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Are there infinitely many primes such that is composite for each such that ?
Source: erdosproblems.com/1059
A full solution has been claimed but not yet accepted. The statement is true.
The site labels the problem OPEN, with the explanation that the question cannot be settled by a finite computation. The site's proof-claims tab carries two entries, neither accepted by the site. Johan Land's full claim, filed 2026-09-05 with AI assistance and followed by a Lean development in a comment of 6 September 2026, is recorded as pending on Land's claim page (2026). The derived standing, claimed, proved, departs from the site's OPEN only by counting that pending claim, which neither the site nor an outside review has accepted; it becomes solved, proved if the claim is accepted. Aakash Gurung's partial claim, filed 2026-08-05, concerns only Erdős's easier auxiliary question on integers; it settles no instance of the prime question, so it has no claim page, and the Current assessment describes it.