← Record Gaps Between Prime 15-tuplets

Pattern d: d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56
_{Gap end} merit = 187823.686118 ·_∫dt / log¹⁵ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 15-tuplet	Merit	Who	When
1	44360646117391789290	11	44360646117391789301	2.746376	Norman Luhn	08 Nov 2022
2	63939610598713839990	140245881111654813611	204185491710368653601	1.136275	Norman Luhn	08 Nov 2022
3	202996042954228073550	238931301405879137171	441927344360107210721	2.913054	Norman Luhn	08 Nov 2022
4	317073923236977286380	590079087912119470781	907153011149096757161	3.539010	Norman Luhn	08 Nov 2022
5	357944865874561195230	932043368797178903381	1289988234671740098611	3.529026	Norman Luhn	08 Nov 2022
6	366342536144399404590	3191291677985662206071	3557634214130061610661	2.566673	Norman Luhn	08 Nov 2022
7	493060964581874338650	3915962764770027206351	4409023729351901545001	3.242472	Norman Luhn	08 Nov 2022
8	609034703996754115080	4707613344406022195261	5316648048402776310341	3.787567	Norman Luhn	08 Nov 2022
Maximal gaps below 1.00 · 10²²

Pattern d: d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56
_{Gap end} merit = 187823.686118 ·_∫dt / log¹⁵ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 15-tuplet	Merit	Who	When
1	2128524666386268150	14094050870111867483	16222575536498135633	0.084296	Norman Luhn	08 Nov 2022
2	11145093752153421060	16222575536498135633	27367669288651556693	0.392214	Norman Luhn	08 Nov 2022
3	20605240474299551070	27367669288651556693	47972909762951107763	0.604148	Norman Luhn	08 Nov 2022
4	34324229637001534230	49198349218890756713	83522578855892290943	0.833941	Norman Luhn	08 Nov 2022
5	58328628796205818050	83522578855892290943	141851207652098108993	1.191917	Norman Luhn	08 Nov 2022
6	138584847566689253730	195690251815182929633	334275099381872183363	2.150492	Norman Luhn	08 Nov 2022
7	163220651445114222960	499698524000527366343	662919175445641589303	1.968333	Norman Luhn	08 Nov 2022
8	227354726001970637070	662919175445641589303	890273901447612226373	2.504557	Norman Luhn	08 Nov 2022
9	329167222840040274690	1857353909915640401093	2186521132755680675783	2.695682	Norman Luhn	08 Nov 2022
10	647010090582023518350	2186521132755680675783	2833531223337704194133	4.963696	Norman Luhn	08 Nov 2022
11	742586625718671543810	5349055849970305427783	6091642475688976971593	4.438856	Norman Luhn	08 Nov 2022
12	882599505501239435910	7388399412888127849043	8270998918389367284953	4.803613	Norman Luhn	08 Nov 2022
Maximal gaps below 1.00 · 10²²

Pattern d: d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56
_{Gap end} merit = 667817.550642 ·_∫dt / log¹⁵ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 15-tuplet	Merit	Who	When
1	17905159760365247370	17	17905159760365247387	4.160211	Norman Luhn	08 Nov 2022
2	26428395117451424370	17905159760365247387	44333554877816671757	2.962410	Norman Luhn	08 Nov 2022
3	60678331811848467990	90798766993022298227	151477098804870766217	4.304917	Norman Luhn	08 Nov 2022
4	170208590999501792010	460097037491731239617	630305628491233031627	7.449043	Norman Luhn	08 Nov 2022
5	181952045427479656980	3843012487245934329617	4024964532673413986597	4.326603	Norman Luhn	08 Nov 2022
6	213711154977170467890	6103761171273290995487	6317472326250461463377	4.430600	Norman Luhn	08 Nov 2022
7	262957505201243439510	6322319926959839062277	6585277432161082501787	5.389395	Norman Luhn	08 Nov 2022
Maximal gaps below 1.00 · 10²²

