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}?

Erdős Problems records this as disproved (Lean).

No Repository has ruled on it here.

How far the record reaches4 of 6 stages
  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal1 retained
  4. Resolutiondisproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
What this record is missingWork

Nothing here has checked that finding.

Reproducing it here turns a report into evidence.

Open the work surface
Where the source files it579 share a topic
Number Theory576Primes61
Erdős problem 321accepted
Carrying a Standing. Browse the topic.
Start workOpen sources