| k | Largest Known Prime k-tuplets to given pattern | Digits | When | Who |
| 1 | 282589933 − 1 | 24862048 | 21 Dec 2018 | P. Laroche, G. Woltman, S. Kurowski, A. Blosser,et al (GIMPS) |
| 2 | 2996863034895 • 21290000 ± 1 | 388342 | 19 Sep 2016 | Tom Greer, TwinGen, PrimeGrid, LLR |
| 3 | 4111286921397 • 266420 - 1 + d, d = 0, 2, 6 | 20008 | 24 Apr 2019 | Peter Kaiser, Polysieve, LLR, Primo |
| 3 | 6521953289619 • 255555 - 5 + d, d = 0, 4, 6 | 16737 | 30 Apr 2013 | Peter Kaiser, Primo |
| 4 | 667674063382677 • 233608 -1 + d, d = 0, 2, 6, 8 | 10132 | 27 Feb 2019 | Peter Kaiser, Primo |
| 5 | 585150568069684836 • 7757# / 85085 + 5 + d, d = 0, 2, 6, 8, 12 | 3344 | 06 Mar 2022 | Peter Kaiser, OpenPFGW, Primo |
| 5 | 566761969187 • 4733# / 2 - 8 + d, d = 0, 4, 6, 10, 12 | 2034 | Dec 2020 | Serge Batalov, NewPgen, OpenPFGW, Primo |
| 6 | 23700 + 33888977692820810260792517451 + d, d = 0, 4, 6, 10, 12, 16 | 1114 | 8 Nov 2021 | Vidar Nakling, Primo, Sixfinder |
| 7 |
113225039190926127209 • 2339# / 57057 + 1 + d, d = 0, 2, 6, 8, 12, 18, 20 |
1002 |
27 Jan 2021 |
Peter Kaiser |
| 7 | 4733578067069 • 940# + 626609 + d, d = 0, 2, 8, 12, 14, 18, 20 | 402 | May 2016 | Norman Luhn, OpenPFGW, Primo |
| 8 | 697723422149271424870176724491962624555 • 701# + 145888993435301 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 |
332 |
28 Apr 2022 |
Michalis Christou, Rieminer 0.91 |
| 8 |
5459882419001036187528246957868441845965757336246132447166042288307309966224027 8837985413217294784653805 • 509# + 226374233346623 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 |
316 |
30 Oct 2021 |
Riecoin #1607166 |
| 8 | 29995576270632 • 550# + 1277 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 |
236 |
Jun 2014 |
Norman Luhn |
| 9 |
762022957483737760368751900146257567932429070353835303845101414065336601637522344113784372 6785037341 • 503# + 220469307413891 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 |
309 | 16 Feb 2022 | Bielawski Mathematicians |
| 9 | 387833514641724600357029749119397331285062620621983133723181869572568059514167753188325960 698719230 • 467# + 226193845148629 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
294 | 27 Oct 2021 | Riecoin #1605403 |
| 9 | 143156149560304187478674888952081995667508735289083169762741742082381914349370114072874796 76495550 • 449# + 226554621544607 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 |
282 | 12 Sep 2021 | Riecoin #1579367 |
| 9 |
290901656335108169864195656135043662615199446375386143995339722400236057821426952579658098 504166333411889 • 401# + 380284918609483 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 |
269 | 27 Jul 2021 | tentuple |
| 10 | 143156149560304187478674888952081995667508735289083169762741742082381914349370114072874796 76495550 • 449# + 226554621544607 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 |
282 | 12 Sep 2021 | Riecoin #1579367, PrimaPoolSolo |
| 10 | 290901656335108169864195656135043662615199446375386143995339722400236057821426952579658098 504166333411889 • 401# + 380284918609481 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 |
269 | 27 Jul 2021 | tentuple |
| 11 | 1324379573137273319190249467515414226361218996699259352225156098159780319762102415257 + 49376500222690335 • 229# + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 |
108 | 23 Sep 2019 | Peter Kaiser, David Stevens, Polysieve, OpenPFGW, Primo |
| 11 | 613176722801194 • 151# + 177321223 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36 | 75 | 30 Sep 2014 | Michael Stocker, Primo |
| 12 | 13243795731372733191902494675154142263612189966992593522251560981597803197621024152571147501 + 27407861785763183 • 229# + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 |
108 | 23 Sep 2019 | Peter Kaiser, David Stevens, Polysieve, OpenPFGW, Primo |
| 12 | 613176722801194 • 151# + 177321217 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 | 75 | 30 Sep 2014 | Michael Stocker, Primo |
| 13 | 9985637467 • 139# + 3629868888791261 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 | 66 | 01 Oct 2021 | Roger Thompson |
| 13 | 4135997219394611 • 109# + 117092849 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 | 61 | 23 Mar 2017 | Norman Luhn |
| 13 | 14815550 • 107# + 4385574275277313 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 | 50 | Feb 2013 | Roger Thompson |
| 13 | 381955327397348 • 79# + 18393211 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 | 46 | Dec 2007 | Norman Luhn |
| 13 | 381955327397348 • 79# + 18393209 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 | 46 | Dec 2007 | Norman Luhn |
| 13 | 100000000000000000000002004740564798426955633 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 | 45 | 06 Mar 2022 | Norman Luhn |
| 14 | 14815550 • 107# + 4385574275277311 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 | 50 | 05 Feb 2013 | Roger Thompson |
| 14 | 381955327397348 • 79# + 18393209 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 | 46 | Dec 2007 | Norman Luhn |
| 15 | 33554294028531569 • 61# + 57800747 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 | 40 | 25 Jan 2017 | Norman Luhn |
| 15 | 10004646546202610858599716515809907 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 | 35 | Sep 2012 | Roger Thompson |
| 15 | 107173714602413868775303366934621 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 | 33 | Apr 2008 | Jens Kruse Andersen |
| 15 | 100000008317726120972779285703 + d, d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 | 30 | Apr 2021 | Norman Luhn |
| 16 | 322255 • 73# + 1354238543317302647 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 | 35 | 18 Nov 2016 | Roger Thompson |
| 16 | 94 • 79# + 1341680294611244014363 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 | 33 | Feb 2021 | Roger Thompson |
| 17 | 3684 • 73# + 880858118723497737821 + d, d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 | 33 | 5 Feb 2021 | Roger Thompson |
