Erdős problem 453 · problems.science

Is it true that, for all sufficiently large $n$ , there exists some $i<n$ such that $p_n^2 < p_{n+i}p_{n-i},$ where $p_k$ is the $k$ th prime?

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1 retained statement2415f78e850a

FormalConjectures/ErdosProblems/

453.lean

Retained formal statement1 of 1

Is it true that, for all sufficiently large $n$ , there exists some $i<n$ such that $p_n^2 < p_{n+i}p_{n-i},$ where $p_k$ is the $k$ th prime?

Pomerance proved that the answer is no.

FormalConjectures/ErdosProblems/453.leanErdos453.erdos_4531 lineExact file

1False ↔ Erdos453.EventuallyHasPrimeWitness

SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.