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.

**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.

© 1996-9

1999-05-25