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Number theory
Date added
Erdős problem 32
Does there exist a set A⊆N such that ∣A∩{1,…,N}∣=o((logN)2)
and every sufficiently large integer can be written as
p+a
for some prime
p
and
a∈A
?
$1,430 bounty·nobody has started
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
18 Sept 2025nothing published against this one yet10 Sept 2026
erdosproblems.com/32
[Erd54] Erdős, Paul, Some results on additive number theory. Proc. Amer. Math. Soc. (1954), 847-853.
[Guy04] Guy, Richard K., Unsolved problems in number theory. (2004), xviii+437
[Ru98c] Ruzsa, Imre Z., On the additive completion of primes. Acta Arith. (1998), 269-275.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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