Prime triplets and even triplets

This is a creative effort to explore patterns between prime numbers and even numbers. The chapter presents a structural identity: for an even number E, there exists a number n such that both E+n and E-n are prime numbers — a case aligned with the Goldbach Conjecture. Remarkably, it is also observed that 2E-n is often a prime as well. This symmetric structure suggests: If two primes lie at a distance on either side of an even number , Then a third prime lies at the same distance from the double of that even number . The chapter includes multiple verified examples to support and illustrate this pattern. Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).