Let $d_{n} = p_{n + 1} - p_{n}$ . Are there infinitely many $n$ such that $d_{n} < d_{n + 1} < d_{n + 2}$ ?

Worked, still open.

number theory · solved · prize $100 · formalized (Lean) · 0 attempts

machinery: prime-distribution,sieve/Brun-Titchmarsh,Hardy-Littlewood,consecutive-integer-window

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · solved (literature)

theorem erdos_6 :
    {n | primeGap n < primeGap (n + 1) ∧ primeGap (n + 1) < primeGap (n + 2)}.Infinite

solved