Erdős problem 6 · problems.science

There are infinitely many $n$ such that $d_n < d_{n+1} < d_{n+2}$ , where $d$ denotes the prime gap function.

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

6.lean

Retained formal statement2 of 3

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]

FormalConjectures/ErdosProblems/6.leanErdos6.erdos_6.variants.decreasing1 lineExact file

1∀ (m : ℕ), {n | ∀ i ∈ Finset.range m, primeGap (n + i) > primeGap (n + i + 1)}.Infinite

SolvedStatement only, no proof

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