Let $ϵ>0$. Is there some $r{\ll }_{ϵ}1$ such that the density of integers of the form $2^k+n$, where $k\ge 0$ and $n$ has at most $r$ prime divisors, is at least $1-ϵ$?

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

In fact it is explicitly listed as **Erdős Problem #851**: whether for every (\epsilon>0) there is a bounded (r=r(\epsilon)) so that the set [ {,2^k+n:\ k\ge 0,\ n\ \text{has at most }r\text{ prime divisors},} ] has (natural) density at least (1-\epsilon). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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