Let $f (n)$ be maximal such that if $A \subseteq N$ has $∣ A ∣ = n$ then $\prod_{a \neq = b \in A} (a + b)$ has at least $f (n)$ distinct prime factors. Is it true that $f (n) / lo g n \to \infty$ ?

Worked, still open.

number theory · open · prize $250 · possible · formalized (Lean) · 0 attempts

machinery: prime-distribution,additive-combinatorics,Sidon/B_h,sieve/Brun-Titchmarsh,consecutive-integer-window

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

This is **not known**. It is an old Erdős–Turán problem and it is still listed as open.

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_126 : answer(sorry) ↔ ∀ (f : ℕ → ℕ), IsMaximalAddFactorsCard f →
    Tendsto (fun n => f n / Real.log n) atTop atTop

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