A Quartic Monic Polynomial with L = 38 Obtained by Translation

Q38-A Polynomial (L = 38) is a monic quartic polynomial that generates a sequence of 38 consecutive prime values for n=0,1,…,37, where primality is tested on the absolute value ∣f(n)∣|f(n)|∣f(n)∣. The polynomial is defined as: f(n)=n4−74n3+1525n2−5772n+10159 All values f(n) in the range 0≤n≤37 are positive primes. The first composite value occurs at n=38 f(38)=17531=47×373 Main Result Run length: L=38 Domain: consecutive integers n≥0 Primality test: applied to f(n) on 64-bit integers Mathematical Context This polynomial belongs to the restricted family of monic quartic prime-generating polynomials, for which long prime runs are known to be rare and difficult to achieve. The result was found during the Q2025 research program on prime-generating polynomials and improves over previously known monic quartic runs. Method The polynomial was discovered and verified using: structured integer coefficient search, deterministic primality testing, full evaluation of the run up to the composite break point. The sequence length L=38 has been independently validated by repeated checking using deterministic primality methods on 64-bit integers. Notes This record is also documented through a PDF report and a dedicated webpage, both included in or linked from this Zenodo deposition.