Consecutive Almost-Primes

Jump To References Section

Authors

  • Magdalen College, Oxford OX 1 4 AU, England ,GB

Abstract

For ϵ>0 we define
P(ϵ)={n∈N: n=pk, p prime, k≤n}.
Thus if ϵ is small, the elements of P(ϵ) are "almost prime”. (Note that this phrase is used here in a different sense from that of the weighted sieve, in which n=Pr is an almost-prime if n has at most r prime factors.) It was conjectured by Erdos [1] that for any ϵ>0 the set P(ϵ) contains infinitely many consecutive pairs n, n+1. This was proved recently by Hildebrand [4]. In the present paper we shall investigate quantitative forms of Hildebrand's result.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

1987-06-01

How to Cite

Heath-Brown, D. R. (1987). Consecutive Almost-Primes. The Journal of the Indian Mathematical Society, 52(1-2), 39–49. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/21975