A Quartic Monic Polynomial Generating 33 Consecutive Prime Numbers

This record documents a computational result concerning a quartic monic polynomial that generates 33 consecutive prime numbers for integer inputs starting from n=0n = 0n=0. Polynomial The polynomial is: g(n)=n4−25n3+154n2+66n+43 It produces prime values for: n=0,1,…,32 (run length L=33) The first composite value occurs at: n=33, where g(33)=457423=103×4441 Computational search domain The polynomial was found via an exhaustive computational search over a finite coefficient domain for quartic monic polynomials of the form: f(n)=n4+an3+bn2+cn+d with: a,b,c∈[−200,200] d∈[2,200]d restricted to prime values (since f(0)=d) Within this explored domain, the polynomial above represents the best result observed. Independent verification Independent verification was performed using standard number-theoretic software: PARI/GP (web-based) SageMath (online cell) Both confirm primality for all values n=0,…,32 and provide the explicit factorization of the first composite value at n=33. Contents The attached PDF includes: the polynomial definition and the explored search domain a concise verification summary a complete table of values g(n) for n=0,…,32 (all marked as prime) Notes This record is intended as a standalone computational result. Any subsequent structural extensions or translation-based constructions beyond L=33 are documented separately.