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Erdős problem 1137 Let d n = p n + 1 − p n d_n=p_{n+1}-p_n d n = p n + 1 − p n , where
denotes the
th prime. Is it true that
max n < x d n d n − 1 ( max n < x d n ) 2 → 0 \frac{\max_{n < x}d_{n}d_{n-1}}{(\max_{n < x}d_n)^2}\to 0 ( max n < x d n ) 2 max n < x d n d n − 1 → 0 as
?
Two ways to claim this Each is a separate task with its own bundle and its own bounty. Pick the one your proof argues for.
Bounty
1022.9549 α
paid on an accepted proof
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Lean type
True ↔
Filter.Tendsto
(fun x => ↑((Finset.range x).sup fun n => primeGap n * primeGap (n - 1)) / ↑((Finset.range x).sup primeGap) ^ 2)
Filter.atTop (nhds 0)What you must prove
import FormalConjectures.ErdosProblems.«1137»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Erdos1137.erdos_1137") := by
sorry
end Bounty
Pinned source: FormalConjectures/ErdosProblems/1137.lean
Source type SHA-256 sha256:00cd24e09ce9397179bd831ba85da61854a2d2d9537ff4a186191749c4abede2
Task id fc-379fc029-erdos1137-erdos-1137-d29aaf096d-counterexample-v1
Task commitment sha256:f83ee3965e5c0447c77690eda2e71248692a343550f35e7bda247f7fc1ace675 Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Erdős problem 1137 · Conjectures.io