This work demonstrates a polynomial producing 54 consecutive prime values, indicating mathematical patterns in prime generation.
This work presents a monic quartic polynomial that generates 54 consecutive prime values in canonical form (for n=0,…,53). The subsequent value is composite, establishing a run length L=54 The polynomial belongs to a translation orbit under integer shifts of the variable. A centered representative within the same orbit produces 28 consecutive primes in canonical form. The relationship between the canonical and centered forms is described explicitly. The document provides the full list of prime values, the composite termination value, and a structural remark on translation invariance.
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Paolo Borghi (2026) studied this question.
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