Let $P (n)$ denote the largest prime factor of $n$ . Show that the set of $n$ with $P (n) < P (n + 1)$ has density $1/2$ .

Worked, still open.

number theory · open · formalized (Lean) · 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

A quick (but important) clarification about what is currently known:

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_371 :
    { n | Nat.maxPrimeFac (n + 1) > Nat.maxPrimeFac n }.HasDensity (1/2)

open