I compute the Bateman–Horn constant CQ for the Titan polynomial Q (n) = n⁴⁷ − (n−1) ⁴⁷, a degree-46 cyclotomic norm form whose values have no prime factor less than 283. The 60 primes below 283 each contribute a factor p/ (p−1) > 1 to the Euler product, yielding a small-primes boost Pₛmall ≈ 10. 19 (consistent with the Mertens approximation e^γ ln (283) ≈ 10. 05). The splitting primes p ≡ 1 (mod 47), starting at p = 283, contribute suppression factors (1−46/p) / (1−1/p) < 1. The net product converges to CQ ≈ 8. 68. Under the Bateman–Horn heuristic, the prime counting function satisfies πQ (x) ~ (CQ/46) Li (x) ≈ 0. 1887 Li (x), meaning prime values of Q (n) occur with a frequency approximately 8. 7 times that predicted for a generic degree-46 polynomial. Direct computation confirms πQ (10, 000) = 232 vs predicted 235 (error −1. 3%) and πQ (20, 000) = 429 vs predicted 432 (error +0. 6%), consistent with the asymptotic prediction. The repository includes the paper (LaTeX source and compiled PDF, 3 pages), three CSV data files (Euler product local factors for 110 primes, convergence of CQ at five truncation limits up to 10⁷, and observed vs predicted prime counts at six checkpoints up to x = 20, 000), and three Python verification scripts. All scripts produce correct results.
Ruqing Chen (Sun,) studied this question.