Prime gap records

[MJansen]

Hi ATH,
thanks for checking the endpoints!
And yes I have all candidates after sieving available. If you wish to check a few candidates, that would be great! Send me a PM, the files are way too large to add here.

Kind regards
Michiel

[MJansen]

Hi ATM,

Here are the zipped text files with the candidates after sieving. The files are rather large because I set the interval till around merit 100. Always the optimist: I did not want to start up another sieve midway ;-)

There are two files (both plain text, without the txt extension), one for the plus side (TestP40000D30030M1p), and another for the minus side (TestP40000D30030M1m)

The first 3 lines are:
1 (= multiplier)
30030 (= divider)
479909 (=40.000th prime for the primorial)

After that are the candidates
-12
-14
-30
-42
-78
-108
etc. etc.

Choose some random candidates within the gap interval to test, If you would be so kind. Thanks in advance! Really appreciated!

Kind regards
Michiel Jansen

[robert44444uk]

Originally Posted by MJansen

The plus side was found 25-2-2022 at 01.40 UTC/GMT+1 hour.

The search stopped at 479909#/30030 + 3.800.092. Which gives a gap of 6.966.714 at merit 14.540

What a shame - just shy of 7 million. You might want to update Wikipedia once it has been checked.

[mart_r]

All good things come to an end... actually, I would never have expected my prime gap record to last for almost five years! Only H. Rosenthal's and J.K. Andersen's gap from 2004 stayed on the top for longer - about eight years - if my notes are correct.

Congrats Michiel!

[MJansen]

Originally Posted by mart_r

All good things come to an end... actually, I would never have expected my prime gap record to last for almost five years! Only H. Rosenthal's and J.K. Andersen's gap from 2004 stayed on the top for longer - about eight years - if my notes are correct.

Congrats Michiel!

Hi Mart,

records are there to be broken ... thanks for the thumbs up!

Kind regards
Michiel

[robert44444uk]

Michiel - Are you happy to have your record credited to MJandJKA rather than yourself?

[MJansen]

Originally Posted by robert44444uk

Michiel - Are you happy to have your record credited to MJandJKA rather than yourself?

Hi Robert,

very happy to share the credit since Jens developed the treesieve program that I used for presieving the candidates. We were in contact untill january 2021, after that he has not responded to my emails. I hope he is well.

Kind regards
Michiel

[ATH]

It is called "APTreesieve" right? It does not seem to be available for download anywhere.

I made my own sieving with GMP and primesieve and sieved to 1e12, I missed some small interval near 1e12 because I split it on many computers, so I "only" found 3,447,400 factors: gap6966714factors.zip
leaving 35,956 candidates instead of your 35,943: gap6966714remaining.txt

I started doing PRP with pfgw64 from the lowest prime, but it will take a long time to double check everything for me.

[MJansen]

Originally Posted by ATH

It is called "APTreesieve" right? It does not seem to be available for download anywhere.

I made my own sieving with GMP and primesieve and sieved to 1e12, I missed some small interval near 1e12 because I split it on many computers, so I "only" found 3,447,400 factors: gap6966714factors.zip
leaving 35,956 candidates instead of your 35,943: gap6966714remaining.txt

I started doing PRP with pfgw64 from the lowest prime, but it will take a long time to double check everything for me.

Hi ATH,

it is called APTreesieve. I have a windows version that I use. If you want it, PM me with a mail adress to forward it to, exe files cannot be send here if I remeber correctly.

Your sieving approach is close enough for me (<<1% deviaton).

Regarding the check of every candidate:
do you really want to check every candidate? This will take many days to finish. It would be great of you to do, but are you sure? I do appreciate it, but if I remember correctly Thomas Nicely did not check the gaps over 1 million, apart from the end points. Doing so would would give the gap extra credibility, so no complaints from me !

Kind regards
Michiel

[ATH]

All the tests are finished the gap checks out:

35,956 composite PRP tests:
gap6966714prptests.zip

All 3,447,400 factors + 35,956 PRP tests in a sorted list:
gap6966714.zip

[MJansen]

Originally Posted by ATH

All the tests are finished the gap checks out:

35,956 composite PRP tests:
gap6966714prptests.zip

All 3,447,400 factors + 35,956 PRP tests in a sorted list:
gap6966714.zip

Thank you sir!

Much appreciated checking the gap!

Ps I said I wanted to run 3 more mega gaps and two have finished already below the current record. The third one has just started.

Kinds regards
Michiel