Note on a conjecture of P. D. T. A. Elliott. (English) Zbl 0629.10038

Badea, Catalin

Arch. Math., Brno 23, 89-93 (1987).

The conjecture in the title asserts that every rational number \(r\) can be expressed in the form \((p+1)/(q+1)\) with \(p,q\) primes. The author observes that a weaker representation, with \(q\) prime and \(p\) having at most three prime factors, follows from the sieve results of H. E. Richert and W. Fluch

Reviewer: Imre Z. Ruzsa (Budapest)

MSC:

11N36	Applications of sieve methods
11N64	Other results on the distribution of values or the characterization of arithmetic functions
11N13	Primes in congruence classes

Keywords:

Elliott’s conjecture; completely additive arithmetic function; multiplicative representations of integers; shifted-prime factorization; sieve methods