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

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


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