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 statement3 of 5

Can the bound $O(\log N)$ be achieved for an additive complement to the primes? [Guy04] writes that Erdős offered $50 for the solution.

FormalConjectures/ErdosProblems/32.leanErdos32.erdos_32.variants.log_bound4 linesExact file

1True ↔2  ∃ A,3    Erdos32.IsAdditiveComplementToPrimes A ∧4      (fun N => ↑{x ∈ Finset.Icc 1 N | x ∈ A}.card) =O[Filter.atTop] fun N => Real.log ↑N

OpenStatement only, no proof

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