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-   -   New Maximal Gaps (https://www.mersenneforum.org/showthread.php?t=26924)

 CraigLo 2021-06-19 15:28

New Maximal Gaps

I found this yesterday
1552 34.9844 18470057946260698231

It isn't proven maximal. I was only sieving and doing a single Fermat test. Does anyone want to help prove this is a new maximal gap? I think ATH has already checked up to at least 2^64 + 7734466511986395.

[URL]https://www.mersenneforum.org/showpost.php?p=521550&postcount=69[/URL]

 SethTro 2021-06-19 19:57

Nice!

I'm happy to throw some CPU at it if someone else coordinates.
I would also require instructions

 ATH 2021-06-19 20:27

Congratulation!

How did you find it, did you start at some random location or used some criteria? Which software did you use?

I reached 2[SUP]64[/SUP] + 1.05*10[SUP]16[/SUP] = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2[SUP]64[/SUP] + 2.33*10[SUP]16[/SUP] so I'm not even half way.

 Bobby Jacobs 2021-06-19 20:39

Congratulations! I was expecting the next maximal prime gap after 1550 to be at least 1600. I am surprised that this gap is only 2 greater than the last maximal gap. However, it is great that you found this gap.

 robert44444uk 2021-06-20 07:03

Astounding, many congrats.

Lets hope it is a new maximal!

 MJansen 2021-06-20 09:22

[QUOTE=CraigLo;581405]I found this yesterday
1552 34.9844 18470057946260698231

It isn't proven maximal. I was only sieving and doing a single Fermat test. Does anyone want to help prove this is a new maximal gap? I think ATH has already checked up to at least 2^64 + 7734466511986395.

[URL]https://www.mersenneforum.org/showpost.php?p=521550&postcount=69[/URL][/QUOTE]

Congrats, nice find! Let's hope it's a max gap.

Ps forgive my curiosity Craig, but how much calculating power (threads, cores) do you have at your disposal? The number of improvements you submit each time, gives me the idea it must be substantial.

Kind regards
Michiel Jansen

 CraigLo 2021-06-20 12:23

[QUOTE=ATH;581410]Congratulation!

How did you find it, did you start at some random location or used some criteria? Which software did you use?

I reached 2[SUP]64[/SUP] + 1.05*10[SUP]16[/SUP] = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2[SUP]64[/SUP] + 2.33*10[SUP]16[/SUP] so I'm not even half way.[/QUOTE]

Thanks. I started at 2^64. I've been writing GPU code. It is still under development and needs more testing. I'll post my code on github when it is finished if anyone is interested.

Did you save any gaps other than the maximal gaps above 2^64 that you posted? I saved all gaps above 1000 up to about 2^64 + 2E16. Anything you could send me would be helpful in testing.

 CraigLo 2021-06-20 12:37

[QUOTE=MJansen;581437]Congrats, nice find! Let's hope it's a max gap.

Ps forgive my curiosity Craig, but how much calculating power (threads, cores) do you have at your disposal? The number of improvements you submit each time, gives me the idea it must be substantial.

Kind regards
Michiel Jansen[/QUOTE]

Thanks. I use 1 1080 TI. My code doesn't work well for large numbers so I decided to switch to the max gap search until I have time to rewrite it. I planned to run it over the summer with the hope of finding 1 new record above 1432. I got lucky that this gap is so close to the previous max gap.

 ATH 2021-06-20 13:24

[QUOTE=CraigLo;581442]Thanks. I started at 2^64. I've been writing GPU code. It is still under development and needs more testing. I'll post my code on github when it is finished if anyone is interested.

Did you save any gaps other than the maximal gaps above 2^64 that you posted? I saved all gaps above 1000 up to about 2^64 + 2E16. Anything you could send me would be helpful in testing.[/QUOTE]

I mostly saved that "maximal gap" list I made for fun starting at 0 at 2[SUP]64[/SUP], 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 2[SUP]64[/SUP].
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.

