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Aug 5, 2013 at 20:15 history edited Thomas Bloom CC BY-SA 3.0
Partially retracted Selberg mention.
Aug 5, 2013 at 20:14 comment added Thomas Bloom Good question. Searching my memory, I think I got that impression, and indeed the content of this answer (including the Erdos conjecture), from 'Lectures on sieves' by Heath-Brown (arxiv.org/abs/math/0209360). The relevant quote is "Erdos apparently believed that the constant may be taken as 1, while Selberg is reputed to have suggested that no constant below is admissible.", without references.
Aug 5, 2013 at 19:37 comment added Mark Lewko Where does Selberg state his belief that the last inequality is false?
Jul 5, 2010 at 10:52 history answered Thomas Bloom CC BY-SA 2.5