small n's that it should not, especially for larger k values. I always just add back in all n's < 25, regardless of the value of k used. Srsieve does not have this problem. (2) If you pick up a k where someone else left off, say at n=30K or 300K, if there are no low primes listed, you might run a quick sieve and LLR on the range of n=0 to 10K. I think that sometimes people will say they've 'tested to 300K' when in reality they tested BETWEEN n=10K (or more) and n=300K.

A good way to catch this is if the k is below the first known true Riesel number at k=509203, has not had a prime found, and it is not being worked by the RieselSieve project, then it must have a prime that is (1) on the top-5000 site -or- (2) is a relatively small prime. Most likely the latter.

Please know that none of this is to say that the current efforts here are in error. I see many small primes listed above for various k's from SB2 and others. But I just want everyone to be aware of it and watch for it. I suspect some people may have searched a very long time on some k's for that 'first prime' and never found it when in reality its first prime is at n=4 or 8 or 15 or something very irritating like that.

I'm currently checking low-weight k's with 2 primes or less from k=200K to 1M that are not being shown as being worked with the low-weight effort here in the last few status reports that I see. There seem to be plenty of them.


Thanks,
Gary

[Kosmaj]

Thanks for your verification efforts.

Other possible causes of missed primes, besides those you mentioned, were discussed here. Early versions of LLR were buggy for large k's, and not designed to find primes for small n's. After the bugs were removed nobody bothered to double check previous work.

I agree that we can remove all reservations by Lipinski, and also by Joss and Keller.

Finally, you say

The following k's are reserved by Marcin, need to be unreserved,
and were found to be missing primes:

k       missing prime(s)
38887   1, 25, 33, 225
84277   9
85807   17

but Marcin never reported anything about them therefore I don't think we can call them missing. Also Joss tested k=179743 to 30k, and now you found a prime at 99k. It's obviously not missing because he never checked beyond 30k, don't you think so?

[gd_barnes]

Originally Posted by Kosmaj

Finally, you say

but Marcin never reported anything about them therefore I don't think we can call them missing. Also Joss tested k=179743 to 30k, and now you found a prime at 99k. It's obviously not missing because he never checked beyond 30k, don't you think so?

In the complexity of all of the situations involved in the various k's that I tested, I made a misleading statement in my original post about the missing primes. I attempted to correct myself with the statement in my lastest post below, where I said:
"I found 9 of them that had unlisted primes, 8 of which whose first primes was n < 1K. 4 of those were explainable because they were either clearly never tested for n < 100K, were never tested for n > 30K, or because they had been reserved by someone who has been inactive for well over a year and had never reported any activity on them.".

So you are correct, 4 of them did not have 'missing' primes, they just had not been tested or had not been tested as high as I did. Only 5 of the 9 had 'missing' primes so to speak.

I'm now in the process of verifying many low-weight k's between k=200K and k=1M. I'll let you know what I come up with.

I wish I could test ALL k's this fast! Low-weight ones are a snap.


Gary

[Cruelty]

864316301*2^1055106-1, after this prime I will not test this k any higher - if someone really wishes to continue where I left, then I can provide a sieve file till n=2M, p=11T (there are 8513 candidates left)

[gd_barnes]

Originally Posted by SB2

Much delayed status report;

239857 - Done to 500k no new primes..testing on hold
248047 - done to 512k no new primes..testing on hold
306251 - Done to 550k no new primes..testing on hold
320107 - Done to 592k no new primes..testing on hold
334147 - Done to 600k no new primes..testing on hold
808477 - Done to 856k no new primes..testing in progress

SB2,

Above is a partial quote from your last status report. Can you tell us where you started your testing? I ask this because in addition to how high you've tested, we also need to know where you started your testing. That is, did you start testing the above k's at n=1 or n=1000 or n=100K?

I'm trying to make sure that all ranges of n are getting tested to avoid missing the listing of small primes. I think what may be happening in many cases is that there may be some confusion or assumptions made on how much testing has been done when someone says they've 'tested thru xxx' or 'done thru xxx' without initially giving a starting point of testing.


Thanks,
Gary