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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

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
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