A Rare 11-Prime Constellation Exhibiting Recursive Closure From Dual Triplet Structure.

We investigate a rare prime configuration defined by the simultaneous occurrence of two prime triplets centered at an integer namely and subject to additional base 10 structural constraints on terminal digits and truncated cores. These conditions induce a highly restrictive system of linear forms whose joint primality would be expected to occur with extremely low density under standard probabilistic heuristics. We identify integers for which all associated linear expressions are prime and show that for such values, the induced mapping generates a secondary prime triplet Iterating once more yields a further triplet at , producing a total of eleven simultaneously prime expressions. This defines a recursive prime constellation exhibiting empirical closure under two levels of iteration. A complete computational search up to identifies fifteen such integers , including the minimal example and larger instances at 10-, 12- and 13-digit scales. The observed distribution is highly sparse but consistent with the behavior of admissible prime constellations predicted by heuristic models such as the Hardy-Littlewood prime k-tuple conjecture. While no claim is made regarding infinitude or deterministic generation, these results demonstrate the existence of a structured prime configuration with recursive propagation properties. This suggests that certain tightly coupled systems of linear forms may exhibit localized stability beyond what is typically anticipated under independence heuristics.