Eratosthene–JC Decantation Interlacing: Internal Emergence of Prime Numbers from the Village of Evens

We present a deterministic process acting exclusively on the even natural numbers,called the JC Decantation, in which no notion of primality is assumed. Starting from thefull set of even integers except 2, we iteratively eliminate elements carrying “internalcharges” defined by the structure n = 2k with k an odd composite. This iterativefiltering, conceptually intertwined with the classical sieve of Eratosthenes, leads to astable residue called the inseparable pairs. We show that dividing these inseparablepairs by two yields exactly the classical set of prime numbers. Thus, primality appearsas an emergent property of the internal dynamics of even integers rather than as aprimitive notion.