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On a problem of G. Golomb.

Published online by Cambridge University Press:  09 April 2009

P. Erdös
P. Erdös
Affiliation:
Technion, Haifa
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In his paper on sets of primes with intermediate density Golomb1 proved the following theorem: Let 2 < p1 < P2 < … be any sequence of primes for whichfor every i and j. Denote by A (x) the number of P's not exceeding x. Then.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 1 , April 1961 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 1961

References

1 Golomb, S., Math. Scand. 3 (1955), 264–74.CrossRefGoogle Scholar

2 Erdös, P. and Jabotinsky, E., Indig. Math. 20 (1958), 115–128.CrossRefGoogle Scholar

3 This is Theorem 2.3 p. 230 of Prachar's book Primzahlverteilung (Springer 1957) where the literature of this question can be found.Google Scholar

4 See e.g. Erdös, P., Proc. Cambridge Phil. Soc. 34 (1957), 8.Google Scholar

5 See e.g. Landau, E., Zahlentheorie Vol. 1.Google Scholar