← Additions in 2021

December 2021

Prime 10-tuplet

(Smallest with 95 digits to given pattern)
10000000000000000000000000000000000000000000000000000000000000000000000000008390609070050144107 + d
d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 (95 digits, 27 Dec 2021, Norman Luhn)
10000000000000000000000000000000000000000000000000000000000000000000000000088417260467478988171 + d
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (95 digits, 25 Dec 2021, Norman Luhn)

November 2021

Prime 10-tuplet

(Smallest with 90 digits to given pattern)
100000000000000000000000000000000000000000000000000000000000000000000030470680515123366127 + d
d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 (90 digits, 05 Nov 2021, Norman Luhn)

Prime 6-tuplet

(NEW RECORD!)
(THE 2ND KNOWN TITANIC PRIME SEXTUPLET !!!)
2³⁷⁰⁰ + 33888977692820810260792517451 + d, d = 0, 4, 6, 10, 12, 16 (1114 digits, 21 Nov 2021 (found on 8 Nov 2021), Vidar Nakling, Primo, Sixfinder)

Prime Quintuplet

2³⁷⁰⁰ + 33888977692820810260792517455 + d, d = 0, 2, 6, 8, 12 (1114 digits, 21 Nov 2021 (found on 8 Nov 2021), Vidar Nakling, Primo, Sixfinder)
2³⁷⁰⁰ + 33888977692820810260792517451 + d, d = 0, 4, 6, 10, 12 (1114 digits, 21 Nov 2021 (found on 8 Nov 2021), Vidar Nakling, Primo, Sixfinder)

Prime Triplet

14059969053 • 2³⁶⁶⁷² - 5 + d, d = 0, 4, 6 (11050 digits, Jun 2018, Serge Batalov, NewPgen, OpenPFGW, Primo)

October 2021

Prime 13-tuplet

(NEW RECORD!)
9985637467 • 139# + 3629868888791261 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 (66 digits, 01 Oct 2021, Roger Thompson)

Prime 12-tuplet

9985637467 • 139# + 3629868888791261 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 (66 digits, 01 Oct 2021, Roger Thompson)
9985397181 • 139# + 249386599747880711 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 (66 digits, 01 Oct 2021, Roger Thompson)

Prime 7-tuplet

51888697286859758286462601904903121005322180580003165953085452054919486657902743310103017711916802670
• 541# + 226374233346629 + d , d = 0, 2, 8, 12, 14, 18, 20 (321 digits , 30 Oct 2021, Riecoin #1607204)

9888625633802605692813554675305569762963812859296733912002209782489914868945557733991918300434626412299934
• 521# + 226554621544619 + d , d = 0, 2, 8, 12, 14, 18, 20 (321 digits , 30 Oct 2021, Riecoin #1607205)

September 2021

Prime 10-tuplet

(Smallest with 90 digit to given pattern)
100000000000000000000000000000000000000000000000000000000000000000000046561545070308183901 + d
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (90 digits, 26 Sep 2021, Norman Luhn)

(NEW RECORD!)
14315614956030418747867488895208199566750873528908316976274174208238191434937011407287479676495550
• 449# + 226554621544607 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 (282 digits, 12 Sep 2021, Riecoin #1579367, PrimaPoolSolo)

Prime Quadruplet

101406820312263 • 2¹²⁰⁴² - 1 + d, d = 0, 2, 6, 8 (3640 digits, Jun 2018, Serge Batalov, OpenPFGW, NewPGen,Primo)

Prime Twins

160204065 • 2²⁶²¹⁴⁸ ±1 (78923 digits, Aug 2021, Erwin Doescher, LLR)

August 2021

Prime 17-tuplet

(Smallest with 25 digits to given pattern)
1024494443639408527082233 + d , d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66 (25 digits, 20 Aug 2021, Norman Luhn)
1234254817970443433617451 + d , d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 (25 digits, 20 Aug 2021, Norman Luhn)
1271960773255490350812797 + d , d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56, 62, 66 (25 digits, 20 Aug 2021, Norman Luhn)
1341829940444122313597407 + d , d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66 (25 digits, 20 Aug 2021, Norman Luhn)

Prime 14-tuplet

(Smallest with 40 digits to given pattern)
1000000000000000014210159036148101380471 + d , d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 (40 digits, 20 Aug 2021, Norman Luhn)

Prime 10-tuplet

(Smallest with 85 digits to given pattern)
1000000000000000000000000000000000000000000000000000000000000000022997034170524527571 + d
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (85 digits, 28 Aug 2021,Norman Luhn)
1000000000000000000000000000000000000000000000000000000000000000001250579054870603617 + d
d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 (85 digits, 28 Aug 2021, Norman Luhn)

