| k | first ... members | up to | pattern d | involved in the search | OEIS |
| 2 | 3 424 506 | 1.00 • 10 9 | d = 0, 2 | Norman Luhn | A001359 |
| 3 |
2 713 347 2 712 226 |
1.00 • 1010 1.00 • 1010 |
d = 0, 2, 6 d = 0, 4, 6 |
Norman Luhn |
A022004 A022005 |
| 4 | 8 398 278 | 1.00 • 1012 | d = 0, 2, 6, 8 | Norman Luhn; Karl Desfontaines | A007530 |
| 5 |
34 709 176 34 701 400 |
1.00 • 1014 1.00 • 1014 |
d = 0, 2, 6, 8, 12 d = 0, 4, 6, 10, 12 |
Norman Luhn; Karl Desfontaines |
A022006 A022007 |
| 6 | 12 432 129 | 1.00 • 1015 | d = 0, 4, 6, 10, 12, 16 | Norman Luhn; Karl Desfontaines | A022008 |
| 7 |
7 294 890 7 297 986 |
1.00 • 1016 1.00 • 1016 |
d = 0, 2, 6, 8, 12, 18, 20 d = 0, 2, 8, 12, 14, 18, 20 |
Norman Luhn; Karl Desfontaines |
A022009 A022010 |
| 8 |
14 696 303 14 692 771 10 932 210 |
5.00 • 1017 5.00 • 1017 1.00 • 1017 |
d = 0, 2, 6, 8, 12, 18, 20, 26 d = 0, 6, 8, 14, 18, 20, 24, 26 d = 0, 2, 6, 12, 14, 20, 24, 26 |
Norman Luhn; Hugo Pförtner Karl Desfontaines |
A022011 A022013 A022012 |
| 9 |
2 251 885 4 502 184 4 501 205 2 250 272 |
1.00 • 1018 1.00 • 1018 1.00 • 1018 1.00 • 1018 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30 d = 0, 2, 6, 12, 14, 20, 24, 26, 30 d = 0, 4, 6, 10, 16, 18, 24, 28, 30 d = 0, 4, 10, 12, 18, 22, 24, 28, 30 |
Norman Luhn; Karl Desfontaines |
A022545 A022546 A022547 A022548 |
| 10 |
5 118 442 5 117 631 |
1.00 • 1020 1.00 • 1020 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 |
Warut Roonguthai; Jörg Waldvogel Norman Luhn |
A027569 A027570 |
| 11 |
205 272 206 279 |
1.00 • 1020 1.00 • 1020 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36 |
Vladimir Vlesycit; Jörg Waldvogel Norman Luhn |
A213647 A213646 |
| 12 |
20 000 20 000 |
1.499 • 1020 1.478 • 1020 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 |
Vladimir Vlesycit; Jörg Waldvogel Matthew C. Anderson; Dana Jacobsen Norman Luhn |
A213645 A213601 |
| 13 |
5 012 6 305 5 290 6 264 5 307 5 579 |
1.16 • 1021 1.29 • 1021 1.29 • 1021 1.29 • 1021 1.29 • 1021 1.32 • 1021 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 |
Vladimir Vlesycit Matthew C. Anderson Dana Jacobsen Norman Luhn |
A257139 A257137 A257138 A257140 A257141 A214947 |
| 14 |
2 063 2 043 |
3.00 • 1022 3.00 • 1022 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 |
D. Betsis & S. Säfholm; Vladimir Vlesycit Tony Forbes; Jörg Waldvogel Tom Hadley; Dana Jacobsen Norman Luhn; Richard Fischer |
A257167 A257168 |
| 15 |
152 139 261 278 |
3.00 • 1022 3.00 • 1022 1.00 • 1022 1.00 • 1022 |
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 |
Tom Hadley; Jörg Waldvogel Dana Jacobsen; Jens Kruse Andersen; Jim Morton; Tony Forbes Norman Luhn; Richard Fischer |
A257304 A257307 A257305 A257306 |
| 16 |
30 37 |
1.00 • 1023 1.00 • 1023 |
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 |
Peter Leikauf; Jörg Waldvogel Tony Forbes |
A257369 A257370 |
| Prime 17-tuplet | |||
| Confirmed first initial members | Digits | When | Discoverer |
| d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66 | |||
|
734975534793324512717947 753314125249587933791677 1341829940444122313597407 |
24 24 25 |
2009 2009 Jun 2021 |
Jörg Waldvogel (PDF-document) Jörg Waldvogel Norman Luhn |
| d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66 | |||
|
13 47624415490498763963983 78314167738064529047713 83405687980406998933663 110885131130067570042703 163027495131423420474913 |
2 23 23 23 24 24 |
2001 2001 2001 2001 2001 |
Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel |
| d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 | |||
|
1620784518619319025971 2639154464612254121531 3259125690557440336631 124211857692162527019731 |
22 22 22 24 |
1997 1998 1998 2001 |
Jörg Waldvogel Jörg Waldvogel Tony Forbes Peter Leikauf & Jörg Waldvogel |
| d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66 | |||
|
17 37630850994954402655487 53947453971035573715707 174856263959258260646207 176964638100452596444067 207068890313310815346497 247620555224812786876877 322237784423505559739147 |
2 23 23 24 24 24 24 24 |
2001 1998 2001 2001 2001 2001 2001 |
Peter Leikauf & Jörg Waldvogel Tony Forbes Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel Peter Leikauf & Jörg Waldvogel |
| Prime 18-tuplet | |||
| Confirmed first initial members | Digits | When | Discoverer |
| d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 | |||
| 2845372542509911868266807 4530085223434265844952597 33755528632220819791319947 |
25 25 26 |
13 Nov 2000 14 Dec 2008 26 Jan 2009 |
Jörg Waldvogel & Peter Leikauf Jaroslaw Wroblewski Jaroslaw Wroblewski |
| d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 | |||
