“Brun's Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Brun's Constant

释义

Brun's Constant

The number obtained by adding the reciprocals of the Twin Primes,

(1)

By Brun's Theorem, the constant converges to a definite number as

. Any finite sum underestimates

. Shanks and Wrench (1974) used all the Twin Primes among the first 2 million numbers. Brent (1976) calculated allTwin Primes up to 100 billion and obtained (Ribenboim 1989, p. 146)

(2)

assuming the truth of the first Hardy-Littlewood Conjecture. Using Twin Primesup to

, Nicely (1996) obtained

(3)

(Cipra 1995, 1996), in the process discovering a bug in Intel's

Pentium

microprocessor. The value given by LeLionnais (1983) is incorrect.

See also Twin Primes, Twin Prime Conjecture, Twin Primes Constant

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 64, 1987.

Brent, R. P. ``Tables Concerning Irregularities in the Distribution of Primes and Twin Primes Up to .'' Math. Comput. 30, 379, 1976.

Cipra, B. ``How Number Theory Got the Best of the Pentium Chip.'' Science 267, 175, 1995.

Cipra, B. ``Divide and Conquer.'' What's Happening in the Mathematical Sciences, 1995-1996, Vol. 3. Providence, RI: Amer. Math. Soc., pp. 38-47, 1996.

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

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 41, 1983.

Nicely, T. ``Enumeration to of the Twin Primes and Brun's Constant.'' Virginia J. Sci. 46, 195-204, 1996. http://lasi.lynchburg.edu/Nicely_T/public/twins/twins.htm.

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

Shanks, D. and Wrench, J. W. ``Brun's Constant.'' Math. Comput. 28, 293-299, 1974.

Wolf, M. ``Generalized Brun's Constants.'' http://www.ift.uni.wroc.pl/~mwolf/.

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