Cunningham Chain
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 SophieGermain Primes.
The two largest known Cunningham chains (of the first kind) of length three are(
, 
, 
) and(
, 
, 
), both discovered by W. Roonguthai in 1998.
References
Guy, R. K. ``Cunningham Chains.'' §A7 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 18-19, 1994. Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, p. 333, 1996. Roonguthai, W. ``Yves Gallot's Proth and Cunningham Chains.'' http://ksc9.th.com/warut/cunningham.html.
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