The largest known & early discovery of a non-trivial prime k-tuplets to given pattern
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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 17823192282008874449172703428792123231110 • 771# + 145933845312371 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 362 12 Jan 2023 Michalis Christou, rieMiner
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 200 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 5 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


k Early discovery of a non-trivial prime k-tuplets to given pattern Digits When? Who?
<12 No reliable information - - -
12 380284918609481 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 15 1982 D. Betsis & S. Säfholm
12 1418575498567 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 13 1982 D. Betsis & S. Säfholm
13 1707898733581273 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 16 1982 D. Betsis & S. Säfholm
13 7697168877290909 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 16 1982 D. Betsis & S. Säfholm
13 7933248530182091 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 16 1982 D. Betsis & S. Säfholm
13 4289907938811613 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 16 1982 D. Betsis & S. Säfholm
13 186460616596321 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 15 1982 D. Betsis & S. Säfholm
13 10527733922579 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 14 1982 D. Betsis & S. Säfholm
14 79287805466244209 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 17 1982 D. Betsis & S. Säfholm
14 21817283854511261 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 17 1982 D. Betsis & S. Säfholm
15 944716030613719714367 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 21 1997 Tony Forbes
15 348214184662549960583 + d, d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 21 1999 Jörg Waldvogel
15 590079087912119470781 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 21 1999 Jörg Waldvogel
15 347709450746519734877 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 21 1996 Jörg Waldvogel
16 695874886175252911063 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 21 1996 Jörg Waldvogel
16 347709450746519734877 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 21 1996 Jörg Waldvogel
17 5797342442373866594673457 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66 25 Dec 2008 Jaroslaw Wroblewski
17 53947453971035573715707 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66 23 1998 Tony Forbes
17 47624415490498763963983 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66 23 2001 Jörg Waldvogel
17 1620784518619319025971 + d, d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 22 1997 Jörg Waldvogel
18 2845372542509911868266807 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 25 14 Nov 2000 Jörg Waldvogel & Peter Leikauf
18 1906230835046648293290043 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 25 31 Jan 2001 Jörg Waldvogel & Peter Leikauf
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 39433867730216371575457664407 + d, d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 29 8 Jan 2015 Raanan Chermoni & Jaroslaw Wroblewski
19 630134041802574490482213901 + d, d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76 27 9 Feb 2011 Raanan Chermoni & Jaroslaw Wroblewski
19 only trivial example is known! 13 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 2 - -
20 14374153072440029138813893241 + d, d = 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80 29 06 Oct 2014 Raanan Chermoni & Jaroslaw Wroblewski
20 3941119827895253385301920029 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80 28 24 Jun 2014 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 39433867730216371575457664399 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84 29 8 Jan 2015 Raanan Chermoni & Jaroslaw Wroblewski