mersenneforum.org Where to find Prime Gap lists?
 Register FAQ Search Today's Posts Mark Forums Read

 2019-07-26, 20:51 #1 jaydfox   Jul 2019 7 Posts Where to find Prime Gap lists? Hi Everyone, I apologize for posting out of the blue. I've skimmed through the forum, and I've read through some of the threads, but I wasn't really sure where to find an easily accessible list of known prime gaps. I don't mean a random large gap here or there. I mean, is there a database or list of ALL the "large" prime gaps above a certain size below a certain limit? For example, on Dr. Nicely's website, I found a list of all the "kilogaps" below 5e16. Actually, it was a list of all known first occurrences of gaps, and a separate list of all the kilogaps below 5e16 that weren't already in the first occurrence list. I had to merge the two lists. But the point stands, this is presumably a list of all the gaps of at least 1000, below 5e16. (Incidentally, I counted 149 such gaps after merging the two lists. I have no way of verifying that number.) But given that the maximal gaps have been proven up to at least 1.8e19, I am hoping that somewhere, someone is maintaining a list of all the kilogaps below 1e19. Actually, I assume Dr. Nicely would have access to this data, but I spent some time going through his website, and I couldn't seem to figure out how to get the data I'm looking for. I realize that there will be several thousand such gaps, but in the grand scheme of things, it seems like a very small amount of data to maintain. Does anyone know where to find it? Is it already listed publicly somewhere? Is there a private list that is accessible to people who are actively participating in these prime gap searches? I'm not necessarily at the point of wanting to throw my spare processor cycles at such a search. I'm still trying to understand the theory and run experiments, and I'm looking for high quality data to verify/challenge my understanding.
2019-07-27, 09:31   #2
robert44444uk

Jun 2003
Oxford, UK

2,039 Posts

Quote:
 Originally Posted by jaydfox Hi Everyone, I apologize for posting out of the blue. I've skimmed through the forum, and I've read through some of the threads, but I wasn't really sure where to find an easily accessible list of known prime gaps. I don't mean a random large gap here or there. I mean, is there a database or list of ALL the "large" prime gaps above a certain size below a certain limit? For example, on Dr. Nicely's website, I found a list of all the "kilogaps" below 5e16. Actually, it was a list of all known first occurrences of gaps, and a separate list of all the kilogaps below 5e16 that weren't already in the first occurrence list. I had to merge the two lists. But the point stands, this is presumably a list of all the gaps of at least 1000, below 5e16. (Incidentally, I counted 149 such gaps after merging the two lists. I have no way of verifying that number.) But given that the maximal gaps have been proven up to at least 1.8e19, I am hoping that somewhere, someone is maintaining a list of all the kilogaps below 1e19. Actually, I assume Dr. Nicely would have access to this data, but I spent some time going through his website, and I couldn't seem to figure out how to get the data I'm looking for. I realize that there will be several thousand such gaps, but in the grand scheme of things, it seems like a very small amount of data to maintain. Does anyone know where to find it? Is it already listed publicly somewhere? Is there a private list that is accessible to people who are actively participating in these prime gap searches? I'm not necessarily at the point of wanting to throw my spare processor cycles at such a search. I'm still trying to understand the theory and run experiments, and I'm looking for high quality data to verify/challenge my understanding.

Hi jaydfox

Originally we had the idea that we would collect all kilogaps in the range 4e18 to 2^64, but in fact it was not done - we opted for faster programme settings, which reported on gaps of 1000 or more, but which did not produce a definitive list of all kilogaps. Given that this program is still available at this site, you could reduce the variables to report all kilogaps, but this would run a bit slower than the settings we used, and would need to be run from 5e16 upwards rather than 4e18. The work we carried out used about 5-10 high performance desktops, and took over a year. So producing the definitive kilogap list to 2^64 is not an insignificant task.

