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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On asymptotic behavior for the Hawkins random sieve

Author: C. C. Heyde
Journal: Proc. Amer. Math. Soc. 56 (1976), 277-280
MSC: Primary 10H30
MathSciNet review: 0404177
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Abstract: This paper is concerned with the Hawkins random sieve which is a probabilistic analogue of the sieve of Eratosthenes. Analogues of the prime number theorem and Mertens' theorem have previously been obtained for this sieve by classical probabilistic methods. In the present paper, sharper results akin to the Riemann hypothesis are obtained by a more elegant martingale approach.

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Keywords: Random sieve, prime numbers, Riemann hypothesis, martingales, strong laws
Article copyright: © Copyright 1976 American Mathematical Society

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