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STATEMENT: Layout & Essentials

Proof of the Goldbach Conjecture (strong form, ≥6)

1. Natural (n), Whole Integer Numbers (WIN) — 0,1,2,3,…infinity — form horizontal and vertical Axis of a simple matrix grid.


2. The square os such WINs — n**2=1**2=1, 2**2=4, 3**2=9,…infinity — forms the central Diagonal of said grid — dividing it into two bilaterally symmetric triangular halves.


3. Every Inner Grid (IG) cell within is simply the difference (∆) between its horizontal and vertical Diagonal intercept values. They extend to infinity. The Diagonal WINs form the base of a 90° R-angled isosceles triangle with said IG cell value at the apex.


4. Every IG cell within is also the product of two Axis WINs (Either horizontal or vertical, not both), that form the base of a 90° R-angled isosceles triangle with said IG cell value at the apex.


5. The complete matrix grid extends to infinity and is referred to as the
BIM (BBS-ISL Matrix).The BIM forms — and informs — a ubiquitous map (algebraic geometry) to:

⁃ The Inverse Square Law (ISL);

⁃ The Pythagorean Triples (PT);

⁃ The PRIMES (stealthily hidden, but revealed by NPS.

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PTOP & Goldbach Conjecture

By RBrooks

While “hidden” on the BIM (BBS-ISL Matrix), the PRIMES form PPsets — pairs — whose members lie in equal, symmetrical steps on either side of the EVENS number that has been divided by 2. This geometric, embedded pattern on the BIM can be presented as the PTOP: Periodic Table Of PRIMES. Here, these PPsets form the EVENS. The PPsets become “Trails” of PPsets, that increasingly overlap such that more than one PPset is present to compose a given EVEN. In doing so, they satisfy and prove the Goldbach Conjecture!