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Let $q_1<q_2<\cdots$ be a sequence of primes such that \[q_{n+1}-q_n\geq q_n-q_{n-1}.\] Must \[\lim_n \frac{q_n}{n^2}=\infty?\]
Richter [Ri76] proved that \[\liminf_n \frac{q_n}{n^2}>2.84\cdots.\]