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
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…
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