“Twin Primes Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Twin Primes Constant

释义

Twin Primes Constant

The twin primes constant is defined by

			(1)


			(2)

where the

s in sums and products are taken over Primes only. Flajolet and Vardi (1996) give series with acceleratedconvergence

	(3)
	(4)

with

(5)

where

is the Möbius Function. (4) has convergence like

The most accurately known value of is

(6)

Le Lionnais (1983, p. 30) calls

the Shah-Wilson Constant, and

the twin prime constant (Le Lionnais1983, p. 37).

See also Brun's Constant, Goldbach Conjecture, Mertens Constant

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/hrdyltl/hrdyltl.html

Flajolet, P. and Vardi, I. ``Zeta Function Expansions of Classical Constants.'' Unpublished manuscript. 1996. http://pauillac.inria.fr/algo/flajolet/Publications/landau.ps.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, 1983.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 202, 1989.

Ribenboim, P. The Little Book of Big Primes. New York: Springer-Verlag, p. 147, 1991.

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 61-66, 1994.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 30, 1993.

Wrench, J. W. ``Evaluation of Artin's Constant and the Twin Prime Constant.'' Math. Comput. 15, 396-398, 1961.

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