2019-07-27, 18:43   #3
jaydfox

Jul 2019

7 Posts

Quote:
 Originally Posted by robert44444uk Hi jaydfox Originally we had the idea that we would collect all kilogaps in the range 4e18 to 2^64, but in fact it was not done - we opted for faster programme settings, which reported on gaps of 1000 or more, but which did not produce a definitive list of all kilogaps. Given that this program is still available at this site, you could reduce the variables to report all kilogaps, but this would run a bit slower than the settings we used, and would need to be run from 5e16 upwards rather than 4e18. The work we carried out used about 5-10 high performance desktops, and took over a year. So producing the definitive kilogap list to 2^64 is not an insignificant task.
Thanks for the reply! I have a six-year-old laptop, rather modest in performance, so I doubt I could add much to the overall search for maximal gaps. But I'll download the code and play around with it, maybe see if I can help extend the list of kilogaps above 5e16.

2019-07-30, 19:51   #4
mart_r

Dec 2008
you know...around...

22·11·17 Posts

Quote:
 Originally Posted by jaydfox Thanks for the reply! I have a six-year-old laptop, rather modest in performance, so I doubt I could add much to the overall search for maximal gaps. But I'll download the code and play around with it, maybe see if I can help extend the list of kilogaps above 5e16.

Two years ago I searched a small range for kilogaps >5e16, because I wanted to find eight more gaps of length 1000 so I'd have a list of the first 20 of them. Didn't find any up to 5.2e16, but if you're interested I could do some more searching there.

Here are results from 5e16 to 5.2e16, all gaps >= 1000:
Code:
1080 50393998281635599
1036 50597782557370831
1038 50662912533154139
1028 50669505541630601
1020 51103842778483477
1006 51178110554293441
1036 51506543650015963
1022 51540068502364151
1030 51821938103395729
1028 51878675840390051
1024 51922353423303283
BTW, aren't you also in the tetration forum?

Last fiddled with by mart_r on 2019-07-30 at 19:54 Reason: grammar

2019-07-31, 00:12   #5
jaydfox

Jul 2019

7 Posts

Quote:
 Originally Posted by mart_r Two years ago I searched a small range for kilogaps >5e16, because I wanted to find eight more gaps of length 1000 so I'd have a list of the first 20 of them. Didn't find any up to 5.2e16, but if you're interested I could do some more searching there. Here are results from 5e16 to 5.2e16, all gaps >= 1000:
Hey, thanks for that! I've downloaded the gap12.c code, and I've been reading through it, but I haven't tried compiling it yet. I'll add these gaps to the list I scraped from Dr. Nicely's site.

I've been trying to do some analysis of the modified Cramér model (after sieving small primes), but I lack quality data for testing the model. I need gaps that are large enough (relative to the average gap) to test the suitability of the model to estimate maximal gaps, but I need enough gaps to actually get statistically significant results. Hence my interest in kilogaps.

I actually think a more interesting set of data to test the model is the nth largest gap (i.e., the nth largest gap seen so far, with a tie considered "smaller" than a previous occurrence of the same gap). The data get smoother as n is increased, so it's easier to see the trends in the data. Having access to a complete list of kilogaps (>= 1000) would facilitate this, since I could start analyzing from the nth kilogap.

Quote:
 Originally Posted by mart_r BTW, aren't you also in the tetration forum?
Yes, I've been active off and on in that forum for... I guess over a dozen years now. But I've taken some long breaks. Family life, work, etc., gets in the way of my math hobby sometimes.