|
13 1906230835046648293290043 5660565448926871568362213 6072209091722134881897313 |
2 25 25 25 |
31 Jan 2001 16 Mar 2026 16 Mar 2026 |
Jörg Waldvogel & Peter Leikauf John Armitage John Armitage |
| Prime 19-tuplet | |||
| Confirmed first initial members | Digits | When | Discoverer |
| d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 | |||
|
13 362446150252909869314435203 428407853295060068253460573 |
2 27 27 |
24 Apr 2026 25 Apr 2026 |
John Armitage John Armitage |
| d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76 | |||
| 204480527545513119437376727 |
27 |
24 Apr 2026 |
John Armitage |
| d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 | |||
|
37 215150755851370395442356007 237171785884995638727760747 |
2 27 27 |
2 May 2026 1 May 2026 |
John Armitage John Armitage |
| d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76 | |||
| 630134041802574490482213901 656632460108426841186109951 |
27 27 |
9 Feb 2011 19 Feb 2011 |
Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski |
| Prime 20-tuplet | |||
| Confirmed first initial members | Digits | When | Discoverer |
| d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80 | |||
|
29 3941119827895253385301920029 38299233570943052294942174849 39433867730216371575457664399 97344384991448238094880899499 111286948968140923889225384099 121888742383899006588229597469 131353007727172552185076031849 138433730977092118055599751669 140005104744811513908777956909 140661282456312925227370009589 248283957683772055928836513589 260786413629117930695179308299 320430661688896578454772807699 349021296319127268299400177269 452101241612347545944528242469 494179332730633784520908832239 562422394447827908154562532159 593820854957327357933627374349 594750459626903777773717631519 639121700726230052098229452019 701870455949526598513130862539 764364269069907627842423582909 789292095021856634277511882469 807462397198198801670343382679 831504454982803270879178298359 957278727962618711849051282459 1094372814043722195189448411199 1153897621507935436463788957529 1188350591359110800209379560799 1236637204227022808686214288579 |
2 28 29 29 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 31 31 31 31 |
24 Jun 2014 9 Jan 2015 8 Jan 2015 11 Jul 2015 12 Aug 2015 9 Sep 2015 8 Oct 2015 8 Oct 2015 8 Oct 2015 8 Oct 2015 1 Aug 2016 7 Dec 2016 24 May 2017 24 May 2017 28 Jan 2018 23 May 2018 30 Aug 2018 23 Dec 2018 23 Dec 2018 23 Dec 2018 7 Apr 2019 17 Jul 2019 19 Aug 2019 25 Sep 2019 17 Oct 2019 23 Mar 2020 20 Oct 2020 26 Dec 2020 21 Jan 2021 23 May 2021 |
Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski |
| d = 0, 2, 6, 8, 12, 20, 26, 30, 36, 38, 42, 48, 50, 56, 62, 66, 68, 72, 78, 80 | |||
|
14374153072440029138813893241 17546231261175189855273591491 40814702190384518551961455541 58228410683159656922037124961 69611500022230424427263424221 114601431611676407654036210321 131900255854906356663126180791 154016910009801751265474541311 161375347518710752668754312691 182129285194786190875974840371 185986500598659638316208079201 187976201367296936422347098471 220974232729147341120519932981 227104691557231224024329351201 242145669497919182306126385461 352259532126245901475150592651 400327605553593948618674105711 403065917762608576939692599261 466435879660522367654413675211 562324418721793120042174985351 622803914376064301858782434521 667424014858149638371951648871 686962597479437604159786541481 839013472011818416634745523991 999627565307688186459783232931 1060475118776959297139870952701 1126002593922465663847897293731 1135540756371356698957890225821 |
29 29 29 29 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 31 31 31 |
6 Oct 2014 11 Dec 2014 6 Feb 2015 30 Apr 2015 22 Apr 2015 3 Sep 2015 20 Oct 2015 16 Dec 2015 3 Jan 2016 16 Mar 2016 16 Mar 2016 16 Mar 2016 31 May 2016 1 Aug 2016 1 Aug 2016 24 May 2017 7 Dec 2017 7 Dec 2017 15 Mar 2018 30 Aug 2018 27 Dec 2018 18 Feb 2019 27 Apr 2019 28 Oct 2019 19 Jun 2020 18 Sep 2020 17 Nov 2020 19 Dec 2020 |
Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski |
| Prime 21-tuplet | |||
| Confirmed first initial members | Digits | When | Discoverer |
| d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76, 82, 84 | |||
| 622803914376064301858782434517 | 30 | 27 Dec 2018 | Raanan Chermoni & Jaroslaw Wroblewski |
| d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80, 84 | |||
|
29 39433867730216371575457664399 138433730977092118055599751669 248283957683772055928836513589 |
2 29 30 30 |
8 Jan 2015 8 Oct 2015 1 Aug 2016 |
Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski Raanan Chermoni & Jaroslaw Wroblewski |