{"id":"palomar/PALOMAR-2026-10-01-000020","url":"https://github.com/enaslund/linniks-constant-3.99/tree/ecdbe3e3e08ad499d2c749ff417cc461f57334c5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-01-000020-v1.json","repo":"https://github.com/enaslund/linniks-constant-3.99","tags":["math.NT","msc:11M20","msc:11M26","msc:11N13","msc:11N35","msc:11Y35","msc:68V15","msc:90C05","number-theory","primes"],"score":0,"title":"Linnik's constant is at most 3.99: A formalization of a weighted version of Heath-Brown's near-density estimate, and of the proof's certificate checker","trust":"high","domain":"math.NT","source":"palomar","authors":["Eric Naslund"],"reviews":0,"subject":"math.NT","summary":"Two components of the proof, in the paper \"Linnik's constant is at most 3.99\" (paper/linnik399.pdf in this repository), that every reduced residue class modulo q contains a prime below q^3.99 for all large q. That bound itself is NOT formally verified here: the paper's zero-location arguments, case analysis and exterior regimes have conventional proofs and computer checks only. (1) The graded near lemma: fix test data (a detector f satisfying Heath-Brown's Condition 1, a Gram test g satisfying his Conditions 1 and 2, a Selberg-sieve weight with heights h_k >= 0 on cells [t_k, t_{k+1}) with…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-01","reactions":{},"formalized":true,"formalizes":[{"title":"Linnik's constant is at most 3.99","identifier":"","relationship":"formalizes"}]}