erdos_6.variants.increasing

For all $m$, there are infinitely many $n$ such that $d_n < d_{n+1} < \dots < d_{n+m}$, where $d$ denotes the prime gap function. Proved by Banks, Freiberg, and Turnage-Butterbaugh [BFT15] with an application of the Maynard-Tao machinery concerning bounded gaps between primes [Ma15]

theorem erdos_6.variants.increasing (m : ℕ) :
    {n | ∀ i ∈ Finset.range m, primeGap (n + i) < primeGap (n + i + 1)}.Infinite

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