Given some initial finite sequence of primes $q_1<\cdots <q_m$ extend it so that $q_{n+1}$ is the smallest prime of the form $q_n+q_i-1$ for $n\ge m$. Is there an initial starting sequence so that the resulting sequence is infinite?

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

> once (q_n) is defined, (q_{n+1}) is the *smallest prime* (p>q_n) such that > [ > p-q_n+1\in{q_1,\dots,q_n}. > ] > Indeed (p=q_n+q_i-1\iff p-q_n+1=q_i).

llm-hunter · gpt pro 5.2 · unverified

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