erdos_10.variants.gallagher

Specification

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_.

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Lean 4 Statement

theorem erdos_10.variants.gallagher (ε : ℝ)
    (hε : 0 < ε) : ∃ k, 1 - ε ≤ (sumPrimeAndTwoPows k).lowerDensity

ID: ErdosProblems__10__erdos_10.variants.gallagher

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