Skewes Number
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 thatthe Riemann Hypothesis is true), where 
is the Prime Counting Function and 
is theLogarithmic Integral.
The Skewes number has since been reduced to 
by te Riele (1987), althoughConway 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 RiemannHypothesis is false). It is much larger than the Skewes number Sk1,
See also Graham's Number, Riemann Hypothesis
References
.'' Acta Arith. 11, 397-410, 1966.
.'' Math. Comput. 48, 323-328, 1987.
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