Are there infinitely many solutions to$$\frac{1}{p_1}+\cdots +\frac{1}{p_k}=1-\frac{1}{m},$$where $m\ge 2$ is an integer and $p_1<\cdots <p_k$ are distinct primes?

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

Let $ \frac1{p_1}+\cdots+\frac1{p_k}=1-\frac1m,\qquad m\ge2,\quad p_1<\cdots<p_k\ \text{distinct primes}. $

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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