OPENNOTORIOUSnumber theoryprimes
Let $C\geq 0$. Is there an infinite sequence of $n_i$ such that $\lim_{i\to \infty}\frac{p_{n_i+1}-p_{n_i}}{\log n_i}=C$?
Notes: The set S of limit points has been shown to contain 0 (Goldston-Pintz-Yildirim) and infinity (Westzynthius). Merikoski proved at least 1/3 of [0,infinity) belongs to S. Erdos asked whether S = [0,infinity].
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