## 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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