Last updated: 23 October 2023

Original record list created and maintained by Dirk Augustin.
Overworked by Norman Luhn.
Hosted by Jens Kruse Andersen (since October 2021 by Norman Luhn).

Programs that were used
Links

Note:
A large Cunningham Chain (abbreviation: CC) of length n will be also listed in the section(s) for CC of length n-1, n-2, ..., if it is large enough. A Cunningham Chain is a sequence of nearly doubled primes.

One distinguishes between
Cunningham Chains of length n of the 1st kind: n primes, each which is twice the proceeding one plus one; for example (p, 2p+1, 4p+3, 8p+7) is a CC of length 4 of the 1st kind, if each of the four numbers is prime,
Cunningham Chains of length n of the 2nd kind: n primes, each which is twice the proceeding one minus one; for example (p, 2p-1, 4p-3, 8p-7) is a CC of length 4 of the 2nd kind, if each of the four numbers is prime,

In the following "CC2" stands for "Cunningham Chain of length 2", "CC3" stands for "Cunningham Chain of length 3" and so on.

Only the first member of each CC is shown below!

As far as the programs that were used to find the CC are known to me they are written in brackets!

The largest known Cunningham chains of length n
n	kind	first member of CCn ; ( CC2 1st kind are "Sophie Germain primes" )	Digits	When?	Discoverer	Record History
2	1st 2nd	2618163402417 ⋅ 21290000 - 1 213778324725 ⋅ 2561417 + 1	388342 169015	29 Feb 2016 17 Mar 2023	Brown, PrimeGrid, TwinGen, LLR Ryan Propper, Serge Batalov	click
3	1st 2nd	1128330746865 ⋅ 266439 - 1 742478255901 ⋅ 240067 + 1	20013 12074	17 Feb 2020 9 Sep 2016	Paridon, NewPGen, OpenPFGW Angel, Augustin, NewPGen, OpenFGW	click
4	1st 2nd	158514759928  ⋅ 8501# - 1 49325406476 ⋅ 9811# + 1	3640 4233	22 Oct 2023 10 Jul 2019	Frank Doornink, mtsieve, OpenPFGW Östlin, NewPGen, OpenPFGW	click
5	1st 2nd	31017701152691334912 ⋅ 4091# - 1 181439827616655015936 ⋅ 4673# + 1	1765 2018	3 Nov 2016 8 Nov 2016	Balyakin Balyakin	click
6	1st 2nd	2799873605326 ⋅ 2371# - 1 52992297065385779421184 ⋅ 1531# + 1	1016 668	25 Mar 2015 15 May 2015	Batalov, NewPGen, OpenPFGW Balyakin	click
7	1st 2nd	82466536397303904 ⋅ 1171# - 1 25802590081726373888 ⋅ 1033# + 1	509 453	1 Jan 2016 17 Dec 2015	Balyakin Balyakin	click
8	1st 2nd	89628063633698570895360 ⋅ 593# - 1 2373007846680317952 ⋅ 761# + 1	265 337	17 Dec 2015 10 Mar 2016	Balyakin Balyakin	click
9	1st 2nd	553374939996823808 ⋅ 593# - 1 173129832252242394185728 ⋅ 401# + 1	260 187	10 Mar 2016 15 May 2015	Balyakin Balyakin	click
10	1st 2nd	3696772637099483023015936 ⋅ 311# - 1 2044300700000658875613184 ⋅ 311# + 1	150 150	10 Mar 2016 10 Mar 2016	Balyakin Balyakin	click
11	1st 2nd	73853903764168979088206401473739410396455001112581722569026969860983656346568919 ⋅ 151# - 1 341841671431409652891648 ⋅ 311# + 1	140 149	3 Aug 2013 3 Nov 2016	Primecoin Balyakin	click
12	1st 2nd	288320466650346626888267818984974462085357412586437032687304004479168536445314040 ⋅ 83# - 1 906644189971753846618980352 ⋅ 233# + 1	113 109	23 May 2014 21 Dec 2013	Primecoin Primecoin	click
13	1st 2nd	106680560818292299253267832484567360951928953599522278361651385665522443588804123392 ⋅ 61# - 1 38249410745534076442242419351233801191635692835712219264661912943040353398995076864 ⋅ 47# + 1	107 101	20 Jan 2014 12 May 2014	Primecoin Primecoin	click
14	1st 2nd	14340319624001770765457042636973902777444526766562062468716553623575545716736 ⋅ 59# - 1 5819411283298069803200936040662511327268486153212216998535044251830806354124236416 ⋅ 47# + 1	98 100	20 Nov 2018 16 May 2014	Primecoin Primecoin	click
15	1st 2nd	14354792166345299956567113728 ⋅ 43# - 1 67040002730422542592 ⋅ 53# + 1	45 40	1 Jan 2016 10 Mar 2016	Balyakin Balyakin	click
16	1st 2nd	91304653283578934559359 3081594850735522012277717761	23 28	29 May 2008 3 Apr 2014	Wroblewski Chermoni, Wroblewski	click
17	1st 2nd	2759832934171386593519 1540797425367761006138858881	22 28	27 May 2008 3 Apr 2014	Wroblewski Chermoni, Wroblewski	click
18	1st 2nd	example is unknown 658189097608811942204322721	- 27	- 9 Mar 2014	- Chermoni, Wroblewski	click
19	1st 2nd	example is unknown 79910197721667870187016101	- 26	- 23 Mar 2014	- Chermoni, Wroblewski	click

