Erdős problem 32 · problems.science

Does there exist a set $A \subseteq \mathbb{N}$ such that $|A \cap \{1, \ldots, N\}| = o((\log N)^2)$ and every sufficiently large integer can be written as $p + a$ for some prime $p$ and $a \in A$ ?

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

32.lean

Retained formal statement5 of 5

Ruzsa proved that any additive complement $A$ to the primes must satisfy $\liminf_{N \to \infty} \frac{|A \cap \{1, \ldots, N\}|}{\log N} \geq e^\gamma$ , where $\gamma$ is the Euler-Mascheroni constant.

FormalConjectures/ErdosProblems/32.leanErdos32.erdos_32.variants.ruzsa4 linesExact file

1∀ (A : Set ℕ),2  Erdos32.IsAdditiveComplementToPrimes A →3    ↑(Real.exp Real.eulerMascheroniConstant) ≤4      Filter.liminf (fun N => ↑{x ∈ Finset.Icc 1 N | x ∈ A}.card / ↑(Real.log ↑N)) Filter.atTop

SolvedStatement only, no proof

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