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The difference between consecutive prime numbers. II

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
R. A. Rankin
Affiliation:
Clare CollegeCambridge
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Extract

In a previous paper, under the same title, I considered the problem of how far apart two consecutive primes can be. The present paper is concerned with the opposite question. How near together can large primes lie? The published literature on this subject is scanty and, though interesting, is mainly negative in character. It appears to be very difficult to give any answer that is not trivial, or that is at all illuminating.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 3 , July 1940 , pp. 255 - 266
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

REFERENCES

(1)Hardy, G. H. and Littlewood, J. E. “Partitio Numerorum III: On the expression of a number as the sum of primes.” Acta Math. 44 (1923), 1–70.CrossRefGoogle Scholar
(2)Landau, E.Handbuch der Lehre von der Verteilung der Primzahlen (Leipzig, 1909).Google Scholar
(3)Landau, E.Vorlesungen über Zahlentheorie (Leipzig, 1927).Google Scholar
(4)Rankin, R. A. “The difference between consecutive prime numbers.” J. London Math. Soc. 13 (1938), 242–247.CrossRefGoogle Scholar
(5)Titchmarsh, E. C. “A Divisor Problem.” Rend. Circ. mat. Palermo, 54 (1930), 414–429.CrossRefGoogle Scholar