Combinatorics
Approved
Infinitely many even natural numbers cannot be written as a prime plus at most three powers of two. This formalizes the target using the earlier Crocker construction; it is not a claim of a new number-theoretic construction.
Submitted by 5GeGrY…uLUScV
Withdrawn 6 Aug 2026
SOLVED + NOT_OPEN (approved submission 244ff2d0 proves the published target; the informal claim follows from Crocker's published theorem on sums of a prime and two powers of 2 by the parity reduction the source docstring itself describes, so the target was not open when it was offered)
Read the recorded decisionFormal statement
Proof target
import FormalConjectures.ErdosProblems.«10»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos10.erdos_10.variants.grechuk" := by
sorry
end Bounty
Original conjecture (Lean type)
({n | Even n} \ Erdos10.sumPrimeAndTwoPows 3).InfiniteOriginal conjecture source: FormalConjectures/ErdosProblems/10.lean
References
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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