Canonical Monic Quartic Polynomials with Run Length L = 41

We document two distinct canonical monic quartic polynomials that generate 41 consecutive prime values when evaluated at consecutive integers starting from n=0n The result L = 41 exceeds by one the classical length obtained by Euler’s quadratic polynomial, but here it is achieved in the more stringent category of monic quartic polynomials. Both examples arise naturally within a translation-based genealogical framework (the Borghi genealogy), in which successive shifts Q(n)=P(n−1) extend prime runs whenever the additional value P(−1) is also prime. The two polynomials are f(n) = n4 − 80n3 + 1817n2 − 8680n + 87119 g(n) = n4 − 80n3 + 1911n2 − 12440n + 188369 both of which generate prime values for all n=0,1,…,40 with the first composite value occurring at n=41. All results were verified independently using deterministic primality tests (SageMath / SageCell).The appended tables list the full sequences of values generated by each polynomial. (Found a new monic quartic polynomial with length 𝐿=49)