number-theory / Analytic number theory; digit distribution of constants

Whether the Erdős–Borwein constant is 2-dense

Determine whether every finite binary word occurs infinitely often in the binary expansion of the Erdős–Borwein constant E=m1(2m1)1E=\sum_{m\ge1}(2^m-1)^{-1}.

25Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

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Acceptance criteria: Keep the result conditional on AGP and PrimeIntervalSupply, and keep the paper's quantitative occurrence bound separate from the qualitative Lean endpoint.

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number-theorySep 7, 2026Significance 25/100

Conditional binary disjunctivity of the Erdős–Borwein constant reported

Prior state unknownConditional binary disjunctivity of the Erdős–Borwein constant source-authenticated; hypotheses and independent review remain explicit

VibeMathed recorded: Conditional binary disjunctivity of the Erdős–Borwein constant reported. Consult the linked registry entry for the original report and scope.

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Under the explicit hypotheses AGP and PrimeIntervalSupply defined in the pinned Lean source, the formal development derives that every finite binary word occurs arbitrarily late, hence infinitely often, in the binary expansion of the Erdős–Borwein constant EE; the accompanying paper reports this as 2-density.

AGP and PrimeIntervalSupply are explicit theorem arguments, not formalized in this package. The source treats them as published mathematical inputs. MFN did not independently check those inputs, the paper's argument, or the Lean build.

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