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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
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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

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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