Cunningham Chain records

The largest known Cunningham Chains of length n
n	kind	Cunningham chains of length n	k's	Digits	When	Discoverer	History
2	1st 2nd	Sophie Germain2618163402417 • 2^{1290000 + k} − 1 213778324725 • 2^{561417 + k} + 1	0,1	388342 169015	29 Feb 2016 17 Mar 2023	Dr. James Scott Brown, PrimeGrid, TwinGen, LLR Ryan Propper, Serge Batalov
3	1st 2nd	1128330746865 • 2^{66439 + k} − 1 214923707595 • 2^{49071 + k} + 1	0..2	20013 14784	17 Feb 2020 2 Jan 2025	Dr. Michael Paridon, NewPGen, OpenPFGW Serge Batalov, NewPGen, OpenPFGW
4	1st 2nd	93003628384 • 10111# • 2^k − 1 162229493368 • 11171# • 2^k + 1	0..3	4362 4809	16 Feb 2025 17 Jul 2026	Serge Batalov, NewPGen, OpenPFGW Serge Batalov, NewPGen, OpenPFGW
5	1st 2nd	475676794046977267 • 4679# • 2^k − 1 181439827616655015936 • 4673# • 2^k + 1	0..4	2019 2018	16 Feb 2024 8 Nov 2016	Shusuke Kubota; NewPGen, OpenPFGW Andrey Balyakin
6	1st 2nd	2799873605326 • 2371# • 2^k − 1 37015322207094 • 2339# • 2^k + 1	0..5	1016 1001	25 Mar 2015 28 Jan 2025	Serge Batalov, NewPGen, OpenPFGW Serge Batalov, NewPGen, OpenPFGW
7	1st 2nd	190721977563410 • 1201# • 2^k − 1 11696328195950 • 1201# • 2^k + 1	0..6	518 517	21 Apr 2026 10 Apr 2026	Serge Batalov Serge Batalov
8	1st 2nd	72368211643254 • 727# • 2^k − 1 2373007846680317952 • 761# • 2^k + 1	0..7	315 337	11 Apr 2026 10 Mar 2016	Serge Batalov Andrey Balyakin
9	1st 2nd	553374939996823808 • 593# • 2^k − 1 316094278095659 • 479# • 2^k + 1	0..8	260 213	10 Mar 2016 09 Apr 2026	Andrey Balyakin Serge Batalov
10	1st 2nd	3696772637099483023015936 • 311# • 2^k − 1 259549635108226 • 347# • 2^k + 1	0..9	150 153	10 Mar 2016 12 Apr 2026	Andrey Balyakin Serge Batalov
11	1st 2nd	x80 • 151# • 2^k − 1 341841671431409652891648 • 311# • 2^k + 1	0..10	140 149	3 Aug 2013 3 Nov 2016	Primecoin Andrey Balyakin
12	1st 2nd	x81 • 83# • 2^k − 1 906644189971753846618980352 • 233# • 2^k + 1	0..11	113 109	23 May 2014 21 Dec 2013	Primecoin Primecoin
13	1st 2nd	x84 • 61# • 2^k − 1 x83 • 47# • 2^k + 1	0..12	107 101	20 Jan 2014 12 May 2014	Primecoin Primecoin
14	1st 2nd	x77 • 59# • 2^k − 1 x82 • 47# • 2^k + 1	0..13	98 100	20 Nov 2018 16 May 2014	Primecoin Primecoin
15	1st 2nd	14354792166345299956567113728 • 43# • 2^k − 1 1932144234211304994 • 71# / 31 • 2^k + 1	0..14	45 44	1 Jan 2016 4 May 2026	Andrey Balyakin Serge Batalov
16	1st 2nd	5201553456122611142 • 41# / 31 • 2^k − 1 109114927349041124 • 41# / 31 • 2^k + 1	0..15	32 31	12 May 2026 17 May 2026	Serge Batalov Serge Batalov
17	1st 2nd	2600776728061305571 • 41# / 31 • 2^k − 1 1540797425367761006138858880 • 2^k + 1	0..16	32 28	5 Mar 2026 3 Apr 2014	Serge Batalov Raanan Chermoni, Jaroslaw Wroblewski
18	1st 2nd	214325014495971624590189130 • 2^k − 1 658189097608811942204322720 • 2^k + 1	0..17	27 27	16 Mar 2026 9 Mar 2014	Nenad Mićić Raanan Chermoni, Jaroslaw Wroblewski
19	1st 2nd	27692774713034525184617670 • 2^k − 1 79910197721667870187016100 • 2^k + 1	0..18	26 26	11 Apr 2026 23 Mar 2014	John Armitage Raanan Chermoni, Jaroslaw Wroblewski
20	1st 2nd	75949683268775452969189500 • 2^k − 1 3352894966466100254851080 • 2^k + 1	0..19	26 25	18 Apr 2026 29 Mar 2026	John Armitage John Armitage

