Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Prime-gap dyadic series: perturbations, exact criteria and certificates
Cook, Will, Prime-Gap Dyadic Series: Perturbations, Exact Criteria and Certificates, September 2026, 47-page author-hosted edition.
The abstract reports sparse perturbations of nonnegative integer coefficients that preserve specified congruence and asymptotic data while permitting rational or irrational dyadic sums. Applied to prime-gap comparison sequences, the construction does not ensure that cumulative positions are consecutive primes. The paper also gives exact tail criteria and finite denominator exclusions; it explicitly leaves irrationality of the actual prime series unresolved.
The PDF was obtained from the author's public download address above. No explicit license was located on that download page or by searching the PDF text for license or copyright terms; the holding term is unstated. No file of this source is held.
Read status. The downloaded PDF abstract and introduction on pages 1–2, and the public section on fixed-block nonconcentration, were read. No complete proof or computational certificate has been verified here.
Source: https://wcook04.github.io/plectis/papers/erdos251-prime-gap-reasoning-surface.pdf.
Bears on. Problem 251: the stated scope above supplies a related result or a limitation of a possible route.