Erdős problem 205 · problems.science

Is it true that all sufficiently large $n$ can be written as $2^k+m$ for some $k\geq 0$ , where $\Omega(m)<\log\log m$ ? (Here $\Omega(m)$ is the number of prime divisors of $m$ counted with multiplicity.)

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

205.lean

Retained formal statement5 of 5

The $n$ constructed in this way are divisible by a large power of $2$ . It remains open whether there exist arbitrarily large odd counterexamples.

FormalConjectures/ErdosProblems/205.leanErdos205.erdos_205.variants.odd_counterexamples1 lineExact file

1True ↔ {n | Odd n ∧ ¬Erdos205.IsRepresentable (fun m => Real.log (Real.log ↑m)) n}.Infinite

OpenStatement only, no proof

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