The largest known Cunningham Chains of length n

kind

Cunningham chains of length n

k's

Digits

When

Discoverer

History

1st
2nd

Sophie Germain2618163402417 • 2^{1290000 + k} − 1
213778324725 • 2^{561417 + k} + 1

0,1

388342
169015

29 Feb 2016
17 Mar 2023

Dr. James Scott Brown, PrimeGrid, TwinGen, LLR
Ryan Propper, Serge Batalov

1st
2nd

1128330746865 • 2^{66439 + k} − 1
214923707595 • 2^{49071 + k} + 1

0..2

20013
14784

17 Feb 2020
2 Jan 2025

Dr. Michael Paridon, NewPGen, OpenPFGW
Serge Batalov, NewPGen, OpenPFGW

1st
2nd

93003628384 • 10111# • 2^k − 1
162229493368 • 11171# • 2^k + 1

0..3

4362
4809

16 Feb 2025
17 Jul 2026

Serge Batalov, NewPGen, OpenPFGW
Serge Batalov, NewPGen, OpenPFGW

1st
2nd

475676794046977267 • 4679# • 2^k − 1
181439827616655015936 • 4673# • 2^k + 1

0..4

2019
2018

16 Feb 2024
8 Nov 2016

Shusuke Kubota; NewPGen, OpenPFGW
Andrey Balyakin

1st
2nd

2799873605326 • 2371# • 2^k − 1
37015322207094 • 2339# • 2^k + 1

0..5

1016
1001

25 Mar 2015
28 Jan 2025

Serge Batalov, NewPGen, OpenPFGW
Serge Batalov, NewPGen, OpenPFGW

1st
2nd

190721977563410 • 1201# • 2^k − 1
11696328195950 • 1201# • 2^k + 1

0..6

518
517

21 Apr 2026
10 Apr 2026

Serge Batalov
Serge Batalov

1st
2nd

72368211643254 • 727# • 2^k − 1
2373007846680317952 • 761# • 2^k + 1

0..7

315
337

11 Apr 2026
10 Mar 2016

Serge Batalov
Andrey Balyakin

1st
2nd

553374939996823808 • 593# • 2^k − 1
316094278095659 • 479# • 2^k + 1

0..8

260
213

10 Mar 2016
09 Apr 2026

Andrey Balyakin
Serge Batalov

1st
2nd

3696772637099483023015936 • 311# • 2^k − 1
259549635108226 • 347# • 2^k + 1

0..9

150
153

10 Mar 2016
12 Apr 2026

Andrey Balyakin
Serge Batalov

1st
2nd

x80 • 151# • 2^k − 1
341841671431409652891648 • 311# • 2^k + 1

0..10

140
149

3 Aug 2013
3 Nov 2016

Primecoin
Andrey Balyakin

1st
2nd

x81 • 83# • 2^k − 1
906644189971753846618980352 • 233# • 2^k + 1

0..11

113
109

23 May 2014
21 Dec 2013

Primecoin
Primecoin

1st
2nd

x84 • 61# • 2^k − 1
x83 • 47# • 2^k + 1

0..12

107
101

20 Jan 2014
12 May 2014

Primecoin
Primecoin

1st
2nd

x77 • 59# • 2^k − 1
x82 • 47# • 2^k + 1

0..13

98
100

20 Nov 2018
16 May 2014

Primecoin
Primecoin

1st
2nd

14354792166345299956567113728 • 43# • 2^k − 1
1932144234211304994 • 71# / 31 • 2^k + 1

