Status
On this page
Status
Topics
Status
On this page
Status
Topics
As ranges over integers
Source: erdosproblems.com/726
No claim settles this problem.
Open, the site's label, with the site's remark that no finite computation can settle the problem; the community database lists the problem as open as of its last update (2025-08-31), with the statement formalized on 2026-06-25 and no formal proof. No unconditional result, refereed publication or accepted proof exists (search scope in Current assessment). Two outstanding items have claim pages and neither is acceptance evidence: a Conjectures.io record of 13 August 2026 that refutes a defective formal statement and, by Conjectures.io's review, "does not refute the intended integer-residue asymptotic" (rejected claim; see Formalization), and a Zenodo preprint of 11 August 2026 that claims the asymptotic only under an unproved equidistribution hypothesis (conditional claim; see Known Results). The standing derives from the claim pages: a rejected claim and a conditional one leave the problem open.