Number theory
1 < a 0 < ... has property Erdos951Prop, is it true that #{a i ≤ x} ≤ π x? $5,056 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-951Command line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«951»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos951.erdos_951" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (a : ℕ → ℝ),
1 < a 0 →
StrictMono a → Erdos951.Erdos951Prop a → ∀ᶠ (x : ℝ) in Filter.atTop, {i | a i ≤ x}.ncard ≤ ⌊x⌋₊.primeCountingOriginal conjecture source: FormalConjectures/ErdosProblems/951.lean
References
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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