0..14

45
44

1 Jan 2016
4 May 2026

Andrey Balyakin
Serge Batalov

1st
2nd

5201553456122611142 • 41# / 31 • 2^k − 1
109114927349041124 • 41# / 31 • 2^k + 1

0..15

32
31

12 May 2026
17 May 2026

Serge Batalov
Serge Batalov

1st
2nd

2600776728061305571 • 41# / 31 • 2^k − 1
1540797425367761006138858880 • 2^k + 1

0..16

32
28

5 Mar 2026
3 Apr 2014

Serge Batalov
Raanan Chermoni, Jaroslaw Wroblewski

1st
2nd

214325014495971624590189130 • 2^k − 1
658189097608811942204322720 • 2^k + 1

0..17

27
27

16 Mar 2026
9 Mar 2014

Nenad Mićić
Raanan Chermoni, Jaroslaw Wroblewski

1st
2nd

27692774713034525184617670 • 2^k − 1
79910197721667870187016100 • 2^k + 1

0..18

26
26

11 Apr 2026
23 Mar 2014

John Armitage
Raanan Chermoni, Jaroslaw Wroblewski

1st
2nd

75949683268775452969189500 • 2^k − 1
3352894966466100254851080 • 2^k + 1

0..19

26
25

18 Apr 2026
29 Mar 2026

John Armitage
John Armitage

x77 = 14340319624001770765457042636973902777444526766562062468716553623575545716736

x80 = 73853903764168979088206401473739410396455001112581722569026969860983656346568919

x81 = 288320466650346626888267818984974462085357412586437032687304004479168536445314040

x82 = 5819411283298069803200936040662511327268486153212216998535044251830806354124236416

x83 = 38249410745534076442242419351233801191635692835712219264661912943040353398995076864

x84 = 106680560818292299253267832484567360951928953599522278361651385665522443588804123392

The smallest Cunningham Chains of given length n
n	kind	Smallest of length n	k's	Digits	When	Discoverer
1	1st 2nd	13 11	-	2 2	- -
2	1st 2nd	4 • 2^k − 1 6 • 2^k + 1	0..1	1 1	- -
3	1st 2nd	42 • 2^k − 1 2^k + 1	0..2	2 1	- -
4	1st 2nd	510 • 2^k − 1 2130 • 2^k + 1	0..3	3 4	- -
5	1st 2nd	3 • 2^k − 1 1530 • 2^k + 1	0..4	1 4	- -
6	1st 2nd	90 • 2^k − 1 385590 • 2^k + 1	0..5	1 6	- 23 Feb 1995	Robert G. Wilson
7	1st 2nd	1122660 • 2^k − 1 16650 • 2^k + 1	0..6	7 5	- -	Derrick Henry Lehmer Derrick Henry Lehmer
8	1st 2nd	19099920 • 2^k − 1 15514860 • 2^k + 1	0..7	8 8	1980/1981 1980/1981	Nelson, W.H. Meeus Lalout, W.H. Meeus
9	1st 2nd	85864770 • 2^k − 1 857095380 • 2^k + 1	0..8	8 9	1989 1989	Günter Löh Günter Löh
10	1st 2nd	26089808580 • 2^k − 1 205528443120 • 2^k + 1	0..9	11 12	1989 1989	Günter Löh Günter Löh
11	1st 2nd	665043081120 • 2^k − 1 1389122693970 • 2^k + 1	0..10	12 13	1989 1989	Günter Löh Günter Löh
12	1st 2nd	554688278430 • 2^k − 1 216857744866620 • 2^k + 1	0..11	12 15	1989 1989	Günter Löh Günter Löh
13	1st 2nd	4090932431513070 • 2^k − 1 758083947856950 • 2^k + 1	0..12	16 15	1998 1989	Jack Brennen Günter Löh
14	1st 2nd	95405042230542330 • 2^k − 1 107588900851484910 • 2^k + 1	0..13	17 18	28 Oct 1999 28 Oct 1999	Paul Jobling Paul Jobling
15	1st 2nd	90616211958465842220 • 2^k − 1 69257563144280940 • 2^k + 1	0..14	20 17	5 Jul 2017 28 Oct 1999	Jonathan P. Sorenson; Jonathan E. Webster Paul Jobling
16	1st 2nd	810433818265726529160 • 2^k − 1 3203000719597029780 • 2^k + 1	0..15	21 19	Feb 2002 5 Dec 1997	Phil Carmody, Paul Jobling Tony Forbes
17	1st 2nd	2759832934171386593520 • 2^k − 1 8058978143544782179440 • 2^k + 1	0..16	22 22	27 May 2008 2020	Jaroslaw Wroblewski John Armitage
18	1st 2nd	776208125345634679522110 • 2^k − 1 773377687199227745520600 • 2^k + 1	0..17	24 24	2020	John Armitage John Armitage (PDF-document)
19	1st 2nd	27692774713034525184617670 • 2^k − 1 6705789932932200509702160 • 2^k + 1	0..18	26 25	11 Apr 2026 28 Mar 2026	John Armitage John Armitage
20	1st 2nd	75949683268775452969189500 • 2^k − 1 3352894966466100254851080 • 2^k + 1	0..19	26 25	1 May 2026 29 Mar 2026	John Armitage (confirmed, it is the smallest) John Armitage

