New Maximal Gaps

CraigLo · 2021-06-19, 15:28

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.

https://www.mersenneforum.org/showpo...0&postcount=69

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 2⁶⁴ + 1.05*10¹⁶ = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2⁶⁴ + 2.33*10¹⁶ 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:

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. 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.

https://www.mersenneforum.org/showpo...0&postcount=69

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:

Originally Posted by ATH

Congratulation!

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

I reached 2⁶⁴ + 1.05*10¹⁶ = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2⁶⁴ + 2.33*10¹⁶ so I'm not even half way.

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:

Originally Posted by MJansen

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

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:

Originally Posted by CraigLo

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.

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.

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

mart_r · 2021-06-20, 14:59

Quote:

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. 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.

https://www.mersenneforum.org/showpo...0&postcount=69

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.

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!

2021-06-19, 15:28	#1
CraigLo Mar 2021 59 Posts	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. https://www.mersenneforum.org/showpo...0&postcount=69

2021-06-19, 19:57	#2
SethTro "Seth" Apr 2019 17×29 Posts	Nice! I'm happy to throw some CPU at it if someone else coordinates. I would also require instructions Last fiddled with by SethTro on 2021-06-19 at 19:58

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2021-06-19, 20:27	#3
ATH Einyen Dec 2003 Denmark 110101111010₂ Posts	Congratulation! How did you find it, did you start at some random location or used some criteria? Which software did you use? I reached 2⁶⁴ + 1.0510¹⁶ = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2⁶⁴ + 2.3310¹⁶ so I'm not even half way.

2021-06-19, 20:39	#4
Bobby Jacobs May 2018 293 Posts	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.

2021-06-20, 07:03	#5
robert44444uk Jun 2003 Suva, Fiji 7FA₁₆ Posts	Astounding, many congrats. Lets hope it is a new maximal!

2021-06-20, 19:56	#11
rudy235 Jun 2015 Vallejo, CA/. 3³·43 Posts	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!