All Prime 9-tuplets, found by Riecoin

All Prime 8-tuplets, found by Riecoin

July 2026

Prime 8-tuplet

(Top-10)
5716442151089165064922536906892118300297679085070173223194211630150486820812580256946615561893513129727
• 571# + 987509658187511 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 (337 digits, 04 Jul 2026, Riecoin #2594064)

142322710736591640822449554543832055520071890622199087379932457346981407563738895215650182876140660688
• 571# + 942393875821241 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 (335 digits, 04 Jul 2026, Riecoin #2594097)

June 2026

Prime 9-tuplet

(NEW RECORD!)
837163292299378809809831143580882941184327783024037036655123255819762448981257171521983032505080537061887625
• 541# + 1364041179719831 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (328 digits, 22 Jun 2026, Riecoin #2587116) (new pattern record)

(Top-10)
42877569503566985613505820804776178189152416349942144609455614600649174825103220997588444265984257091094204
• 503# + 1504635130657271 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (316 digits, 14 Jun 2026, Riecoin #2582657)

4285751631692088000126518209968335837927754380804975143495528564341172180485736311713399226383303406
• 523# + 114023297140211 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (317 digits, 10 Jun 2026, Riecoin #2580307)

Prime Quintuplet

(Some smallest n-digits to given pattern)
10⁶⁰⁰ + 2186744428231227 + d, d = 0, 4, 6, 10, 12 (601 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁹² + 101148508918557 + d, d = 0, 4, 6, 10, 12 (593 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁸⁴ + 114409098481317 + d, d = 0, 4, 6, 10, 12 (585 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁷⁶ + 1679002253879787 + d, d = 0, 4, 6, 10, 12 (577 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁶⁸ + 215861169250827 + d, d = 0, 4, 6, 10, 12 (569 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁶⁰ + 21285858360477 + d, d = 0, 4, 6, 10, 12 (561 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵⁵² + 70438785232527 + d, d = 0, 4, 6, 10, 12 (553 digits, 03 Jun 2026, Richard J. Miller, Primo)
10⁵⁴⁴ + 555349392343797 + d, d = 0, 4, 6, 10, 12 (545 digits, 03 Jun 2026, Richard J. Miller, Primo)

May 2026

Prime 19-tuplet

237171785884995638727760747 + d, d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 (27 digits, 1 May 2026, John Armitage)

Smallest non-trivial to given pattern
215150755851370395442356007 + d, d = 0, 4, 6, 10, 16, 22, 24, 30, 34, 36, 42, 46, 52, 60, 64, 66, 70, 72, 76 (27 digits, 2 May 2026, John Armitage)

Prime 11-tuplet

First known with more than 100 decimal digits to given pattern
930197240142688565 • 257# / 66 − 12 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36 (120 digits, 15 May 2026, Ryan Propper; Serge Batalov) (new pattern record)

(NEW RECORD!)
13728478336951097431 • 257# / 66 − 24 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36 (121 digits, 10 May 2026, Ryan Propper; Serge Batalov) (new pattern record)

Prime 10-tuplet

(NEW RECORD!)
579710479520342109625940943530662371712401130676120845184496339991749901787102632038699464477823675
• 461# + 114189340938131 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (289 digits, 30 May 2026, Riecoin #2573586) (new pattern record)

Prime 9-tuplet

(Top-10)
1265409924273442189390068600950844823117816143681402022767091762553106665514078323071191380675721
• 541# + 1551874222066781 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (316 digits, 31 May 2026, Riecoin #2574207)

579710479520342109625940943530662371712401130676120845184496339991749901787102632038699464477823675
• 461# + 114189340938133 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 (289 digits, 30 May 2026, Riecoin #2573586) (new pattern record)

(NEW RECORD!)
7825155455302680838443868295240222508595426182186400355599126265708283132641994303176641265100579060057
• 541# + 727784228389061 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (323 digits, 16 May 2026, Riecoin #2565712) (new pattern record)

April 2026

Prime 19-tuplet

428407853295060068253460573 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 ( 27 digits, 25 Apr 2026, John Armitage ) (new pattern record)

First non-trivial to given pattern
362446150252909869314435203 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 ( 27 digits, 24 Apr 2026, John Armitage )

Smallest to given pattern
204480527545513119437376727 + d, d = 0, 4, 6, 10, 12, 16, 24, 30, 34, 40, 42, 46, 52, 54, 60, 66, 70, 72, 76 (27 digits, 24 Apr 2026, John Armitage)

Prime 9-tuplet

(NEW RECORD!)
37580549717273841362575577450020434041309777593805719349333005558376031534348903107117175124674939059012
• 521# + 727343907387941 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (318 digits, 28 Apr 2026, Riecoin #2555502) (new pattern record)

(Top-10)
1596912234078062520628348340144497421568623858681978611390222593206475875091194567842625059716133
• 523# + 235290683530361 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (314 digits, 16 Apr 2026, Riecoin #2548581)

March 2026

Prime Quintuplet

78531447842897 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
65570903845003 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
65424037203265 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
54187672664641 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
53855091173483 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
52345103788365 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 15 Mar 2026, Serge Batalov, EMSieve, CM)
46748874080435 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 14 Mar 2026, Serge Batalov, EMSieve, CM)
43883009289905 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 13 Mar 2026, Serge Batalov, EMSieve, CM)
38697755083345 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 08 Mar 2026, Serge Batalov, EMSieve, CM)
38268054455905 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 07 Mar 2026, Serge Batalov, EMSieve, CM)
37241409151249 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 07 Mar 2026, Serge Batalov, EMSieve, CM)
36367857549177 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 05 Mar 2026, Serge Batalov, EMSieve, CM)
33417752554103 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 05 Mar 2026, Serge Batalov, EMSieve, CM)
30315856703599 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 02 Mar 2026, Serge Batalov, EMSieve, CM)
30300464027503 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 01 Mar 2026, Serge Batalov, EMSieve, CM)

