# On the difference between consecutive primes

@article{Huxley1971OnTD,
title={On the difference between consecutive primes},
author={Martin N. Huxley},
journal={Inventiones mathematicae},
year={1971},
volume={15},
pages={164-170}
}
• M. Huxley
• Published 1 June 1971
• Chemistry
• Inventiones mathematicae
This disclosure relates to prostaglandins of the PG3 series including PGE3, PGF3 alpha , PGF3 beta , and PGB3, to various analogs of those in racemic form, and to novel processes for making those. This disclosure also relates to certain fluorine and alkyl substituted analogs and certain acetylenic analogs of PGE3, PGF3 alpha , PGF3 beta , PGA3, and PGB3 in both racemic and optically active form, and to processes for making those. These various analogs are useful for the same pharmacological…
On the difference between consecutive primes
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## References

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On the difference between consecutive primes
[Received 3 August 1937] 1. LET pn denote the nth. prime, and 77(2;) the number of primes p not exceeding x. The existence of an absolute constant 6 < 1 such that a (1) n(x) ~ . log a; when x -> 00,
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Zeros ofL-functions
for some fixed A and B. Both (2) and (3) are proved by the use of mean value theorems, the large sieve in the case of (3). The lack of a bound for (1) which is good with respect to both Q and Tmay be