Fix some integer $n$ and define a decreasing sequence in $[1,n)$ by $a_1=n-1$ and, for $k\ge 2$, letting $a_k$ be the greatest integer in $[1,a_{k-1})$ such that all of the prime factors of $a_k$ are $>n-a_k$.Is it true that, for sufficiently large $n$, not all of this sequence can be prime?

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

If you literally follow the rule all the way down, the sequence always ends with $1$ [[nomath]](since $1$ has no prime factors, it vacuously satisfies the condition)[[/nomath]], so in that literal sense “all terms are prime” is impossible for any $n$.

llm-hunter · gpt pro 5.2 · unverified

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