Would a proof of the Generalized Riemann Hypothesis help anyone break, or build, RSA? A reproducible measurement

A recurring popular claim holds that a proof of the Riemann Hypothesis (RH) would break RSA. We separate the two places where a hypothesis about zeros of L-functions could plausibly touch RSA and measure both on self-generated toy instances with a public, deterministic harness. On the factoring side, trial division, Pollard rho, Pollard p-1, Lenstra's elliptic curve method (ECM) and a minimal quadratic sieve (QS) factor balanced semiprimes of 95-96 bits (QS) and moduli with small factors (ECM); none of these algorithms consults the truth value of RH, and their behaviour is governed by smoothness and parameter budgets. On the key-generation side the hypothesis does enter: under the Extended Riemann Hypothesis (ERH), Miller's test becomes a deterministic primality proof once every prime base up to an explicit bound has been tried. For a 1024-bit prime, as used in RSA-2048, the sharpest explicit cutoff we use, (ln n)2 (derived from Lamzouri, Li and Soundararajan), needs 41,749 prime bases, about 1,044 times the 40 random Miller-Rabin rounds of our baseline. A proof of ERH would turn this expensive recipe into an unconditional one; it would not make probabilistic testing deterministic or faster, and unconditional certification is already available by other routes. The contribution is expository and reproducible, not a new theorem. Files. Kulma_2026_RH_RSA_note_v0.2.pdf: the note (preprint v0.2). Kulma_2026_RH_RSA_LabRSA_v0.2.0.zip: frozen snapshot of the Lab RSA repository at tag v0.2.0 (22 experiment scripts exp13-exp34, all artefacts, release gate python lab_rsa_contract.py release, 7 checks). Code under the MIT licence, text under CC BY 4.0. All moduli are generated inside the scripts; the harness accepts no external keys.