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 2618163402417 • 2^{1290000 + k} − 1 ; Sophie Germain prime pair
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
49325406476 • 9811# • 2^k + 1 0..3 4362
4233 16 Feb 2025
10 Jul 2019 Serge Batalov, NewPGen, OpenPFGW
Oscar Östlin, 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 82466536397303904 • 1171# • 2^k − 1
25802590081726373888 • 1033# • 2^k + 1 0..6 509
453 1 Jan 2016
17 Dec 2015 Andrey Balyakin
Andrey Balyakin

8 1st
2nd 89628063633698570895360 • 593# • 2^k − 1
2373007846680317952 • 761# • 2^k + 1 0..7 265
337 17 Dec 2015
10 Mar 2016 Andrey Balyakin
Andrey Balyakin

9 1st
2nd 553374939996823808 • 593# • 2^k − 1
173129832252242394185728 • 401# • 2^k + 1 0..8 260
187 10 Mar 2016
15 May 2015 Andrey Balyakin
Andrey Balyakin

10 1st
2nd 3696772637099483023015936 • 311# • 2^k − 1
2044300700000658875613184 • 311# • 2^k + 1 0..9 150
150 10 Mar 2016
10 Mar 2016 Andrey Balyakin
Andrey Balyakin

11 1st
2nd 73853903764168979088206401473739410396455001112581722569026969860983656346568919 • 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 288320466650346626888267818984974462085357412586437032687304004479168536445314040 • 83# • 2^k − 1
906644189971753846618980352 • 233# • 2^k + 1 0..11 113
109 23 May 2014
21 Dec 2013 Primecoin
Primecoin

13 1st
2nd 106680560818292299253267832484567360951928953599522278361651385665522443588804123392 • 61# • 2^k − 1
38249410745534076442242419351233801191635692835712219264661912943040353398995076864 • 47# • 2^k + 1 0..12 107
101 20 Jan 2014
12 May 2014 Primecoin
Primecoin

14 1st
2nd 14340319624001770765457042636973902777444526766562062468716553623575545716736 • 59# • 2^k − 1
5819411283298069803200936040662511327268486153212216998535044251830806354124236416 • 47# • 2^k + 1 0..13 98
100 20 Nov 2018
16 May 2014 Primecoin
Primecoin

15 1st
2nd 14354792166345299956567113728 • 43# • 2^k − 1
67040002730422542592 • 53# • 2^k + 1 0..14 45
40 1 Jan 2016
10 Mar 2016 Andrey Balyakin
Andrey Balyakin

16 1st
2nd 91304653283578934559360 • 2^k − 1
3081594850735522012277717760 • 2^k + 1 0..15 23
28 29 May 2008
3 Apr 2014 Jaroslaw Wroblewski
Raanan Chermoni, Jaroslaw Wroblewski

17 1st
2nd 2759832934171386593520 • 2^k − 1
1540797425367761006138858880 • 2^k + 1 0..16 22
28 27 May 2008
3 Apr 2014 Jaroslaw Wroblewski
Raanan Chermoni, Jaroslaw Wroblewski

18 1st
2nd example is unknown
658189097608811942204322720 • 2^k + 1 0..17 -
27 -
9 Mar 2014 -
Raanan Chermoni, Jaroslaw Wroblewski

19 1st
2nd example is unknown
79910197721667870187016100 • 2^k + 1 0..18 -
26 -
23 Mar 2014 -
Raanan Chermoni, Jaroslaw Wroblewski