The smallest CC's of given length
n	kind	first member of CCn	Digits	When?	Discoverer
7	1st 2nd	1122659 16651	7 5	- -	Lehmer Lehmer
8	1st 2nd	19099919 15514861	8 8	1980/1981 1980/1981	Nelson, Meeus Lalout, Meeus
9	1st 2nd	85864769 857095381	8 9	1989 1989	Loeh Loeh
10	1st 2nd	26089808579 205528443121	11 12	1989 1989	Loeh Loeh
11	1st 2nd	665043081119 1389122693971	12 13	1989 1989	Loeh Loeh
12	1st 2nd	554688278429 216857744866621	12 15	1989 1989	Loeh Loeh
13	1st 2nd	4090932431513069 758083947856951	16 15	1998 1989	Brennen Loeh
14	1st 2nd	95405042230542329 107588900851484911	17 18	28 Oct 1999 28 Oct 1999	Jobling Jobling
15	1st 2nd	90616211958465842219 69257563144280941	20 17	5 Jul 2017 28 Oct 1999	Jobling Jobling
16	1st 2nd	810433818265726529159 3203000719597029781	21 19	Feb 2002 Dec 1997	Carmody, Jobling Tony Forbes

Programs that were used:

NewPGen:
Sieving program mainly for numbers of the form k ⋅ bⁿ ± 1, k ⋅ p# ± 1, written by Paul Jobling. click

PFGW:
Prime testing program which allows nearly every form of numbers, written by Chris Nash and speeded up with some additional code from G.Woltman and Y.Gallot. click

PRP:
Probable primality test program for numbers of the form k ⋅ bⁿ ± 1, written by George Woltman. click

Proth:
Full primality test program for numbers of the form k ⋅ bⁿ ± 1, written by Yves Gallot. click

GenSv:
A Generic Siever for finding ultra-sparse forms, such as exceptionally long Cunningham Chains.
Used by Phil Carmody and Paul Jobling for their longest records.No URL yet, sorry.

Primo:
Primo is a primality proving program based on the ECPP algorithm:
Elliptic Curve Primality Proving. It will test numbers that are not of any special form. click

TwinGen:
TwinGen is a program to rapidly presieve a set of candidates of the form k ⋅ 2ⁿ ± 1 and
remove those candidates which are composite; written by David Underbakke. click

LLR:
Takes an input file from Paul Jobling's NewPgen, and proves the primality of numbers of the form k ⋅ 2ⁿ - 1 with k < 2ⁿ ;written by Jean Penné. click

sgsieve:
A specialized sieving program developed by Tom Wu for sieving of Sophie-Germain candidates over a range of k and n values.
It generates NewPGen/LLR-format output. click

PrimeGrid:
PrimeGrid's primary goal is to bring the excitement of prime finding to the "everyday" computer user.
By simply downloading and installing BOINC and attaching to the PrimeGrid project, participants can choose
from a variety of prime forms to search. click

Primecoin:
Primecoin, developed by Sunny King, is the first proof-of-work based cryptocurrency that has come up
with any kind of workable solution. The central premise of Primecoin is that, instead of useless SHA256 hashes,
the proof of work protocol would require miners to find long chains of prime numbers (Cunningham chains and BiTwins). click

Remark:
Sometimes the "old" Primeform was used to test the full primality of the members of a CC,
but I have marked them all with PFGW because PFGW is the successor of Primeform.

Please send any new records, corrections or remarks to dirk.augustin@gmx.de

Please check all primes for full primality before sending them to me.
In addition all submitted primes are always double checked by me with PFGW.

Links:
Links to Chris Caldwell's The Prime Pages:
The Top Twenty: Cunningham Chain (1st kind) (only titanic primes)
The Top Twenty: Cunningham Chain (2nd kind) (only titanic primes)
The Prime Glossary: Cunningham Chain

Other links about CC's:
Carlos Rivera's The Prime Puzzles & Problem Connection: Problem 26.- The earliest Cunningham Chains.
Warut Roonguthai's Yves Gallot's Proth.exe and Cunningham Chains. (archived, last update in 2000)
Eric Weisstein's MathWorld, Cunningham Chain
Wikipedia: Cunningham chain

Pages with similar records:
Tony Forbes'and Norman Luhn Prime k-tuplets click
Henri Lifchitz' BiTwin records click