New Maximal Gaps

[R. Gerbicz]

Originally Posted by CraigLo

I found this yesterday
1552 34.9844 18470057946260698231

It isn't proven maximal. I was only sieving and doing a single Fermat test.

That is great! So we were really close to this (p ~ 2^64+23e15) by our exhaustive search up to 2^64 with my code (+some code improvements from users here).

[CraigLo]

Originally Posted by mart_r

Congrats! That's a spectacular result, albeit a rather lucky one.
At the current rate of progress, I wouldn't have expected the next maximal gap to be found so soon.

It was definitely lucky. 2^64 + 2.3E16 is only 0.59% higher than the previous max gap. The average step is around 70% which would have taken 3 years instead of a few days. Although there are 3 max gaps closer to the previous max gap so it isn't totally unexpected.
Gap = 132, 0.56%
Gap = 514, 0.40%
Gap = 1132, 0.37%

[CraigLo]

Originally Posted by ATH

I mostly saved that "maximal gap" list I made for fun starting at 0 at 2⁶⁴, which you already linked.
I did save some gaps > 1000 but only briefly in the beginning. My program jumps ahead the minimum gapsize I want to find and then searches backwards until it finds a prime, if I set minimum gapsize to 1000 it would run even slower than it already does when I have it at 1320 which is my "maximal gap" above 2⁶⁴.
I do not think this is an exhaustive list of gaps > 1000 even in the internal it covers, because I might have turned on and off the feature of saving gaps>1000, I do not remember exactly, but I guess you can test if your program has found these gaps. Very exciting with GPU code for this, I did dream about making my program for GPU, but I never found the motivation to learn programming for GPUs.

My code found all of these so it seems to be working pretty well. Thanks.

[CraigLo]

Originally Posted by R. Gerbicz

That is great! So we were really close to this (p ~ 2^64+23e15) by our exhaustive search up to 2^64 with my code (+some code improvements from users here).

What does your code use for testing primes?

[Uncwilly]

@CraigLo there is no need to quote an entire post when responding.

[Bobby Jacobs]

Have you found any other first occurrence gaps besides this one?

[rudy235]

It used to be that new first occurrences and/or new maximal gaps were reported to Dr. Nicely. Unfortunately as we all know he passed away on October 2019.

This is the first time I am aware a new first occurrence has happened in the table from 1 to 1998
The entry. 1552 C?C Spielaur 2017 28.15 24 876129783640337274493519
Should be replaced by a similar one with the information of CraigLo
1552 C?C CraigLo 2021 34.98 20 18470057946260698231

This is independently of the gap being found to be maximal or not.

How has, for instance, our friend robert4444uk been reporting his many first occurrences in other sections of the Tables?

[MJansen]

Hi Rudy235,

Seth Troisi keeps a github database that has all the record gaps. A view can be found at : https://primegap-list-project.github...gh-watermarks/ this page included Craig's newfound 1552 gap. More lists can be found at: https://primegap-list-project.github.io/lists/.

The entry page is off line now, but can be found at: https://primegaps.cloudygo.com/

Kind regards
Michiel

[CraigLo]

The second largest gap I've found so far is 1430.

[robert44444uk]

Originally Posted by MJansen

Hi Rudy235,



The entry page is off line now, but can be found at: https://primegaps.cloudygo.com/

Kind regards
Michiel

Hi - does anyone know when the entry page is coming back online?

[MJansen]

Seth just send a PM, he is moving house in the middle of the heat-wave. Takes a little longer to set up internet again. So a little patience, he'll be back ;-)