A sequence of primes is a Cunningham
chain of the first kind (second kind) of length if () for , ..., . Cunningham primes of the
first kind are Sophie Germain primes.
It is conjectured there are arbitrarily long Cunningham chains. The longest known Cunningham chains are of length 17, with the first examples found corresponding to
(first kind;
J. Wroblewski, May 2008) and (second kind; J. Wroblewski,
Jun. 2008).
The smallest prime beginning a complete Cunningham chain of the first kind of lengths , 2, ... are 13, 3, 41, 509, 2, 89,
1122659, 19099919, 85864769, 26089808579, ... (OEIS A005602).
The smallest prime beginning a complete Cunningham chain of the second kind of lengths , 2, ... are 11, 7, 2, 2131, 1531,
33301, 16651, 15514861, 857095381, 205528443121, ... (OEIS A005603).
is a Cunningham
chain of the first kind (second kind) of length 
if 
(
) for 
, ..., 
. Cunningham primes of the
first kind are Sophie Germain primes.
(first kind;
J. Wroblewski, May 2008) and 
(second kind; J. Wroblewski,
Jun. 2008).
, 2, ... are 13, 3, 41, 509, 2, 89,
1122659, 19099919, 85864769, 26089808579, ... (OEIS A005602).
, 2, ... are 11, 7, 2, 2131, 1531,
33301, 16651, 15514861, 857095381, 205528443121, ... (OEIS A005603).
