Demonstrates the infinite nature of prime class P₁ in base-10, indicating a new understanding of prime positional structure.
This paper introduces and formalises the concept of Relative Base-10 Prime Sets, a classification of prime numbers by their ordinal position within consecutive decade blocks of the form Dₙ = [10n, 10n+10) ∩ ℕ. The central result is that of the four naturally occurring position classes (P₁ through P₄), only the first seeded by the prime 2 is infinite. All higher-order sets terminate within the first hundred integers. This phenomenon is termed Asymptotic Minimality: the positional structure of primes in base 10 converges irreversibly to a single active position class, after which no new positional complexity emerges. We further establish a connection between this classification and the theory of super primes, and explore the primordial status of 2 as the origin point of the entire positional hierarchy. Conjectures regarding base-dependence and index-origin sensitivity of super prime sets are presented for further investigation.
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Nicolas Antony Brown (2026) studied this question.
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