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The Skewes number (or first Skewes number) is the number Sk1 above which
The second Skewes number Sk2 is the number above which
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
te Riele, H. J. J. ``On the Sign of the Difference
Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 30, 1991.
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.
must fail (assuming that the Riemann
Hypothesis is false). It is much larger than the Skewes number Sk1,
References
.'' Acta Arith. 11, 397-410, 1966.
.'' Math. Comput. 48, 323-328, 1987.
© 1996-9 Eric W. Weisstein
1999-05-26