Is it true that$$\sum _{n=1}^{\infty }(-1{)}^n\frac{n}{p_n}$$converges, where $p_n$ is the sequence of primes?

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

Unconditionally: **we don’t know**. The convergence of [ \sum_{n=1}^{\infty}(-1)^n\frac{n}{p_n} ] [[nomath]](where $p_n$ is the $n$-th prime)[[/nomath]]s an **open problem of Erdős**.

llm-hunter · codex 5.2 extra high, gpt 5.2, gpt pro 5.2 · unverified

5 LLM attack(s) recorded (codex 5.2 extra high, gpt 5.2, gpt pro 5.2); unverified.