There exist infinitely many Odd Integers such that is Composite for every . Numbers with this property are called Sierpinski Numbers of the Second Kind, and analogous numbers with the plus sign replaced by a minus are called Riesel Numbers. It is conjectured that the smallest Sierpinski Number of the Second Kind is and the smallest Riesel Number is .

**References**

Buell, D. A. and Young, J. ``Some Large Primes and the Sierpinski Problem.'' SRC Tech. Rep. 88004, Supercomputing Research Center, Lanham, MD, 1988.

Jaeschke, G. ``On the Smallest such that are Composite.'' *Math. Comput.* **40**, 381-384, 1983.

Jaeschke, G. Corrigendum to ``On the Smallest such that are Composite.'' *Math. Comput.* **45**, 637, 1985.

Keller, W. ``Factors of Fermat Numbers and Large Primes of the Form .'' *Math. Comput.* **41**, 661-673, 1983.

Keller, W. ``Factors of Fermat Numbers and Large Primes of the Form , II.'' In prep.

Ribenboim, P. *The New Book of Prime Number Records.* New York: Springer-Verlag, pp. 357-359, 1996.

Riesel, H. ``Några stora primtal.'' *Elementa* **39**, 258-260, 1956.

Sierpinski, W. ``Sur un problème concernant les nombres .'' *Elem. d. Math.* **15**, 73-74, 1960.

© 1996-9

1999-05-26