Skip to content

Erdős problem 1138

Start work

Erdős Problem 1138. Let x/2<y<xx/2 < y < x and C>1C > 1. If d=max⁡pn<x(pn+1−pn)d = \max_{p_n < x}(p_{n+1} - p_n), where pnp_n denotes the nn-th prime, then is it true that π(y+Cd)−π(y)∼Cdlog⁡y\pi(y + Cd) - \pi(y) \sim \frac{Cd}{\log y}?

How the state got here

1 of 6 recorded
  1. Prior stateNone retained
  2. WorkNo submitted work retained
  3. VerificationNo check retained
  4. DecisionNo Repository has decided
  5. StandingA Result stands here
  6. Next gapNot recorded

Result history

Published changes, performers, checks, and later corrections.

No result history yet
No proposed change is retained for this Problem, so there is nothing to show a decision on.

Correction history

No correction history

Technical detailsExact roots, source, and retained record identifiers

Exact provenance

Problem row
sha256:25119d2769a69b5603f22b2839c56dc1e26dec81562ebe7f6c8ba912c0b2aa3c
Metadata
sha256:a8e56146e1a6a048fc8836273d0cf9d2da36d00611655677bf8b2708c027946c
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:229406a402710c84618626f15b534928d429ecc602f59e2904099e743f74a813
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
Upstream sourceInspect recordsSource JSON