Binary Digits of the Erdős-Borwein Constant

Does the block $11$ occur infinitely often in the base-$2$ expansion of the Erdős-Borwein constant $E = \sum_{n \ge 1} \frac{1}{2^n - 1}$? Posed by Crandall in 2012.

Result

Proved

Status

Resolved

AI contribution

AI co-developed

Method

Argument

Field

Digital number theory

Posed by

Richard Crandall

Year posed

2012

Years open

14y

Solved

2026-05-22

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

John M. Campbell

Verification

Unreviewed

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article