Is it true that for any $n, k \geq 1$ , if $n + 1, \dots, n + k$ are all composite then there are distinct primes $p_{1}, \dots, p_{k}$ such that $p_{i} ∣ n + i$ for $1 \leq i \leq k$ ?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **exactly Grimm’s conjecture** (posed by C. A. Grimm in 1969), and **it is not proved in general**. ([Wikipedia][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_375 : answer(sorry) ↔ Erdos375Prop

open