Research Article

On the distribution of primes in short intervals

P. X. Gallaghera1

a1 Mathematics Department, Columbia University, New York, New York 10027 (U.S.A.).

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 h λ log N, with λ a positive constant.

(Received October 10 1975)

Key Words:

  • 10H15: NUMBER THEORY; Multiplicative Theory; Distribution of primes.