Cunningham Chain records

last updated: 16 Aug 2020

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

The largest known CC of length n
The smallest existing CC's of given length

Programs that were used
Links

NEWSFLASH:
A new record for Cunningham chains of length 2 of the second kind was found by Bela Szekeres, Peter Magyar, Gabor E. Gevay, Gabor Fakas and Antal Jarai.

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 CC 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
3622179275715 ⋅ 2256002 + 1
388342
77077
29 Feb 2016
31 May 2020
Brown, PrimeGrid, TwinGen, LLR
Szekeres, Magyar, Gevay, Farkas, Jarai
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
13720852541 ⋅ 7877# - 1
49325406476 ⋅ 9811# + 1
3384
4233
31 Oct 2016
10 Jul 2019
Angel, Augustin, NewPGen, OpenPFGW
Ístlin, 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
121
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 complete CC's of given length

n kind first member of CCn Digits When? Discoverer
1
1st
2nd
13
11
2
2
-
-
-
-
2
1st
2nd
3
7
1
1
-
-
-
-
3
1st
2nd
41
2
2
1
-
-
-
-
4
1st
2nd
509
2131
3
4
-
-
-
-
5
1st
2nd
2
1531
1
4
-
-
-
-
6
1st
2nd
89
385591
2
6
-
-
-
-
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 Penne. 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
Jens Kruse Andersen's and Norman Luhn The largest known CPAP's click
Jens Kruse Andersen's and Norman Luhn The Largest Known Simultaneous Primes click