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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 2.746376Norman Luhn08 Nov 2022
2 63939610598713839990 140245881111654813611 204185491710368653601 1.136275Norman Luhn08 Nov 2022
3 202996042954228073550 238931301405879137171 441927344360107210721 2.913054Norman Luhn08 Nov 2022
4 317073923236977286380 590079087912119470781 907153011149096757161 3.539010Norman Luhn08 Nov 2022
5 357944865874561195230 932043368797178903381 1289988234671740098611 3.529026Norman Luhn08 Nov 2022
6 366342536144399404590 3191291677985662206071 3557634214130061610661 2.566673Norman Luhn08 Nov 2022
7 493060964581874338650 3915962764770027206351 4409023729351901545001 3.242472Norman Luhn08 Nov 2022
8 609034703996754115080 4707613344406022195261 5316648048402776310341
3.787567
 Norman Luhn08 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 0.084296Norman Luhn08 Nov 2022
2 11145093752153421060 16222575536498135633 27367669288651556693 0.392214Norman Luhn08 Nov 2022
3 20605240474299551070 27367669288651556693 47972909762951107763 0.604148Norman Luhn08 Nov 2022
4 34324229637001534230 49198349218890756713 83522578855892290943 0.833941Norman Luhn08 Nov 2022
5 58328628796205818050 83522578855892290943 141851207652098108993 1.191917Norman Luhn08 Nov 2022
6 138584847566689253730 195690251815182929633 334275099381872183363 2.150492Norman Luhn08 Nov 2022
7 163220651445114222960 499698524000527366343 662919175445641589303 1.968333Norman Luhn08 Nov 2022
8 227354726001970637070 662919175445641589303 890273901447612226373 2.504557Norman Luhn08 Nov 2022
9 329167222840040274690 1857353909915640401093 2186521132755680675783 2.695682Norman Luhn08 Nov 2022
10 647010090582023518350 2186521132755680675783 2833531223337704194133
4.963696
 Norman Luhn08 Nov 2022
11 742586625718671543810 5349055849970305427783 6091642475688976971593 4.438856Norman Luhn08 Nov 2022
12 882599505501239435910 7388399412888127849043 8270998918389367284953 4.803613Norman Luhn08 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 4.160211Norman Luhn08 Nov 2022
2 26428395117451424370 17905159760365247387 44333554877816671757 2.962410Norman Luhn08 Nov 2022
3 60678331811848467990 90798766993022298227 151477098804870766217 4.304917Norman Luhn08 Nov 2022
4 170208590999501792010 460097037491731239617 630305628491233031627
7.449043
 Norman Luhn08 Nov 2022
5 181952045427479656980 3843012487245934329617 4024964532673413986597 4.326603Norman Luhn08 Nov 2022
6 213711154977170467890 6103761171273290995487 6317472326250461463377 4.430600Norman Luhn08 Nov 2022
7 262957505201243439510 6322319926959839062277 6585277432161082501787 5.389395Norman Luhn08 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 0.027809Norman Luhn08 Nov 2022
2 1003222801207669770 1240068005144831867 2243290806352501637 0.302103Norman Luhn08 Nov 2022
3 5229964613725866210 3172206835341609797 8402171449067476007 1.042772Norman Luhn08 Nov 2022
4 7063711881732853620 9422138120166964847 16485850001899818467 1.055106Norman Luhn08 Nov 2022
5 9402144712901687670 16679857156627718057 26082001869529405727 1.182481Norman Luhn08 Nov 2022
6 13202593450794337590 50035247022695224217 63237840473489561807 1.196725Norman Luhn08 Nov 2022
7 16221211531184310000 71606347081895458487 87827558613079768487 1.313814Norman Luhn08 Nov 2022
8 17323770158004747360 87827558613079768487 105151328771084515847 1.318041Norman Luhn08 Nov 2022
9 52811743131804631170 138220583274981803327 191032326406786434497 3.383587Norman Luhn08 Nov 2022
10 53760328560100920030 470807023319315838887 524567351879416758917 2.417552Norman Luhn08 Nov 2022
11 102280075927617010500 682602241675669898237 784882317603286908737 4.073001Norman Luhn08 Nov 2022
12 125240508064038847830 974398068059013370427 1099638576123052218257 4.478077Norman Luhn08 Nov 2022
13 131948782266661670310 2159756252392414938917 2291705034659076609227 3.729551Norman Luhn08 Nov 2022
14 258926568259916659830 3940794344489079457307 4199720912748996117137
6.094257
 Norman Luhn08 Nov 2022
15 293683225790499104910 8656584739541825489057 8950267965332324593967 5.487557Norman Luhn08 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