Abstract
I don’t know any subject other than number theory where one can give a talk on mathematics centered around major unsolved problems, but understandable with almost no background in mathematics. High school students with slight calculus background should be able to understand most of this talk on prime numbers. The presentation is reworked from talks I have given to several audiences.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
P. Bateman and R. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962) pp. 363–367
V. J. Bouniakowsky, Sur les diviseurs numériques invariables des fonctions rationnelles entières, Mem. Sci. Math et Phys. T. VI (1854) pp. 307–329
V. Brun, Über das Goldbachsche Gesetz und die Anzahl der Primzahlpaare, Archiv for Mathematik (Christiania) 34 Part 2 (1915) pp. 1–15
H. Halberstam and H. Richert, Sieve Methods, Academic Press, 1974
G. H. Hardy and J. E. Littlewood, Some problems of Partitio Numerorum, Acta Math. 44 (1923) pp. 1–70
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth edition, Oxford University Press, 1980
A. E. Ingham, The Distribution of Prime Numbers, Cambridge University Press, 1932
S. Lang, Complex Analysis, Third edition, Springer-Verlag, 1993 (Fourth edition, 1999)
S. Lang and H. Trotter, Frobenius Distributions in GL 2-Extensions, Springer Lecture Notes 504, Springer-Verlag, 1976
D. J. Newman, Simple analytic proof of the prime number theorem, Amer. Math. Monthly 87 (1980) pp. 693–696
S. J. Patterson, An Introduction to the Theory of the Riemann Zeta Function, Cambridge Studies in Advanced Mathematics, vol. 14, Cambridge University Press, 1988
A. Schinzel and W. Sierpinsky, Sur certaines hypothèses concernant les nombres premiers, Acta Arith. 4 (1958) pp. 185–208
L. Schoenfeld, Some sharper Tchebychev estimates II, Math. Comp. 30 (1976) pp. 337–360
J. Sylvester, On the partition of an even number into two prime numbers, Nature 56 (1896–1897) pp. 196–197 (= Math. Papers 4 pp. 734-737).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lang, S. (1999). Prime Numbers. In: Math Talks for Undergraduates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1476-2_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1476-2_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7157-4
Online ISBN: 978-1-4612-1476-2
eBook Packages: Springer Book Archive