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.
The two largest known Cunningham chains (of the first kind) of length three are ( , , ) and ( , , ), both discovered by W. Roonguthai in 1998.
See also Prime Arithmetic Progression, Prime Cluster
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.