The largest known Cunningham chains of length n
n	kind	Cunningham chains of length n	k's	Digits	When	Discoverer	History
2	1st 2nd	2618163402417 • 2^{1290000 + k} − 1 ; *Sophie Germain prime pair* 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 49325406476 • 9811# • 2^k + 1	0..3	4362 4233	16 Feb 2025 10 Jul 2019	Serge Batalov, NewPGen, OpenPFGW Oscar Östlin, 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	82466536397303904 • 1171# • 2^k − 1 25802590081726373888 • 1033# • 2^k + 1	0..6	509 453	1 Jan 2016 17 Dec 2015	Andrey Balyakin Andrey Balyakin
8	1st 2nd	89628063633698570895360 • 593# • 2^k − 1 2373007846680317952 • 761# • 2^k + 1	0..7	265 337	17 Dec 2015 10 Mar 2016	Andrey Balyakin Andrey Balyakin
9	1st 2nd	553374939996823808 • 593# • 2^k − 1 173129832252242394185728 • 401# • 2^k + 1	0..8	260 187	10 Mar 2016 15 May 2015	Andrey Balyakin Andrey Balyakin
10	1st 2nd	3696772637099483023015936 • 311# • 2^k − 1 2044300700000658875613184 • 311# • 2^k + 1	0..9	150 150	10 Mar 2016 10 Mar 2016	Andrey Balyakin Andrey Balyakin
11	1st 2nd	73853903764168979088206401473739410396455001112581722569026969860983656346568919 • 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	288320466650346626888267818984974462085357412586437032687304004479168536445314040 • 83# • 2^k − 1 906644189971753846618980352 • 233# • 2^k + 1	0..11	113 109	23 May 2014 21 Dec 2013	Primecoin Primecoin
13	1st 2nd	106680560818292299253267832484567360951928953599522278361651385665522443588804123392 • 61# • 2^k − 1 38249410745534076442242419351233801191635692835712219264661912943040353398995076864 • 47# • 2^k + 1	0..12	107 101	20 Jan 2014 12 May 2014	Primecoin Primecoin
14	1st 2nd	14340319624001770765457042636973902777444526766562062468716553623575545716736 • 59# • 2^k − 1 5819411283298069803200936040662511327268486153212216998535044251830806354124236416 • 47# • 2^k + 1	0..13	98 100	20 Nov 2018 16 May 2014	Primecoin Primecoin
15	1st 2nd	14354792166345299956567113728 • 43# • 2^k − 1 67040002730422542592 • 53# • 2^k + 1	0..14	45 40	1 Jan 2016 10 Mar 2016	Andrey Balyakin Andrey Balyakin
16	1st 2nd	91304653283578934559360 • 2^k − 1 3081594850735522012277717760 • 2^k + 1	0..15	23 28	29 May 2008 3 Apr 2014	Jaroslaw Wroblewski Raanan Chermoni, Jaroslaw Wroblewski
17	1st 2nd	2759832934171386593520 • 2^k − 1 1540797425367761006138858880 • 2^k + 1	0..16	22 28	27 May 2008 3 Apr 2014	Jaroslaw Wroblewski Raanan Chermoni, Jaroslaw Wroblewski
18	1st 2nd	example is unknown 658189097608811942204322720 • 2^k + 1	0..17	- 27	- 9 Mar 2014	- Raanan Chermoni, Jaroslaw Wroblewski
19	1st 2nd	example is unknown 79910197721667870187016100 • 2^k + 1	0..18	- 26	- 23 Mar 2014	- Raanan Chermoni, Jaroslaw Wroblewski

The smallest CC's of given length n
n kind Smallest Cunningham chains of length n k's Digits When Discoverer
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 Paul Jobling
Paul Jobling

16 1st
2nd 810433818265726529160 • 2^k − 1
3203000719597029780 • 2^k + 1 0..15 21
19 Feb 2002
Dec 1997 Phil Carmody, Paul Jobling
Tony Forbes

n	kind	Smallest Cunningham chains of length n	k's	Digits	When	Discoverer
The smallest CC's of given length n
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	Paul Jobling Paul Jobling
16	1st 2nd	810433818265726529160 • 2^k − 1 3203000719597029780 • 2^k + 1	0..15	21 19	Feb 2002 Dec 1997	Phil Carmody, Paul Jobling Tony Forbes