A Sierpiński number is a positive odd integer k such that k · 2ⁿ + 1 is composite for all positive integers n. Serialism is a compositional technique wherein various elements of a musical piece (pitches, rhythms, dynamics, etc.) are determined by a central repeating, ordered pattern. By formalizing auditory analogues to the mathematical concepts and information encoded in Sierpiński numbers, we produce a direct musical analogue to the smallest known Sierpiński number, as well as a methodology for musically interpreting similar mathematical objects. Further, using this source material, we present a serial composition.