Bases 6-32 reservations/statuses/primes

[MisterBitcoin]

Reserving R30 up to n=550K.

[rebirther]

R15 tested to n=600k (450-600k) (0-10M)

2 primes found, 6 remain

Results emailed - extending to 1M

[rebirther]

Reserving S10 to n=3M (2-3M) for SRBase

[rebirther]

R15 tested to n=1M (600k-1M) (0-10M)

1 prime found, 5 remain

Results emailed - Base released

[rebirther]

S10 tested to n=3M (2-3M)

nothing found, 1 remain

Results emailed - Base released

[rebirther]

Reserving R10 to n=3M (2-3M) for SRBase

[gd_barnes]

In an effort to account for all of the k's on R25 in order to create the "all k's" file on our webpage, I ran a double-check to n=25K. In doing so, I found that 7 primes had been missed as follows:

41562*25^9925-1
47238*25^8802-1
56016*25^9722-1
69330*25^9077-1
70344*25^8213-1
70680*25^8956-1
126114*25^15419-1

The files that I had were a mess. Part of the problem was that a lot of primes were pulled over from base 5. Another was that many different people were involved on it back in the early days of CRUS so primes were pulled from many sources. I had many different files with quite a few gaps, many likely as a result of primes posted in the forum here that I did not copy off to my machine, which has become a recurrent theme from our old team efforts. (My bad!) Based on the tight bunching of all but 1 of the primes, I suspect that this was more of a coordination problem than any software issues. Perhaps k=40K-75K for n=8K-10K was simply missed.

Fortunately 4 of the k's already had larger primes. But that left the following 3 k's that were remaining at n=300K and have now been removed from our pages:
47238
56016
70680

That now leaves exactly 100 k's remaining at n=300K. Included are all primes for n>300K that were found from the SR5 effort that is now being worked on by PrimeGrid.

The R25 "all-ks" file is now posted on the page.

Thankfully the files that I have for S25 are much cleaner. Although I'm double-checking it to n=25K now, I anticipate very few or no problems.

Thanks to Mark for the very cool srbsieve program that is very effective in working on these double-checks to as high of an n-limit as I want!

[rebirther]

R10 tested to n=3M (2-3M)

nothing found, 1 remain

Results emailed - Base released

[gd_barnes]

Originally Posted by MyDogBuster

Sierp 15 tested n=10K-25K with the following primes found:

6598*15^11715+1
977594*15^12860+1
148548*15^13101+1
966148*15^14630+1
62900*15^16936+1
633342*15^22404+1

Range Released

From a post from 2010. It's funny how these things pop up. I was ready to post my "all k's" file for S15 k<=10M but there was one k that I could not account for, k=148458. My files showed that it remained at n=10K but I couldn't find it remaining in any files for higher n and could find no prime for it.

Before posting my all k's files, I double-check everything to n=25K if I don't have a clear set of files, which I often haven't had on these huge-conjectured small bases. k=148458 showed as remaining at n=25K after my run of srbsieve. I then did a standalone double-check of myself on a different machine. Nope; still remaining. I could not find a prime for it in my files, the forum here, the CRUS pages where we have a page/file of primes n>25K for bases 3/7/15, and the top-5000 site. I finally tried one last thing: I manually went through and did searches on each page in this thread for "15^". My sleuthing finally came to an end at the above post.

k=148548 had been searched for n>10K instead of k=148458. 148548*15^13101+1 is definitely prime but unfortunately that doesn't help us. k=148548 already had 3 primes for n<50.

Either the k-value or a sieve file was incorrectly posted on the CRUS pages at the time or the searcher just picked it up incorrectly.

So going forward: It showed as remaining at n=10K in my files so it's been effectively triple-checked to n=10K and double checked for n=10K-25K. I have completed sieving for n=25K-100K and am searching it. It's currently at n=40K. It's only running on one core and will be done in about a day if no prime is found.

For S15, all k<=5M have been searched to n=200K. If it still remains at n=100K, I'll sieve it for n=100K-200K and add more resources to it to bring it up to the other k's on the base.