Pattern d: d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56
_{Gap end} merit = 667817.550642 ·_∫dt / log¹⁵ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 15-tuplet	Merit	Who	When
1	81345024020683500	1158722981124148367	1240068005144831867	0.027809	Norman Luhn	08 Nov 2022
2	1003222801207669770	1240068005144831867	2243290806352501637	0.302103	Norman Luhn	08 Nov 2022
3	5229964613725866210	3172206835341609797	8402171449067476007	1.042772	Norman Luhn	08 Nov 2022
4	7063711881732853620	9422138120166964847	16485850001899818467	1.055106	Norman Luhn	08 Nov 2022
5	9402144712901687670	16679857156627718057	26082001869529405727	1.182481	Norman Luhn	08 Nov 2022
6	13202593450794337590	50035247022695224217	63237840473489561807	1.196725	Norman Luhn	08 Nov 2022
7	16221211531184310000	71606347081895458487	87827558613079768487	1.313814	Norman Luhn	08 Nov 2022
8	17323770158004747360	87827558613079768487	105151328771084515847	1.318041	Norman Luhn	08 Nov 2022
9	52811743131804631170	138220583274981803327	191032326406786434497	3.383587	Norman Luhn	08 Nov 2022
10	53760328560100920030	470807023319315838887	524567351879416758917	2.417552	Norman Luhn	08 Nov 2022
11	102280075927617010500	682602241675669898237	784882317603286908737	4.073001	Norman Luhn	08 Nov 2022
12	125240508064038847830	974398068059013370427	1099638576123052218257	4.478077	Norman Luhn	08 Nov 2022
13	131948782266661670310	2159756252392414938917	2291705034659076609227	3.729551	Norman Luhn	08 Nov 2022
14	258926568259916659830	3940794344489079457307	4199720912748996117137	6.094257	Norman Luhn	08 Nov 2022
15	293683225790499104910	8656584739541825489057	8950267965332324593967	5.487557	Norman Luhn	08 Nov 2022
Maximal gaps below 1.00 · 10²²

Record Gaps Between Prime 15-tuplets Over All Patterns

_{Gap end} merit = 1711282.4735201 ·_∫dt / log¹⁵ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 15-tuplet	Merit	Who	When
1	6	11	17	6.725641	Norman Luhn	18 Jan 2023
2	1158722981124148350	17	1158722981124148367	2.892673	Norman Luhn	18 Jan 2023
3	5229964613725866210	3172206835341609797	8402171449067476007	2.672104	Norman Luhn	18 Jan 2023
4	8176842109164158340	17905159760365247387	26082001869529405727	2.607421	Norman Luhn	18 Jan 2023
5	13202593450794337590	50035247022695224217	63237840473489561807	3.066608	Norman Luhn	18 Jan 2023
6	16068633250000458954	64777971223063936127	80846604473064395081	3.435938	Norman Luhn	18 Jan 2023
7	24414869006900201214	166270537650069307283	190685406656969508497	3.899439	Norman Luhn	18 Jan 2023
8	26370658297525951794	470807023319315838887	497177681616841790681	3.065123	Norman Luhn	18 Jan 2023
9	44903964137948468280	524567351879416758917	569471316017365227197	5.022481	Norman Luhn	18 Jan 2023
10	51656273486207498550	823491664526499042287	875147938012706540837	5.034865	Norman Luhn	18 Jan 2023
11	54428723707573302360	1210392827233162795877	1264821550940736098237	4.720439	Norman Luhn	18 Jan 2023
12	63565395868366297710	1343339881857931111367	1406905277726297409077	5.336534	Norman Luhn	18 Jan 2023
13	67699545660476515500	3191426144896963821137	3259125690557440336637	4.380293	Norman Luhn	18 Jan 2023
14	84170188184334529290	3940794344489079457307	4024964532673413986597	5.109544	Norman Luhn	18 Jan 2023
15	109688713092436935996	6439563382863366440801	6549252095955803376797	5.749854	Norman Luhn	18 Jan 2023
16	155621007510816489816	8667033223088203698851	8822654230599020188667	7.465987	Norman Luhn	18 Jan 2023
Maximal gaps below 1.00 · 10²²