 2019-07-31, 19:06 #6 mart_r     Dec 2008 you know...around... 22×11×17 Posts One of my PCs is still dedicated to the twin prime gaps search (probably another week or two, there was a slight delay due to a little heatwave here in Germany last week with up to 41°C, and I paused the calculation for a few days). With the other I can currently search a range of about 7e14 per day, which is not much, but I'll continue unless you (or someone else) have significantly more resources.
 2019-08-27, 18:35 #7 mart_r     Dec 2008 you know...around... 13548 Posts Kilogaps between 5e16 and 6.1e16: Code: 1080 50393998281635599 1036 50597782557370831 1038 50662912533154139 1028 50669505541630601 1020 51103842778483477 1006 51178110554293441 1036 51506543650015963 1022 51540068502364151 1030 51821938103395729 1028 51878675840390051 1024 51922353423303283 1068 52604763098088133 1040 52888336638766061 1012 52924388177774671 1004 52940197762336457 1038 53190502026869531 1030 53424413597601847 1098 53638706154728053 1012 53660015663845999 1002 53707322644803361 1020 53914110235891273 1010 54014460400754531 1016 54238958822744543 1074 54406581745449079 1036 54440388168355723 1020 54882837712797953 1028 55113259135704059 1004 55163718630690983 1004 55200837956308043 1002 55283761083282649 1198 55350776431903243 1058 55449498692096303 1008 55487720105088083 1020 55488741963678451 1056 55682178862196023 1050 55732090121186321 1020 55823579213985769 1020 55891416733516277 1018 56091766320454369 1000 56136441023068027 1034 56158582731193853 1000 56670104952987829 1062 56981519303622899 1050 57155528198687827 1024 57222906071591899 1040 57654402011303759 1128 57701567767397551 1032 57753877128029321 1050 57776087064021863 1008 58194865424950141 1068 58555411853875691 1018 58598010042460591 1028 58616959313839973 1020 58819143208929863 1010 58838200694113361 1160 58904398834827743 1014 58962322496980073 1018 59040706748307103 1026 59196144582231763 1030 59407829528206891 1026 59490062497256117 1020 59541933150765029 1032 59589625441970119 1050 59818063210518643 1134 59847994456941689 1050 59871385309648697 1032 59914213666020719 1038 60133080805428509 1010 60502367225643683 1022 60553417610117651 1146 60592199607166471 1056 60638802299711093 1022 60765773554580597 1016 60802458897362753 1008 60896327833261201 Still doing some searching, but not with the highest priority.
2019-08-29, 00:50   #8
jaydfox

Jul 2019

7 Posts

Quote:
 Originally Posted by mart_r Kilogaps between 5e16 and 6.1e16: Still doing some searching, but not with the highest priority.
Hey, wow, thanks for this! That's 75 more to add to my list of 149. I.e., 149 kilogaps under 5e16, and 224 total under 6.1e16.

Of the 75 in your list, I had 6 from Dr. Nicely's website, so that added 69 more kilogaps!

