20210619, 15:28  #1 
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 
20210619, 19:57  #2 
"Seth"
Apr 2019
2×193 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 20210619 at 19:58 
20210619, 20:27  #3 
Einyen
Dec 2003
Denmark
2×3×13×41 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 2^{64} + 1.05*10^{16} = 18,457,244,073,709,551,616 but I have not worked on it recently. The gap is at 2^{64} + 2.33*10^{16} so I'm not even half way. 
20210619, 20:39  #4 
May 2018
3·79 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.

20210620, 07:03  #5 
Jun 2003
Oxford, UK
1982_{10} Posts 
Astounding, many congrats.
Lets hope it is a new maximal! 
20210620, 09:22  #6  
Jan 2018
2^{2}×3×7 Posts 
Quote:
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 

20210620, 12:23  #7  
Mar 2021
59_{10} Posts 
Quote:
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. 

20210620, 12:37  #8  
Mar 2021
73_{8} Posts 
Quote:


20210620, 13:24  #9  
Einyen
Dec 2003
Denmark
2×3×13×41 Posts 
Quote:
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^{64}. 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 Last fiddled with by ATH on 20210620 at 13:30 

20210620, 14:59  #10  
Dec 2008
you know...around...
2AF_{16} Posts 
Quote:
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. 

20210620, 19:56  #11 
Jun 2015
Vallejo, CA/.
2002_{8} 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 wonâ€™t go empty handed!
CONGRATULATIONS! 
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