| 17 | 100845391935878564991556707107 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66 | 30 | Feb 2013 | Roger Thompson |
| 17 | 11413975438568556104209245223 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66 | 29 | Jan 2012 | Roger Thompson |
| 17 | 5867208169546174917450987997 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66 | 28 | Mar 2014 | Raanan Chermoni & Jaroslaw Wroblewski |
| 18 | 5867208169546174917450987997 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 | 28 | Mar 2014 | Raanan Chermoni & Jaroslaw Wroblewski |
| 18 | 183837276562811649018077773 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 | 27 | Apr 2010 | Jaroslaw Wroblewski |
| 19 | 622803914376064301858782434517 + d, d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76 | 30 | 27 Dec 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 19 | 248283957683772055928836513597 + d, d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 | 30 | 01 Aug 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| 19 | 2406179998282157386567481191 + d, d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76 | 28 | Dec 2012 | Raanan Chermoni & Jaroslaw Wroblewski |
| 19 | non-trivial is unknown ! d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 | - | - | - |
| 20 | 1236637204227022808686214288579 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80 |
31 | 23 May 2021 | Raanan Chermoni & Jaroslaw Wroblewski |
| 20 | 1135540756371356698957890225821 + d, d = 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80 |
31 | 19 Dec 2020 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 622803914376064301858782434517 + d, d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84 |
30 | 27 Dec 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| 21 | 248283957683772055928836513589 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84 |
30 | 01 Aug 2016 | Raanan Chermoni & Jaroslaw Wroblewski |
| Early discovery of non-trivial prime k-tuplets to given pattern | ||||
| k | Digits | Prime k-tuplet | Who | When |
| <12 | - | No reliable information | - | - |
| 12 | 15 | 380284918609481 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 | D. Betsis & S. Säfholm | 1982 |
| 12 | 13 | 1418575498567 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 | D. Betsis & S. Säfholm | 1982 |
| 13 | 16 | 1707898733581273 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 | D. Betsis & S. Säfholm | 1982 |
| 13 | 16 | 7697168877290909 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 | D. Betsis & S. Säfholm | 1982 |
| 13 | 16 | 7933248530182091 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 | D. Betsis & S. Säfholm | 1982 |
| 13 | 16 | 4289907938811613 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 | D. Betsis & S. Säfholm | 1982 |
| 13 | 15 | 186460616596321 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 | D. Betsis & S. Säfholm | 1982 |
| 13 | 14 | 10527733922579 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 | D. Betsis & S. Säfholm | 1982 |
| 14 | 17 | 79287805466244209 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 | D. Betsis & S. Säfholm | 1982 |
| 14 | 17 | 21817283854511261 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 | D. Betsis & S. Säfholm | 1982 |
| 15 | 21 | 944716030613719714367 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 | Tony Forbes | 1997 |
| 15 | 21 | 348214184662549960583 + d, d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 | Jörg Waldvogel | 1999 |
| 15 | 21 | 590079087912119470781 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 | Jörg Waldvogel | 1999 |
| 15 | 21 | 347709450746519734877 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 | Jörg Waldvogel | 1996 |
| 16 | 21 | 695874886175252911063 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 | Jörg Waldvogel | 1996 |
| 16 | 21 | 347709450746519734877 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 | Jörg Waldvogel | 1996 |
| 17 | 25 | 5797342442373866594673457 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66 | Jaroslaw Wroblewski | Dec 2008 |
| 17 | 23 | 53947453971035573715707 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66 | Tony Forbes | 1998 |
| 17 | 23 | 47624415490498763963983 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66 | Jörg Waldvogel | 2001 |
| 17 | 22 | 1620784518619319025971 + d, d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 | Jörg Waldvogel | 1997 |
| 18 | 25 | 2845372542509911868266807 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 | Jörg Waldvogel & Peter Leikauf | 14 Nov 2000 |
| 18 | 25 | 1906230835046648293290043 + d, 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 | Jörg Waldvogel & Peter Leikauf | 31 Jan 2001 |
| 19 | 30 | 622803914376064301858782434517 + d, 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76 | Raanan Chermoni & Jaroslaw Wroblewski | 27 Dec 2018 |
| 19 | 29 | 39433867730216371575457664407 + d, d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 | Raanan Chermoni & Jaroslaw Wroblewski | 8 Jan 2015 |
| 19 | 27 | 630134041802574490482213901 + d, d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76 | Raanan Chermoni & Jaroslaw Wroblewski | 9 Feb 2011 |
| 20 | 29 | 14374153072440029138813893241 + d, d = 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80 | Raanan Chermoni & Jaroslaw Wroblewski | 06 Oct 2014 |
| 20 | 28 | 3941119827895253385301920029 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80 | Raanan Chermoni & Jaroslaw Wroblewski | 24 Jun 2014 |
| 21 | 30 | 622803914376064301858782434517 + d, 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84 | Raanan Chermoni & Jaroslaw Wroblewski | 27 Dec 2018 |
| 21 | 29 | 39433867730216371575457664399 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84 | Raanan Chermoni & Jaroslaw Wroblewski | 8 Jan 2015 |