Erdős problem 1137

Let $d_n=p_{n+1}-p_n$ , where $p_n$ denotes the $n$ th prime. Is it true that $\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$ as $x\to \infty$ ?

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FormalConjectures/ErdosProblems/

1137.lean

Retained formal statement1 of 1

Let $d_n=p_{n+1}-p_n$ , where $p_n$ denotes the $n$ th prime. Is it true that $\frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0$ as $x\to \infty$ ?

FormalConjectures/ErdosProblems/1137.leanErdos1137.erdos_11374 linesExact file

1True ↔2  Filter.Tendsto3    (fun x => ↑((Finset.range x).sup fun n => primeGap n * primeGap (n - 1)) / ↑((Finset.range x).sup primeGap) ^ 2)4    Filter.atTop (nhds 0)

OpenStatement only, no proof