Prime gap records

[SethTro]

Originally Posted by CraigLo

Hi everyone. I've been doing some prime gap searches for a couple weeks. Yesterday I tried to submit


2724 28.1621 3808817329*83# + 8863


I got a message in the queue

(2724, '3808817329', 'end not prime')


Am I doing something wrong or does the code not support positive offsets?

Server code just doesn't support it yet (if you add "/1" after 83# it probably would).

Should be fixed now

[robert44444uk]

Originally Posted by CraigLo

Hi everyone. I've been doing some prime gap searches for a couple weeks. Yesterday I tried to submit


2724 28.1621 3808817329*83# + 8863

Nice gap! It is really tough to find records <3000

[mart_r]

Originally Posted by CraigLo

2724 28.1621 3808817329*83# + 8863

I recognize that search strategy.
You get about 10% higher merits in the range around p# + or - p² than in a random search.
Still not as efficient as the deficient primorials though, but perhaps useful for "small" gaps.


Edit:

Originally Posted by SethTro

Server code just doesn't support it yet (if you add "/1" after 83# it probably would).

Should be fixed now

Pierre Cami had a gap in the list with a positive offset, 44909*43037# + 188014 (gap=230478).
(I haven't yet figured out how to attain the complete list of the github data... some help here, maybe?)
There are also some gaps with expression 6^n + ... and 2^n + ..., are they still there?

[SethTro]

Originally Posted by mart_r

I recognize that search strategy.
You get about 10% higher merits in the range around p# + or - p² than in a random search.
Still not as efficient as the deficient primorials though, but perhaps useful for "small" gaps.


Edit:


Pierre Cami had a gap in the list with a positive offset, 44909*43037# + 188014 (gap=230478).
(I haven't yet figured out how to attain the complete list of the github data... some help here, maybe?)
There are also some gaps with expression 6^n + ... and 2^n + ..., are they still there?

You can see the raw list (it's too large for github to display in the nice editor)

https://raw.githubusercontent.com/pr...er/allgaps.sql

The issue would only affect records submitted via my front-end. I see some records starting with "6^13004 + ..." from MJPC&JKA (141970, 142450, and 144170)

It looks like Pierre Cami's 230478 gap record was improved by M.Jansen in 2021 22123#/210 - 64882.

[MJansen]

I was a little surpised to have my name attached to these records, since I was only aware of primorial searches, I guess Pierre must have send these to Tom.

Kind regards
Michiel Jansen

[mart_r]

Originally Posted by SethTro

You can see the raw list (it's too large for github to display in the nice editor)

https://raw.githubusercontent.com/pr...er/allgaps.sql

Thanks a lot!
Though my tablet has problems downloading/viewing the list, my dinosaur PC with a direct cable connection to the web handles it nicely and fast.

[Bobby Jacobs]

Good job on the records!

[CraigLo]

I found 3 pretty large merits that are just outside the top 100.

10470 33.7912 17497330955201*307#/30 -6066
10470 33.7896 17755704968891*307#/30 -7496
10470 33.7881 18011066308391*307#/30 -4196

There is a larger merit for 10470. Is there a record for largest merit that is not a record?

[CraigLo]

Originally Posted by mart_r

I recognize that search strategy.
You get about 10% higher merits in the range around p# + or - p² than in a random search.
Still not as efficient as the deficient primorials though, but perhaps useful for "small" gaps.

I did a test with A*97#/30, A mod 30 = 1 and A*97#/1. Both were run over the same number of A values.
With 97#/30 I found 1459 merits > 25.
With 97#/1 I found 1057 merits > 25.

I was checking a larger region for the 97#/1 case so it took longer but if I only checked the most promising regions I could probably get performance to within a factor of 2-3.

[henryzz]

Originally Posted by CraigLo

I found 3 pretty large merits that are just outside the top 100.

10470 33.7912 17497330955201*307#/30 -6066
10470 33.7896 17755704968891*307#/30 -7496
10470 33.7881 18011066308391*307#/30 -4196

There is a larger merit for 10470. Is there a record for largest merit that is not a record?

We only keep the smallest for each gap size. A version of https://primegap-list-project.github...gh-watermarks/ that also listed gaps that were second best could be quite fun though. I tend to target my searches based on this list trying to get gaps on it. A second-best list would mean more targets. Some of the existing records are quite hard to beat.
Speaking of which I have just submitted: 232194 29.501 6099881 * 7993#/505915410 -59322 to +172872 which pushes 5 gaps off the list(including one of my own).

Still missing two personal targets: a gap of 1M and a 30 merit gap

[SethTro]

Originally Posted by CraigLo

I found 3 pretty large merits that are just outside the top 100.

10470 33.7912 17497330955201*307#/30 -6066
10470 33.7896 17755704968891*307#/30 -7496
10470 33.7881 18011066308391*307#/30 -4196

There is a larger merit for 10470. Is there a record for largest merit that is not a record?

If it was every a record it ends up in the git log and you can find them, if isn't a record at the time of discovery I don't know of any record keeping (you can submit them to my website and they end up in some log file but that's likely to be deleted at somepoint)

The highest merit non record gap I could find was a merit 33.5 by Jacobsen edged out by GapCoin this year

9738 Jacobsen 2016 33.4953 7850579863*283#/30 - 5534