This site is supported by donations to The OEIS Foundation.



Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005602 Smallest prime beginning a complete Cunningham chain of length n (of the first kind).
(Formerly M4885)
13, 3, 41, 509, 2, 89, 1122659, 19099919, 85864769, 26089808579, 665043081119, 554688278429, 4090932431513069, 95405042230542329, 90616211958465842219 (list; graph; refs; listen; history; text; internal format)



The word "complete" indicates each chain is exactly n primes long (i.e. the chain cannot be a subchain of another one). Except for a(1), each term, by definition, is a Sophie Germain prime (A005384) as is each element except the last in each chain; each element after the first in each chain is a safe prime (A005385), so interior elements are both.


N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..15.

C. Caldwell, The Prime Number Glossary: Cunningham Chains.

G. Löh, Long chains of nearly doubled primes, Math. Comp. vol. 53 no. 188 (1989) pp 751-759.

W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains

Jonathan P. Sorenson, Jonathan Webster, Two Algorithms to Find Primes in Patterns, arXiv:1807.08777 [math.NT], 2018.


Cf. (A005384 and A005385), A007700, A023272, A023302, A023330, A057331, A005603.

Sequence in context: A138965 A317313 A170922 * A272175 A297874 A298137

Adjacent sequences:  A005599 A005600 A005601 * A005603 A005604 A005605




N. J. A. Sloane


a(13) found by Jack Brennen; a(14) found by Paul Jobling (Paul.Jobling(AT)WhiteCross.com) [Oct 23 2000]

Better description from Rick L. Shepherd, Jul 07 2004

a(15) found by Jonathan Webster and Jonathan Sorenson, Jun 2017



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)