A Prime-Step Conjecture for Symmetric Prime Triples.

This note proposes that for every prime p > 103 there exists a prime k, with 2 ≤ k ≤ floor((p − 3)/6), such that both p − 6k and p + 6k are prime. It gives a complete explanation of the failure at p = 103 and reports finite verification for every prime centre 103 < p ≤ 1,000,000, comprising 78,471 centres. The prime-step requirement strengthens the related integer-step conjecture recorded in OEIS A196934. The conjecture remains unproved, and priority relative to the full existing literature has not been established.