Cunningham Chain records  CC
Note:
Original record list created and maintained by Dirk Augustin.
This page is developed and maintained by Norman Luhn (since Oct 2021).
Contact: pzktupel[at]pzktupel[dot]de.
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 

2  1st 2nd 
2618163402417 • 2^{1290000}  1 213778324725 • 2^{561417} + 1 
388342 169015 
29 Feb 2016 17 Mar 2023 
Brown, PrimeGrid, TwinGen, LLR Ryan Propper, Serge Batalov 
click 
3  1st 2nd 
1128330746865 • 2^{66439}  1 742478255901 • 2^{40067} + 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 
475676794046977267 • 4679#  1 181439827616655015936 • 4673# + 1 
2019 2018 
16 Feb 2024 8 Nov 2016 
Shusuke Kubota; NewPGen; OpenPFGW 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 


n  kind  first member of CC_{n}  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 
Günter Löh Günter Löh 
10  1st 2nd 
26089808579 205528443121 
11 12 
1989 1989 
Günter Löh Günter Löh 
11  1st 2nd 
665043081119 1389122693971 
12 13 
1989 1989 
Günter Löh Günter Löh 
12  1st 2nd 
554688278429 216857744866621 
12 15 
1989 1989 
Günter Löh Günter Löh 
13  1st 2nd 
4090932431513069 758083947856951 
16 15 
1998 1989 
Brennen Günter Löh 
14  1st 2nd 
95405042230542329 107588900851484911 
17 18 
28 Oct 1999 28 Oct 1999 
Paul Jobling Paul Jobling 
15  1st 2nd 
90616211958465842219 69257563144280941 
20 17 
5 Jul 2017 28 Oct 1999 
Paul Jobling Paul Jobling 
16  1st 2nd 
810433818265726529159 3203000719597029781 
21 19 
Feb 2002 Dec 1997 
Phil Carmody, Paul Jobling Tony Forbes 
NewPGen:
Sieving program mainly for numbers of the form k • b^{n} ± 1, k • p# ± 1, written by Paul 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 Phil Carmody and Paul 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 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