Sergey Zheleznov

About this site

This site publishes part of an ongoing research program on the binary Goldbach conjecture. The material includes partial results with explicit status labels, a Lean 4 formalization of selected statements, an analysis of the parity barrier, numerical experiments, and draft manuscripts.

Every claim on this site carries an explicit status label. The labels are:

TheoremCorollary of sourcesConditional resultConjectureClaimed, write-up pendingPreprint, not peer-reviewedEmpirical observationOpen problemRefuted

The Goldbach conjecture is not proved — neither here nor anywhere else. Nothing on this site should be read as a claimed proof.

Research

The long-term goal of the program is an unconditional proof of the conjecture: that for every even integer $2n\ge 4$ there exist primes $p,q$ with $2n=p+q$. The central obstruction is the parity barrier for representations of a fixed even integer $N$ — the boundary beyond which known sieve methods do not pass. The partial results published here include a source-derived Proposition $(1+1.8)$ Corollary of sources, obtained as a corollary of published work, and a conditional statement in the Siegel-zero regime Conditional result whose derivation additionally rests on an unverified dominance input (see the results page for the exact status).

The program, its results, and its open problems are described on the research page.

Publications

Three draft manuscripts arising from the program — working texts that have not been peer reviewed — are available on the publications page.