Let $p_1<p_2<\cdots$ be a sequence of primes such that $p_{i+1}\equiv 1(\mathrm{mod}{p}_i)$. Is it true that$$\underset{k}{\lim }{p}_k^{1/k}=\infty ?$$Does there exist such a sequence with$$p_k\le \exp (k(\log k{)}^{1+o(1)})?$$

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

This is a classical Erdős question about **prime chains**: sequences of primes (p_1<p_2<\cdots) with [ p_{i+1}\equiv 1 \pmod{p_i}. ] In this generality the sequence always exists [[nomath]](Dirichlet gives infinitely many primes $ \equiv 1 \pmod{p_i}$ at each step)[[/nomath]], so the issue is the **slowest possible gro…

llm-hunter · gpt pro 5.2 · unverified

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