Let $h (n)$ be the largest $ℓ$ such that there is a sequence of primes $p_{1} < \dots < p_{ℓ}$ all dividing $n$ with $p_{i + 1} \equiv 1 (mod p_{i})$ . Let $H (n)$ be the largest $u$ such that there is a sequence of integers $d_{1} < \dots < d_{u}$ all dividing $n$ with $d_{i + 1} \equiv 1 (mod d_{i})$ .Estimate $h (n)$ and $H (n)$ . Is it true that $H (n) / h (n) \to \infty$ for almost all $n$ ?

Worked, still open.

number theory · solved · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

Write (n\ge 2) with prime divisors ({p:,p\mid n}).

llm-hunter · gpt pro 5.2 · unverified

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

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