Erdős problem 10 · problems.science

Is there some $k$ such that every integer is the sum of a prime and at most $k$ powers of $2$ ?

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6 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

10.lean

Retained formal statement2 of 6

Gallagher [Ga75] has shown that for any $ϵ > 0$ there exists $k(ϵ)$ such that the set of integers which are the sum of a prime and at most $k(ϵ)$ many powers of $2$ has lower density at least $1 - ϵ$ .

Ref: Gallagher, P. X., _Primes and powers of 2_.

FormalConjectures/ErdosProblems/10.leanErdos10.erdos_10.variants.gallagher1 lineExact file

1∀ (ε : ℝ), 0 < ε → ∃ k, 1 - ε ≤ (Erdos10.sumPrimeAndTwoPows k).lowerDensity

SolvedStatement only, no proof

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