(Some smallest n-digits to given pattern)
10⁴⁸⁸ + 217642964345517 + d, d = 0, 4, 6, 10, 12 (489 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁴⁹⁶ + 104683701584547 + d, d = 0, 4, 6, 10, 12 (497 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵⁰⁴ + 236879349361107 + d, d = 0, 4, 6, 10, 12 (505 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵¹² + 173987707357797 + d, d = 0, 4, 6, 10, 12 (513 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵²⁰ + 34213679599107 + d, d = 0, 4, 6, 10, 12 (521 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵²⁸ + 253175346562737 + d, d = 0, 4, 6, 10, 12 (529 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵³⁶ + 372132099757827 + d, d = 0, 4, 6, 10, 12 (537 digits, 22 Mar 2026, Richard J. Miller, Primo)
10⁵⁶⁰ + 21285858360477 + d, d = 0, 4, 6, 10, 12 (561 digits, 22 Mar 2026, Richard J. Miller, Primo)

Prime 18-tuplet

6072209091722134881897313 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 ( 25 digits, 16 Mar 2026, John Armitage )
5660565448926871568362213 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 ( 25 digits, 16 Mar 2026, John Armitage )

February 2026

Prime 9-tuplet

(Top-10)
4508189394687569669892449233288341072142785900896972239317164025669247306161476293414736322317923577414
• 503# + 987351005463281 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (312 digits, 14 Feb 2026, Riecoin #2513332)

Prime 6-tuplet

(NEW RECORD!)
8063878333289 • 2647# / 2 − 8 + d, d = 0, 4, 6, 10, 12, 16 (1125 digits, 12 Feb 2026, Serge Batalov, EMSieve, CM) (new pattern record)

Prime Quintuplet

26800711521925 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 28 Feb 2026, Serge Batalov, EMSieve, CM)
25273062994487 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 27 Feb 2026, Serge Batalov, EMSieve, CM)
23151402614401 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 24 Feb 2026, Serge Batalov, EMSieve, CM)
22945951899105 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1605 digits, 21 Feb 2026, Serge Batalov, EMSieve, CM)
22013465312191 • 3727# / 2 − 8 + d, d = 0, 4, 6, 10, 12 (1605 digits, 19 Feb 2026, Serge Batalov, EMSieve, CM)
1932149198555 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1603 digits, 14 Feb 2026, Serge Batalov, EMSieve, CM)
112137465233 • 3727# / 2 − 4 + d, d = 0, 2, 6, 8, 12 (1602 digits, 14 Feb 2026, Serge Batalov, EMSieve, CM)

(Some smallest n-digits to given pattern)
10⁴⁸⁰ + 91583432652807 + d, d = 0, 4, 6, 10, 12 (481 digits, 17 Feb 2026, Richard J. Miller, Primo)
10⁴⁷² + 2824724779977 + d, d = 0, 4, 6, 10, 12 (473 digits, 17 Feb 2026, Richard J. Miller, Primo)
10⁴⁵⁶ + 189843672583947 + d, d = 0, 4, 6, 10, 12 (457 digits, 17 Feb 2026, Richard J. Miller, Primo)
10⁴⁴⁸ + 113273979485367 + d, d = 0, 4, 6, 10, 12 (449 digits, 17 Feb 2026, Richard J. Miller, Primo)
10⁴⁴⁰ + 13370788891407 + d, d = 0, 4, 6, 10, 12 (441 digits, 17 Feb 2026, Richard J. Miller, Primo)
10⁴³² + 47490101168907 + d, d = 0, 4, 6, 10, 12 (433 digits, 02 Feb 2026, Richard J. Miller, Primo)
10⁴²⁴ + 219964342585527 + d, d = 0, 4, 6, 10, 12 (425 digits, 02 Feb 2026, Richard J. Miller, Primo)
10⁴¹⁶ + 26114591682687 + d, d = 0, 4, 6, 10, 12 (417 digits, 02 Feb 2026, Richard J. Miller, Primo)

January 2026

Prime Quintuplet

(Some smallest n-digits to given pattern)
10⁴⁰⁰ + 18479740708437 + d, d = 0, 4, 6, 10, 12 (401 digits, 21 Jan 2026, Richard J. Miller, Primo)
10⁴⁰⁸ + 128789300130537 + d, d = 0, 4, 6, 10, 12 (409 digits, 21 Jan 2026, Richard J. Miller, Primo)

Prime Triplet

(NEW RECORD!)
57612705200181 • 2⁶⁹⁸⁰¹ − 1 + d, d = 0, 2, 6 (21026 digits, 25 Jan 2026, Serge Batalov, PolySieve, CM) (new pattern record)

Twin Prime

(Top-10)
152748736824915 • 2⁴⁸⁰⁴⁸⁰ ± 1 (144654 digits, 10 Jan 2026, Daniel Brockwell, Göran Schmidt, Carlos Eduardo Pinho, Michael Kwok, Richard Kapek, Stephan Vink, TwinGen, NewPGen, TPS, PRST)