Let $f (n)$ count the number of solutions to $n = p + 2^{k}$ for prime $p$ and $k \geq 0$ . Is it true that $f (n) = o (lo g n)$ ?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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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 an **open problem** of Erdős (it appears as Erdős Problem #236). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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

AMS 5 11 · open (literature)

theorem erdos_236: (fun n => (f n : ℝ)) =o[atTop] (fun n => Real.log (n : ℝ))

n

n > 105

n - 2^{k}

1 < 2^{k} < n

open