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

unreviewedOpen. Worked here; no verified result yet.

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

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

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Formal proof

AMS 11 · solved (literature)

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

OEIS1

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