单词 | Prime-Generating Polynomial | ||||||||||||||||||||||||||||||||||||||
释义 | Prime-Generating PolynomialLegendre
The above table gives some low-order polynomials which generate only Primes for the first few Nonnegative values(Mollin and Williams 1990). The best-known of these formulas is that due to Euler (Euler 1772, Ball and Coxeter 1987). LeLionnais (1983) has christened numbers
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Abel, U. and Siebert, H. ``Sequences with Large Numbers of Prime Values.'' Am. Math. Monthly 100, 167-169, 1993. Baker, A. ``Linear Forms in the Logarithms of Algebraic Numbers.'' Mathematika 13, 204-216, 1966. Baker, A. ``Imaginary Quadratic Fields with Class Number Two.'' Ann. Math. 94, 139-152, 1971. Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 60, 1987. Boston, N. and Greenwood, M. L. ``Quadratics Representing Primes.'' Amer. Math. Monthly 102, 595-599, 1995. Conway, J. H. and Guy, R. K. ``The Nine Magic Discriminants.'' In The Book of Numbers. New York: Springer-Verlag, pp. 224-226, 1996. Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 26, 1996. Euler, L. Nouveaux Mémoires de l'Académie royale des Sciences. Berlin, p. 36, 1772. Forman, R. ``Sequences with Many Primes.'' Amer. Math. Monthly 99, 548-557, 1992. Garrison, B. ``Polynomials with Large Numbers of Prime Values.'' Amer. Math. Monthly 97, 316-317, 1990. Hendy, M. D. ``Prime Quadratics Associated with Complex Quadratic Fields of Class Number 2.'' Proc. Amer. Math. Soc. 43, 253-260, 1974. Le Lionnais, F. Les nombres remarquables. Paris: Hermann, pp. 88 and 144, 1983. Mollin, R. A. and Williams, H. C. ``Class Number Problems for Real Quadratic Fields.'' Number Theory and Cryptology; LMS Lecture Notes Series 154, 1990. Rabinowitz, G. ``Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkörpern.'' Proc. Fifth Internat. Congress Math. (Cambridge) 1, 418-421, 1913. Ribenboim, P. The Little Book of Big Primes. New York: Springer-Verlag, 1991. Sloane, N. J. A. Sequence A014556in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html. Stark, H. M. ``A Complete Determination of the Complex Quadratic Fields of Class Number One.'' Michigan Math. J. 14, 1-27, 1967. Stark, H. M. ``An Explanation of Some Exotic Continued Fractions Found by Brillhart.'' In Computers in Number Theory, Proc. Science Research Council Atlas Symposium No. 2 held at Oxford, from 18-23 August, 1969 (Ed. A. O. L. Atkin and B. J. Birch). London: Academic Press, 1971. Stark, H. M. ``A Transcendence Theorem for Class Number Problems.'' Ann. Math. 94, 153-173, 1971. |
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