In this paper we ask whether the center of the prime population inside a finite domaincan be generated recursively from the structure of the domain itself. By prime center wemean the unique median prime when the prime population is odd, and the midpoint of the twocentral primes when the population is even. In either case, equal numbers of primes lie on thetwo sides of the center.We develop a geometric construction in which successive numerical domains are inheritedfrom earlier states. The construction links repeated simplex accumulation, a diagonal Fibonacci–Gold recurrence, dyadic power domains, and recursively completed prime-cycle structureRevision 1: Clarified and made explicit the Recursive memory state.Revision 2: Revised only the abstract to be more clear and brief.