 2019-10-24, 21:25 #9 mart_r     Dec 2008 you know...around... 10111011002 Posts Some more kilogaps between 6.1e16 and 7.4e16: Code: 1000 61289814801068713 1166 61499427052410467 1022 61608029101269257 1026 61707218844150821 1002 61852389306473867 1032 62045478361471351 1002 62269241894354171 1000 62361936121863601 1040 62808550411710269 1008 63030750779743111 1068 63585518075296193 1076 63751388393794781 1002 64025048118749989 1022 64064698065478949 1046 64178237253890621 1022 64435216702531091 1004 64437453352197017 1010 64489035614704343 1038 64656379256421941 1072 64681887054028429 1040 64903409232167393 1018 65171327701466443 1016 65303784137621093 1008 65541152120090963 1004 65656259060122589 1082 65850655232778077 1018 65865648969941053 1050 66282988287629461 1010 66295898802923987 1008 66316366986016003 1122 66322416129057029 1012 66389213712846301 1004 66507821823362993 1020 66677148675716687 1064 66712486906360703 1008 66803921756273941 1002 66820739930230501 1014 67033743226720297 1002 67306562390173597 1014 67419425658776777 1004 67631621153942789 1032 67646010960504871 1006 67699163242627531 1174 67777708053772723 1128 68248526808384701 1090 68402499016330903 1058 68428465104182033 1024 68475318115749673 1008 68483650739629969 1076 68607677530724921 1028 68680143205806719 1020 68858613651275563 1006 68889111160953541 1002 69096269699560111 1002 69146992679052011 1050 69363019583598199 1038 69414990756773269 1014 69603276634606153 1000 69672350035847929 1022 69707999361413111 1022 69887880784634327 1050 70072593169404983 1014 70133104083953173 1012 70207452984829309 1020 70514057617500059 1080 70682835348242081 1038 71291937976937471 1002 71334390972787619 1006 71732350211993017 1040 71912635508975399 1060 72091252389474481 1020 72119924546819353 1032 72245286734288309 1078 72638824545480979 1014 72660209757895937 1012 72714085593695191 1034 73081138652291327 1006 73132086814502323 1030 73280655706629409 1026 73320383505423721 1036 73342849465603087 1002 73456185314120771 1040 73606458765637037 1008 73960629782222201 Maybe one or two entries before 7.3e16 are still missing, as that range is not yet fully processed (spare CPU time on my laptop which is ... slow).
 2019-12-14, 16:55 #10 mart_r     Dec 2008 you know...around... 10111011002 Posts Now that I found my 20 gaps with g=1000 and stopping this search, here are the kilogaps for 74e15 to 81e15, including one I was hinting at in my previous post: Code: 1008 72785657893044751 1158 74224828152967109 1008 74253247947930853 1014 74427355957362047 1068 74566933953299951 1050 74672144302283221 1040 74732186510943107 1036 74949586587024841 1020 74986031869324259 1010 75120665420746919 1020 75781977412958353 1008 75925671745922261 1034 76082709975153047 1002 76087968329099347 1038 76357211355690061 1074 76485516106246547 1050 76641652530262307 1020 76706609121161687 1002 77033734179518617 1062 77099714753631979 1004 77481882268446659 1000 77564216289320659 1000 77671773242528989 1022 77702137670610647 1008 77744782220928523 1016 77787200404407383 1014 78038973615245437 1092 78120687162386527 1132 78137034924137419 1118 78661510510855829 1010 78781883279456333 1156 78944802602538877 1030 78993860918645443 1140 79017505670475503 1038 79140537078226669 1072 79525408741854637 1038 79647230167781779 1032 79714152290449507 1012 79836836014438207 1044 80285560147848283 1036 80416867635858673 1056 80444074990611217 1132 80464625759765719 1014 80564519093188279 1002 80597718041848247 1034 80630172261943979 1002 80806550204385689 1220 80873624627234849 1018 80909422108812589 1000 81065679461847721 1030 81171954964536067 1018 81264833949895861 1014 81269972698996723 1020 81330531155678237
 2019-12-17, 17:48 #11 storm5510 Random Account     Aug 2009 40728 Posts Fascinating! This was something I experimented with many years ago. I wrote a few programs. The problem was that I did not have access to a big integer library. Now, I do. So, I revisited it, adding the big integer capability. I do not know what the ceiling of this library is, but it is way up there. I had it display the decimal digits of 2^1619-1. It filled the screen. It is sort of hard to tell what all of you are searching for by looking at your lists. Smallest gap, largest gap, I am not sure. Either way, I cannot run my little program flat-out. The accumulated data would be overwhelming to pick through. I choked it down as much as I could. Below is a sample of the output Code: 12-17-2019 12:30:42: 14739, 160669 - 160663 = 6 12-17-2019 12:30:42: 14740, 160681 - 160669 = 12 12-17-2019 12:30:42: 14741, 160687 - 160681 = 6 12-17-2019 12:30:42: 14742, 160697 - 160687 = 10 12-17-2019 12:30:42: 14743, 160709 - 160697 = 12 12-17-2019 12:30:42: 14744, 160711 - 160709 = 2 It needs a filter for the output data. What this would be, again, I am not sure.

 Similar Threads Thread Thread Starter Forum Replies Last Post paulunderwood NeRDs 0 2014-02-03 05:09 R.D. Silverman Cunningham Tables 1 2010-09-21 16:16 MooooMoo Twin Prime Search 2 2006-05-11 23:38 xilman Forum Feedback 1 2006-04-23 18:14 ATH Lounge 20 2006-03-27 18:36

All times are UTC. The time now is 04:06.

Sat May 28 04:06:20 UTC 2022 up 44 days, 2:07, 0 users, load averages: 1.94, 1.90, 1.73

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