## 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 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.

© 1996-9 Eric W. Weisstein
1999-05-25