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THE DIFFERENCE BETWEEN CONSECUTIVE PRIMES, II

Published online by Cambridge University Press:  22 October 2001

R. C. BAKER ,
G. HARMAN  and
J. PINTZ
R. C. BAKER
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USAbaker@math.byu.edu
G. HARMAN
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, g.harman@rhbnc.ac.uk
J. PINTZ
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Reàltanoda u. 13–15, H-1053 Budapest, Hungary
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Abstract

The authors sharpen a result of Baker and Harman (1995), showing that [x, x + x0.525] contains prime numbers for large x. An important step in the proof is the application of a theorem of Watt (1995) on a mean value containing the fourth power of the zeta function. 2000 Mathematical Subject Classification: 11N05.

Keywords

primesWatt's mean value theoremDirichlet polynomialsieves
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 83 , Issue 3 , November 2001 , pp. 532 - 562
Copyright
2001 London Mathematical Society

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