The smallest Cunningham Chains of given length n

kind

Smallest of length n

k's

Digits

When

Discoverer

1st
2nd

13
11

2
2

-
-

1st
2nd

4 • 2^k − 1
6 • 2^k + 1

0..1

1
1

-
-

1st
2nd

42 • 2^k − 1
2^k + 1

0..2

2
1

-
-

1st
2nd

510 • 2^k − 1
2130 • 2^k + 1

0..3

3
4

-
-

1st
2nd

3 • 2^k − 1
1530 • 2^k + 1

0..4

1
4

-
-

1st
2nd

90 • 2^k − 1
385590 • 2^k + 1

0..5

1
6

-
23 Feb 1995

Robert G. Wilson

1st
2nd

1122660 • 2^k − 1
16650 • 2^k + 1

0..6

7
5

-
-

Derrick Henry Lehmer
Derrick Henry Lehmer

1st
2nd

19099920 • 2^k − 1
15514860 • 2^k + 1

0..7

8
8

1980/1981
1980/1981

Nelson, W.H. Meeus
Lalout, W.H. Meeus

1st
2nd

85864770 • 2^k − 1
857095380 • 2^k + 1

0..8

8
9

1989
1989

Günter Löh
Günter Löh

1st
2nd

26089808580 • 2^k − 1
205528443120 • 2^k + 1

0..9

11
12

1989
1989

Günter Löh
Günter Löh

1st
2nd

665043081120 • 2^k − 1
1389122693970 • 2^k + 1

0..10

12
13

1989
1989

Günter Löh
Günter Löh

1st
2nd

554688278430 • 2^k − 1
216857744866620 • 2^k + 1

0..11

12
15

1989
1989

Günter Löh
Günter Löh

1st
2nd

4090932431513070 • 2^k − 1
758083947856950 • 2^k + 1

0..12

16
15

1998
1989

Jack Brennen
Günter Löh

1st
2nd

95405042230542330 • 2^k − 1
107588900851484910 • 2^k + 1

0..13

17
18

28 Oct 1999
28 Oct 1999

Paul Jobling
Paul Jobling

1st
2nd

90616211958465842220 • 2^k − 1
69257563144280940 • 2^k + 1

0..14

20
17

5 Jul 2017
28 Oct 1999

Jonathan P. Sorenson; Jonathan E. Webster
Paul Jobling

1st
2nd

810433818265726529160 • 2^k − 1
3203000719597029780 • 2^k + 1

0..15

21
19

Feb 2002
5 Dec 1997

Phil Carmody, Paul Jobling
Tony Forbes

1st
2nd

2759832934171386593520 • 2^k − 1
8058978143544782179440 • 2^k + 1

0..16

22
22

27 May 2008
2020

Jaroslaw Wroblewski
John Armitage

1st
2nd

776208125345634679522110 • 2^k − 1
773377687199227745520600 • 2^k + 1

0..17

24
24

2020

John Armitage
John Armitage (PDF-document)

1st
2nd

27692774713034525184617670 • 2^k − 1
6705789932932200509702160 • 2^k + 1

0..18

26
25

11 Apr 2026
28 Mar 2026

John Armitage
John Armitage

1st
2nd

75949683268775452969189500 • 2^k − 1
3352894966466100254851080 • 2^k + 1

0..19

26
25

1 May 2026
29 Mar 2026

John Armitage (confirmed, it is the smallest)
John Armitage