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.

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