[CODE]GAP: 1062 M=23.9397 CSG=0.539652 18446747749629047369 = 2^64+3675919495753
GAP: 1050 M=23.6692 CSG=0.533554 18446749424543324977 = 2^64+5350833773361
GAP: 1010 M=22.7675 CSG=0.513228 18446749672316868389 = 2^64+5598607316773
GAP: 1036 M=23.3536 CSG=0.52644 18446757511464660451 = 2^64+13437755108835
GAP: 1044 M=23.534 CSG=0.530505 18446760966709446359 = 2^64+16892999894743
GAP: 1008 M=22.7224 CSG=0.512212 18446762802362416693 = 2^64+18728652865077
GAP: 1024 M=23.0831 CSG=0.520342 18446763681622535443 = 2^64+19607912983827
GAP: 1014 M=22.8577 CSG=0.515261 18446764906595085317 = 2^64+20832885533701
GAP: 1034 M=23.3085 CSG=0.525424 18446769723502347797 = 2^64+25649792796181
GAP: 1152 M=25.9685 CSG=0.585385 18446779902697426681 = 2^64+35828987875065
GAP: 1002 M=22.5872 CSG=0.509163 18446787953189723131 = 2^64+43879480171515
GAP: 1046 M=23.579 CSG=0.531521 18446795884964577593 = 2^64+51811255025977
GAP: 1028 M=23.1733 CSG=0.522375 18446809183097018309 = 2^64+65109387466693
GAP: 1014 M=22.8577 CSG=0.515261 18446814868797283063 = 2^64+70795087731447
GAP: 1066 M=24.0299 CSG=0.541684 18446815504958901043 = 2^64+71431249349427
GAP: 1082 M=24.3906 CSG=0.549815 18446826240052088519 = 2^64+82166342536903
GAP: 1008 M=22.7224 CSG=0.512212 18446832337462467179 = 2^64+88263752915563
GAP: 1010 M=22.7675 CSG=0.513228 18446834480319631049 = 2^64+90406610079433
GAP: 1032 M=23.2635 CSG=0.524407 18446837965455400181 = 2^64+93891745848565
GAP: 1026 M=23.1282 CSG=0.521358 18446839378382506093 = 2^64+95304672954477
GAP: 1050 M=23.6692 CSG=0.533554 18446839576483513649 = 2^64+95502773962033
GAP: 1028 M=23.1733 CSG=0.522375 18446839708582188941 = 2^64+95634872637325
GAP: 1020 M=22.9929 CSG=0.51831 18446842024842919381 = 2^64+97951133367765
GAP: 1044 M=23.534 CSG=0.530505 18446852276777385049 = 2^64+108203067833433
GAP: 1012 M=22.8126 CSG=0.514244 18446855924744238139 = 2^64+111851034686523
GAP: 1020 M=22.9929 CSG=0.51831 18446858566936374767 = 2^64+114493226823151
GAP: 1004 M=22.6323 CSG=0.510179 18446859568323746303 = 2^64+115494614194687
GAP: 1092 M=24.616 CSG=0.554896 18446866320952044589 = 2^64+122247242492973
GAP: 1008 M=22.7224 CSG=0.512212 18446869081479001931 = 2^64+125007769450315
GAP: 1002 M=22.5872 CSG=0.509163 18446870028613768249 = 2^64+125954904216633
GAP: 1026 M=23.1282 CSG=0.521358 18446877536936961383 = 2^64+133463227409767
GAP: 1044 M=23.534 CSG=0.530505 18446878448228545247 = 2^64+134374518993631
GAP: 1050 M=23.6692 CSG=0.533554 18446881999487799761 = 2^64+137925778248145
GAP: 1060 M=23.8946 CSG=0.538635 18446882369862589303 = 2^64+138296153037687
GAP: 1040 M=23.4438 CSG=0.528472 18446884791762922619 = 2^64+140718053371003
GAP: 1026 M=23.1282 CSG=0.521358 18446885204269142597 = 2^64+141130559590981
GAP: 1036 M=23.3536 CSG=0.52644 18446885242027025197 = 2^64+141168317473581
GAP: 1016 M=22.9028 CSG=0.516277 18446890318078148273 = 2^64+146244368596657
GAP: 1008 M=22.7224 CSG=0.512212 18446894754557835029 = 2^64+150680848283413
GAP: 1016 M=22.9028 CSG=0.516277 18447124224395493323 = 2^64+380150685941707
GAP: 1038 M=23.3987 CSG=0.527456 18447124475560111561 = 2^64+380401850559945
GAP: 1038 M=23.3987 CSG=0.527456 18447144890682053239 = 2^64+400816972501623
GAP: 1038 M=23.3987 CSG=0.527456 18447164069237234579 = 2^64+419995527682963
GAP: 1068 M=24.075 CSG=0.5427 18447166052641000471 = 2^64+421978931448855
GAP: 1192 M=26.8702 CSG=0.60571 18447174410466704389 = 2^64+430336757152773
GAP: 1054 M=23.7594 CSG=0.535586 18447194450543281309 = 2^64+450376833729693[/CODE]

 mart_r 2021-06-20 14:59

[QUOTE=CraigLo;581405]I found this yesterday
1552 34.9844 18470057946260698231

It isn't proven maximal. I was only sieving and doing a single Fermat test. Does anyone want to help prove this is a new maximal gap? I think ATH has already checked up to at least 2^64 + 7734466511986395.

[URL]https://www.mersenneforum.org/showpost.php?p=521550&postcount=69[/URL][/QUOTE]

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

 rudy235 2021-06-20 19:56

Even if does not become the new maximal gap. (I would say it has a better than even chance of being that) it will almost certainly become the first occurrence of a gap of 1552. So you won’t go empty handed!

CONGRATULATIONS!

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