In the mean time, I'm holding off on updating the pages or posting the all k's file until I'm done with it.

If it still remains at n=200K, it will be the smallest remaining k for S15.

I've had my fun for the night. :-)

[gd_barnes]

That didn't last too long:

148458*15^51788+1 is prime

[gd_barnes]

I was doing an accounting of all k<=10M for S7. I initially ran a double-check for the range to n=25K. I found some serious problems only for the k=5M-10M range.

First, there were 16 missing primes as follows:

5072244*7^6+1
5203866*7^4+1
5452324*7^6+1
5629252*7^6+1
5770774*7^5+1
6302236*7^4+1
6609082*7^6+1
7069908*7^5+1
8122398*7^4+1
8566504*7^6+1
8738868*7^6+1
8760604*7^5+1
9126852*7^4+1
9462126*7^4+1
9494736*7^5+1
9542640*7^5+1

Second, there were 24 k's that were unaccounted for. I had the following k's remaining on my check to n=25K but they were not shown as remaining on our page and had no prime shown anywhere for n>25K in my files, on the page, or in the forum here:

5117814
5371308
5497278
5638338
5663272
5673636
5771676
6212106
6338104
6427404
6464844
6638776
6828694
6874968
7131814
7362214
7458994
7961172
8153368
8631642
8643682
8791996
9316288
9967266

After encountering this, I then double-checked myself on a different machine. They were confirmed as having no prime to n=25K.

For the first group of 16 missed primes, 15 of them already had primes n>25K found for them:

5072244*7^137454+1
5203866*7^26944+1
5452324*7^277094+1
5629252*7^44310+1
5770774*7^66269+1
6302236*7^37531+1
6609082*7^31919+1
7069908*7^28577+1
8122398*7^26548+1
8738868*7^37910+1
8760604*7^67010+1
9126852*7^31582+1
9462126*7^66933+1
9494736*7^35275+1
9542640*7^39624+1

k=8566504 was the only k in the first group not to have been primed and was still shown as remaining at n=300K on the page. It has now been removed. Additionally the above primes were removed from our list of n>25K primes since the k's all have small primes.

For the second group of k's not accounted for, to be consistent with our already tested range, all 24 k's had to be searched to n=300K or a prime was found. The following 20 primes were found for n=25K-300K:

5117814*7^30654+1
5371308*7^37869+1
5497278*7^166454+1
5638338*7^34308+1
5663272*7^28034+1
5771676*7^30380+1
6212106*7^30133+1
6338104*7^143570+1
6427404*7^25265+1
6464844*7^46841+1
6638776*7^59672+1
6828694*7^34298+1
6874968*7^34409+1
7131814*7^46690+1
7362214*7^112357+1
7458994*7^59314+1
7961172*7^63582+1
8153368*7^35073+1
8631642*7^39830+1
8791996*7^143761+1

The above primes were added to our list of n>25K primes.

That left the following 4 k's remaining at n=300K that were added to our page:

5673636
8643682
9316288
9967266

Net additions to our pages:
4 - 1 = 3 k's remaining
20 - 15 = 5 primes n>25K

Due to my concern about this, I also completed the following double-check:
All k<10M to n=50K.
All k=10M-20M to n=25K.

No additional problems were found (thankfully). Note that all k=10M-1G to n=25K was done quite a bit later than k<=10M. It is only the smaller k's that had been searched for n>25K.

As for what caused this, I can only speculate that a software issue caused the first problem. They aren't all in the range of the 40-bit problem but some are. So there could have been a similar problem somewhere at the time. I also speculate that human error caused the second problem. There was a range of 11 consecutive k's for k=5M-6.5M that were in between two consecutive k's previously shown on our remaining page. A range likely got missed somewhere and it didn't stick out at me enough at the time when I posted everything. But it doesn't fully explain the other k's that were more randomly dispersed throughout the range.

So finally all k<=10M for S7 are accounted for. (Actually all k<=20M but I'm only showing k<=10M for now.)