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On the distribution of primes in short intervals

  • P. X. Gallagher (a1)
  • DOI:
  • Published online: 01 February 2010

One of the formulations of the prime number theorem is the statement that the number of primes in an interval (n, n + h], averaged over nN, tends to the limit λ, when N and h tend to infinity in such a way that hλ log N, with λ a positive constant.

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1.E. Bombieri and H. Davenport . “Small differences between prime numbers”, Proc. Roy. Soc. Ser. A. 293 (1966), 118.

3.G. H. Hardy and J. E. Littlewood . “Some problems of ‘Partitio Numerorum’: III. On the expression of a number as a sum of primes“, Acta Mathematica, 44 (1922), 170.

5.C. Hooley . “On the intervals between consecutive terms of sequences”, Proc. Symp. Pure Math., 24 (1973), 129140.

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