Problem 251 Page, Discussion and Proof Claims

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bloom_2026_erdos_problem_251_discussion: Identifies the dated public page, discussion comments, proof claim and history for Problem 251, with the commenters' own qualifications.

reformulation_gap_series: Proves Tao's identity that the prime series equals two plus the dyadic series of prime gaps, so the two irrationality questions coincide.

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The source record identifies the inspected public problem page, its nine discussion comments, its single registered proof claim and its revision history, all snapshotted on 2026-09-17 (UTC). This is a web source unit; no canonical PDF exists for the online material. The only mathematics compiled from it is Tao's two-line reformulation, proved in full here. The other comments announce or discuss manuscripts that have their own source cards or are recorded as claims with their authors' qualifications; nothing on the forum is treated as acceptance or review. The capture discussion_20260917.html.gz (the page titled "251 Discussion Thread | Erdős Problems", snapshotted 2026-09-17) contains no copyright, license or terms line, and the site's homepage and FAQ (https://www.erdosproblems.com/ and https://www.erdosproblems.com/faq, read 2026-10-02) state no copyright, license or terms of use, the only reuse-related text on the captured pages being a recommended citation format; the term is unstated. The capture history_20260917.html.gz (the page titled "Erdős Problems", snapshotted 2026-09-17) contains no copyright, license or terms line, and the same site pages state no terms; the term is unstated. The capture problem_20260917.html.gz (the page titled "251 | Erdős Problems", snapshotted 2026-09-17) contains no copyright, license or terms line, and the same site pages state no terms; the term is unstated. The capture proof_claims_20260917.html.gz (the page titled "Erdős Problems", snapshotted 2026-09-17) contains no copyright, license or terms line, and the same site pages state no terms; the term is unstated.

Compilation scope. The reformulation is a complete elementary identity, checked here. Everything else in this unit is a dated record of what the site displayed; comments are author claims and confer no mathematical standing.

Bears on. #251.

No file of this source is held: no license on record permits its redistribution, and the card cites the edition it names above.