R. C. Baker, G. Harman and J. Pintz

The authors sharpen a result of Baker and Harman (1995), showing that [x, x + x^0.525] 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: primes, Watt's mean value theorem, Dirichlet polynomial, sieves.