A Quartic Monic Polynomial with L = 37 Obtained by Translation

f(n) = n^4 − 41*n^3 + 550*n^2 − 2622*n + 4099 L= 37 This record presents a structural extension of a previously established computational result for a quartic monic prime-generating polynomial.Starting from a polynomial that generates 33 consecutive prime numbers, an iterative translation method n↦n−1n \mapsto n - 1n↦n−1 is applied to reuse the same arithmetic structure and extend the prime run. Using this method, a quartic monic polynomial generating 37 consecutive prime numbers is obtained.The extension is not the result of a new exhaustive computational search, but follows from explicit arithmetic properties of the original polynomial. The document explains the translation principle, constructs the resulting polynomial explicitly, and shows that the process necessarily terminates at L=37 due to the appearance of a composite value at the next translation step.A complete genealogical table of the associated polynomials, from L=37 down to the initial ancestor, is included. Independent verification of the final polynomial was performed using PARI/GP and SageMath.