Constant improvement over the argument as posted: KoishiChan's parameters (p prime ~ n^{1/12}, union bound over all p residue classes, the L^{10} packaging) yield asymptotic error coefficient 1/(2log₂(12/11)) ≈ 3.983; Tao's in-thread suggestion p = 2^m plus restricting the union bound to the m+1 classes actually consumed by the splicing allows p ≈ N^{1/4}, recursion ratio 3/4 + o(1), and coefficient 1/(2log₂(4/3)) ≈ 1.2047. The second-moment method caps p near N^{1/4}; higher moments would push toward N^{1/2} and coefficient 1/2.