(Smallest googol)
10000000000000000000000000000000000000000000000000000000000000000000000000000000000426534752174683621 + d
d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (101 digits, 23 Aug 2021, Norman Luhn)
10000000000000000000000000000000000000000000000000000000000000000000000000000000083943549068390212567 + d
d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32 (101 digits, 23 Aug 2021, Norman Luhn)

(NEW RECORD!)
(First known with more than 200 digits)
290901656335108169864195656135043662615199446375386143995339722400236057821426952579658098504166333411889
• 401# + 380284918609481 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32 (269 digits, 27 Jul 2021, tentuple)

Prime 9-tuplet

(NEW RECORD!)
(First known with more than 300 digits)
3662943827507055653453285926700023101620402654194921037456914703634367453333223968004841750810165461896894501
• 463# + 2325810733931801 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (302 digits, 22 Aug 2021, #1567399, PrimaPoolSolo)

(NEW RECORD!)
1620259924615470570706663156278905026372754732844252658390408090245313172792664271166384219300680488342402961778
• 450# + 1487854607298791 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (296 digits, 20 Aug 2021, PrimaPoolSolo)

Prime 6-tuplet

(Smallest with 600 digits)
10⁵⁹⁹ + 314360191056418137 + d, d = 0, 4, 6, 10, 12, 16 (600 digits, 20 Aug 2021, Norman Luhn)

Twin Primes

17976255129 • 2¹⁸³²⁴¹ ± 1 (55172 digits, May 2021, Frank Doornink, TwinGen, OpenPFGW)

Handing over from Tony Forbes

June 2021

Prime 20-tuplet

(NEW RECORD!)
1236637204227022808686214288579 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80
(31 digits, May 23, 2021, Raanan Chermoni & Jaroslaw Wroblewski)

Prime 9-tuplet

(NEW RECORD!)
1712614057442769844303829275179903227939212023517518611133550038875063021572377776139492086991109134537768
• 421# + 980125031081081 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (277 digits, 29 May 2021, XpoolX)

Prime Triplet

(The smallest 3000, 4000 and 5000 digit proven prime triplets. Certificates was uploaded to factordb.com)
10²⁹⁹⁹ + 25740029131 + d, d = 0, 2, 6 (3000 digits, May 2021, Norman Luhn)
10²⁹⁹⁹ + 37274603937 + d, d = 0, 4, 6 (3000 digits, May 2021, Norman Luhn)
10³⁹⁹⁹ + 182402621497 + d, d = 0, 2, 6 (4000 digits, May 2021, Norman Luhn)
10³⁹⁹⁹ + 243095638113 + d, d = 0, 4, 6 (4000 digits, May 2021, Norman Luhn)
10⁴⁹⁹⁹ + 70852892827 + d, d = 0, 2, 6 (5000 digits, May 2021, Norman Luhn)
10⁴⁹⁹⁹ + 244793127627 + d, d = 0, 4, 6 (5000 digits, May 2021, Norman Luhn)

April 2021

Prime 15-tuplet

(The smallest with 30-digit to given pattern)
100000001341915517111319670637 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 36, 42, 44, 50, 54, 56 (30 digits, Apr 2021, Norman Luhn)
100000001651438068367136632687 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56 (30 digits, Apr 2021, Norman Luhn)
100000008317726120972779285703 + d, d = 0, 6, 8, 14, 20, 24, 26, 30, 36, 38, 44, 48, 50, 54, 56 (30 digits, Apr 2021, Norman Luhn)
100000005745569203832854981801 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50, 56 (30 digits, Apr 2021, Norman Luhn)

Prime 9-tuplet

(NEW RECORD!)
22155746670321555200168732483559041439782078981076434573266849483171717294207993515336980845763232977257432862782607440
• 313# + 855709 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 (247 digits, 10 Apr 2021, ric1quau6a3z8qu4ar204pwgz2vdndyta455vsn99lq)

(The smallest with 101-digit to given pattern)
10¹⁰⁰ + 715673142884481067 + d, d = 0, 2, 6, 12, 14, 20, 24, 26, 30 (101 digits, Apr 2021, Norman Luhn)
10¹⁰⁰ + 176872574833767633 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30 (101 digits, Apr 2021, Norman Luhn)
10¹⁰⁰ + 426534752174683621 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30 (101 digits, Apr 2021, Norman Luhn)
10¹⁰⁰ + 1165893539316503169 + d, d = 0, 4, 10, 12, 18, 22, 24, 28, 30 (101 digits, Apr 2021, Norman Luhn)

