Hostname: page-component-6bb9c88b65-dwch4 Total loading time: 0 Render date: 2025-07-22T20:10:15.827Z Has data issue: false hasContentIssue false
  • English
  • Français

On twin ‘primes’ and gaps between successive ‘primes’ for the Hawkins random sieve†

Published online by Cambridge University Press:  24 October 2008

Werner Neudecker
Werner Neudecker
Affiliation:
University College, Swansea, Wales
Get access Rights & Permissions [Opens in a new window]

Extract

1. In this paper we shall use the methods of (6) to give a short proof of Wunderlich's result (7, 8) on the distribution of twin ‘primes’ for the Hawkins random sieve. We shall also obtain a sharp estimate on the gaps between successive ‘primes’.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 365 - 367
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Breiman, L.Probability Addison Wesley (Reading, Massachusetts, 1968).Google Scholar
(2)Erdös, P.On the difference of consecutive primes. Quart. J. Oxford 6 (1935), 124–128.CrossRefGoogle Scholar
(3)Hawkins, D.The random sieve. Math. Mag. 31 (1958), 1–3.CrossRefGoogle Scholar
(4)Hawkins, D.Random sieves. II. J. Number Theory 6, No. 3 (1974), 192–200.CrossRefGoogle Scholar
(5)Loeve, M.Probability theory van Nostrand (Princeton, N.J., 1963).Google Scholar
(6)Neudeczker, W. and Williams, D.The ‘Riemann Hypothesis’ for the Hawkins random sieve (to appear in Compositio Mathematics 29 Fasc. 2 (1974)).Google Scholar
(7)Wunderlich, M. C.The prime number theorem for random sequences (to appear in J. Number Theory).Google Scholar
(8)Wunderlich, M. C.A probabilistic setting for prime number theory. Acta Arithmetica 26. 1 (1974), 59–81.CrossRefGoogle Scholar