Last updated: 17 March 2023
Cunningham Chain records 
Original record list created and maintained by Dirk Augustin.
Overworked by Norman Luhn.
Hosted by Jens Kruse Andersen (since October 2021 by Norman Luhn).
Note:
A large Cunningham Chain (abbreviation: CC) of length n will be also listed in the section(s) for CC of length n1, n2, ..., 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, 2p1, 4p3, 8p7) 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!


n  kind  first member of CC_{n} ; ( CC_{2} 1st kind are "Sophie Germain primes" )  Digits  When?  Discoverer  Record History 

2nd 
2618163402417 ⋅ 2^{1290000}  1 213778324725 ⋅ 2^{561417} + 1 
169015 
17 Mar 2023 
Brown, PrimeGrid, TwinGen, LLR Ryan Propper, Serge Batalov 

2nd 
1128330746865 ⋅ 2^{66439}  1 742478255901 ⋅ 2^{40067} + 1 
12074 
9 Sep 2016 
Paridon, NewPGen, OpenPFGW Angel, Augustin, NewPGen, OpenFGW 

2nd 
13720852541 ⋅ 7877#  1 49325406476 ⋅ 9811# + 1 
4233 
10 Jul 2019 
Angel, Augustin, NewPGen, OpenPFGW Östlin, NewPGen, OpenPFGW 

2nd 
31017701152691334912 ⋅ 4091#  1 181439827616655015936 ⋅ 4673# + 1 
2018 
8 Nov 2016 
Balyakin Balyakin 

2nd 
2799873605326 ⋅ 2371#  1 52992297065385779421184 ⋅ 1531# + 1 
668 
15 May 2015 
Batalov, NewPGen, OpenPFGW Balyakin 

2nd 
82466536397303904 ⋅ 1171#  1 25802590081726373888 ⋅ 1033# + 1 
453 
17 Dec 2015 
Balyakin Balyakin 

2nd 
89628063633698570895360 ⋅ 593#  1 2373007846680317952 ⋅ 761# + 1 
337 
10 Mar 2016 
Balyakin Balyakin 

2nd 
553374939996823808 ⋅ 593#  1 173129832252242394185728 ⋅ 401# + 1 
187 
15 May 2015 
Balyakin Balyakin 

2nd 
3696772637099483023015936 ⋅ 311#  1 2044300700000658875613184 ⋅ 311# + 1 
150 
10 Mar 2016 
Balyakin Balyakin 

2nd 
73853903764168979088206401473739410396455001112581722569026969860983656346568919 ⋅ 151#  1 341841671431409652891648 ⋅ 311# + 1 
149 
3 Nov 2016 
Primecoin Balyakin 

2nd 
288320466650346626888267818984974462085357412586437032687304004479168536445314040 ⋅ 83#  1 906644189971753846618980352 ⋅ 233# + 1 
109 
21 Dec 2013 
Primecoin Primecoin 

2nd 
106680560818292299253267832484567360951928953599522278361651385665522443588804123392 ⋅ 61#  1 38249410745534076442242419351233801191635692835712219264661912943040353398995076864 ⋅ 47# + 1 
101 
12 May 2014 
Primecoin Primecoin 

2nd 
14340319624001770765457042636973902777444526766562062468716553623575545716736 ⋅ 59#  1 5819411283298069803200936040662511327268486153212216998535044251830806354124236416 ⋅ 47# + 1 
100 
16 May 2014 
Primecoin Primecoin 

2nd 
14354792166345299956567113728 ⋅ 43#  1 67040002730422542592 ⋅ 53# + 1 
40 
10 Mar 2016 
Balyakin Balyakin 

2nd 
91304653283578934559359 3081594850735522012277717761 
28 
3 Apr 2014 
Wroblewski Chermoni, Wroblewski 

2nd 
2759832934171386593519 1540797425367761006138858881 
28 
3 Apr 2014 
Wroblewski Chermoni, Wroblewski 

2nd 
example is unknown 658189097608811942204322721 
27 
9 Mar 2014 
 Chermoni, Wroblewski 

2nd 
example is unknown 79910197721667870187016101 
26 
23 Mar 2014 
 Chermoni, Wroblewski 


n  kind  first member of CC_{n}  Digits  When?  Discoverer 

2nd 
1122659 16651 
5 
 
Lehmer Lehmer 

2nd 
19099919 15514861 
8 
1980/1981 
Nelson, Meeus Lalout, Meeus 

2nd 
85864769 857095381 
9 
1989 
Loeh Loeh 

2nd 
26089808579 205528443121 
12 
1989 
Loeh Loeh 

2nd 
665043081119 1389122693971 
13 
1989 
Loeh Loeh 

2nd 
554688278429 216857744866621 
15 
1989 
Loeh Loeh 

2nd 
4090932431513069 758083947856951 
15 
1989 
Brennen Loeh 

2nd 
95405042230542329 107588900851484911 
18 
28 Oct 1999 
Jobling Jobling 

2nd 
90616211958465842219 69257563144280941 
17 
28 Oct 1999 
Jobling Jobling 

2nd 
810433818265726529159 3203000719597029781 
19 
Dec 1997 
Carmody, Jobling Tony Forbes 
NewPGen:
Sieving program mainly for numbers of the form k ⋅ b^{n} ± 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 ⋅ b^{n} ± 1, written by George Woltman.
click
Proth:
Full primality test program for numbers of the form k ⋅ b^{n} ± 1, written by Yves Gallot.
click
GenSv:
A Generic Siever for finding ultrasparse 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 ⋅ 2^{n} ± 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 ⋅ 2^{n}  1 with k < 2^{n} ;written by Jean Penné.
click
sgsieve:
A specialized sieving program developed by Tom Wu for sieving of SophieGermain candidates over a range of k and n values.
It generates NewPGen/LLRformat 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 proofofwork 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 ktuplets click
Henri Lifchitz' BiTwin records click