March 2021

Prime 14-tuplet

(Smallest with 40 digits to given pattern)
1000000000000000000349508508460276218889 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 (40 digits, 10 Mar 2021, Norman Luhn)

Prime 13-tuplet

(Smallest with 40 digits to given pattern)
1000000000000000002713562652524314606953 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 (40 digits, 10 Mar 2021, Norman Luhn)
1000000000000000002334523699629280598673 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 (40 digits, 10 Mar 2021, Norman Luhn)
1000000000000000000368816080526066037739 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 (40 digits, 10 Mar 2021, Norman Luhn)
1000000000000000000349508508460276218891 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 (40 digits, 10 Mar 2021, Norman Luhn)
1000000000000000000349508508460276218889 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 (40 digits, 10 Mar 2021, Norman Luhn)
1000000000000000000282197071067938130221 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 (40 digits, 10 Mar 2021, Norman Luhn)

Prime 12-tuplet

(Smallest with 50 digits to given pattern)
10000000000000000000000000000929532973818094710897 + d, d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 (50 digits, 24 Feb 2021, Norman Luhn)
10000000000000000000000000000896396147387349765031 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 (50 digits, 24 Feb 2021, Norman Luhn)

Prime 8-tuplet

(NEW RECORD!)
6879356578124627875380298699944709053335 • 677# + 980125031081081 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 (324 digits, 12 Mar 2021, Michalis Christou)

February 2021

Prime 17-tuplet

(NEW RECORD!)
150048143328514263089612453401301 + d, d = 0, 6, 8, 12, 18, 20, 26, 32, 36, 38, 42, 48, 50, 56, 60, 62, 66 (33 digits, 5 Feb 2021, Roger Thompson)

Prime 16-tuplet

302458608131364933637125192102583 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 (33 digits, 5 Feb 2021, Roger Thompson)

(Smallest with 25 digits to given pattern)
1015074281315414986743013 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60 (25 digits, 5 Feb 2021, Norman Luhn)
1008037335701436528651167 + d, d = 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60 (25 digits, 5 Feb 2021, Norman Luhn)

Prime 14-tuplet

(Smallest with 35 digits to given pattern)
10000000000001275924044876917671361 + d, d = 00, 02, 06, 08, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000009283441665311798539399 + d, d = 00, 02, 08, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48, 50 (35 digits, 5 Feb 2021, Norman Luhn)

Prime 13-tuplet

(Smallest with 35 digits to given pattern)
10000000000000325778825790175217703 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000000324000701496110723931 + d, d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000000108412629077454977119 + d, d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000000094989640220894283993 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000000054122451329461300669 + d, d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48 (35 digits, 5 Feb 2021, Norman Luhn)
10000000000000015141548551355951851 + d, d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48 (35 digits, 5 Feb 2021, Norman Luhn)

Prime 7-tuplet

(NEW RECORD!)
( FIRST KNOWN TITANIC PRIME SEPTUPLET !!!)
113225039190926127209 • 2339# / 57057 + 1 + d, d = 0, 2, 6, 8, 12, 18, 20 (1002 digits, 27 Jan 2021, Peter Kaiser)

January 2021

Prime 20-tuplet

(NEW RECORD!)
1188350591359110800209379560799 + d, d = 0, 2, 8, 12, 14, 18, 24, 30, 32, 38, 42, 44, 50, 54, 60, 68, 72, 74, 78, 80
(31 digits, January 21, 2021, Raanan Chermoni & Jaroslaw Wroblewski)

Prime 8-tuplet

(Smallest with 150 digits to given pattern)
10¹⁴⁹ + 177107310312127411 + d, d = 0, 2, 6, 8, 12, 18, 20, 26 (150 digits, January 2021, Norman Luhn)
10¹⁴⁹ + 883945334707753267 + d, d = 0, 2, 6, 12, 14, 20, 24, 26 (150 digits, January 2021, Norman Luhn)
10¹⁴⁹ + 935628779313782743 + d, d = 0, 6, 8, 14, 18, 20, 24, 26 (150 digits, January 2021, Norman Luhn)

Prime Quintuplet

(NEW RECORD!)
566761969187 • 4733# / 2 -8 + d, d = 0, 4, 6, 10, 12 (2034 digits, from 6 Dec 2020, Serge Batalov, NEWPGEN, OPENPFGW, PRIMO)