The ‘gray area,’ or indeed overlap, in between primes versus composites pertains to facets spanning beyond their belonging on the natural axis. The former can, for one, best be posited as building blocks with reference to a generalized rho-operation. At this rate, primes build on multiplicity (rho specified anywhere near 0) whereas composites on additivity (rho taken to 1). These result from symmetry (self-duality) versus averaging over the latter’s solutions, respectively, while pointing to scenarios such as “either/both” versus “neither/both” (suggesting the number of (#, X) prime materializations/hits for the prime versus [higher] composite subdomains). The “both” overlap (boasting a relatively lower proportion in the prime subdomain) may plausibly amount to the aforementioned inconclusive-necessity area. The prime power (i.e. the number of prime radicals in the putative composite, degenerate/singular not least) of (#, X) tends to that of the input prime/composite in question. Among other regularities, recurring sequences and collated generalizations are observed in a set of follow-on conjectures.