Problem Statement
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\[\lim_n \frac{q_n}{n^2}=\infty?\]
Categories:
Number Theory
Progress
Richter [Ri76] proved that\[\liminf_n \frac{q_n}{n^2}>0.352\cdots.\]Source: erdosproblems.com/455 | Last verified: January 15, 2026