Erdős problem 32

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 $a \in A$ ?

Sources

The source's own material, retained exactly.

5 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

32.lean

Retained formal statement4 of 5

Erdős proved in [Erd54] that there exists an additive complement $A$ to the primes with $|A \cap \{1, \ldots, N\}| = O((\log N)^2)$ .

FormalConjectures/ErdosProblems/32.leanErdos32.erdos_32.variants.log_squared3 linesExact file

1∃ A,2  Erdos32.IsAdditiveComplementToPrimes A ∧3    (fun N => ↑{x ∈ Finset.Icc 1 N | x ∈ A}.card) =O[Filter.atTop] fun N => Real.log ↑N ^ 2

SolvedStatement only, no proof