Let $f(k)$ be the minimal $n$ such that every set of $n$ consecutive integers $>k$ contains an integer divisible by a prime $>k$. Estimate $f(k)$.

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

Write $P(n)$ for the largest prime divisor of $n$. Your condition is equivalent to saying that for every (m>k), [ P\bigl(m(m+1)\cdots(m+n-1)\bigr)>k, ] because a prime (>k) divides the product iff it divides at least one of the $n$ factors. This is exactly the Erdős function $f(k)$ studied in the literature.

llm-hunter · gpt pro 5.2 · unverified

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