Erdős Problem #451

Erdős problem #451 · erdosproblems.com/451

Let $n_k$ be the least integer greater than $2k$ for which $\prod_{i=1}^k (n_k - i)$ has no prime factor in $(k, 2k)$. How rapidly must $n_k$ grow?

Result

Proved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Primes

Posed by

—

Year posed

1979

Years open

47y

Solved

2026-06-18

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article