The Skewes number (or first Skewes number) is the number Sk_{1} above which
must fail (assuming that
the Riemann Hypothesis is true), where is the Prime Counting Function and
is the
Logarithmic Integral.

The Skewes number has since been reduced to by te Riele (1987), although Conway and Guy (1996) claim that the best current limit is . In 1914, Littlewood proved that the inequality must, in fact, fail infinitely often.

The second Skewes number Sk_{2} is the number above which
must fail (assuming that the Riemann
Hypothesis is false). It is much larger than the Skewes number Sk_{1},

**References**

Asimov, I. ``Skewered!'' *Of Matters Great and Small.* New York: Ace Books, 1976. Originally published
in *Magazine of Fantasy and Science Fiction,* Nov. 1974.

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.* New York: Dover, p. 63, 1987.

Boas, R. P. ``The Skewes Number.'' In *Mathematical Plums*
(Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., 1979.

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, p. 61, 1996.

Lehman, R. S. ``On the Difference
.'' *Acta Arith.* **11**, 397-410, 1966.

te Riele, H. J. J. ``On the Sign of the Difference
.'' *Math. Comput.* **48**, 323-328, 1987.

Wagon, S. *Mathematica in Action.* New York: W. H. Freeman, p. 30, 1991.

© 1996-9

1999-05-26