POB (PRIMES on the BIM) and the Goldbach Conjecture:
Symmetry—Fractals—Inverse Square Law
~A MathspeedST Supplement~

Fractal — Symmetry — Inverse Square Law (ISL). These are not the usual descriptive terms associated with the Prime numbers (PRIMES) Yet that is exactly what best describes the PRIMES!

The PRIMES, when brought together as P₁ & P₂ members of PRIME Pair Sets (PPsets) demonstrate a robust symmetry and an intimate relationship with the ISL when shown on the BIM (BBS-ISL Matrix grid of the Inverse Square Law). This symmetry is brought out in the geometric relationship between the PPsets and the EVEN numbers (EVENS) that they inform consistent with Euler’s Strong Form of the Goldbach Conjecture.

This come about as the well established PRIMES Sequence (PS) — 3-5-7-11-13-17-19-23-29-31-... acts in a fractal-like manner, i.e., it demonstrates redundant, repetitive and re-iterative behavior in presenting self-similar reflection of itself as it constructs PPsets and PPset “TRAILS.”

The TRAILS are formed from the concatenation of PS’s progressively onto each successive PRIME of a given PS — forming a series of PPsets along the way. The TRAILS can also be seen to be formed directly as individual PPsets on the BIM. Here, each PPset is easily seen to be intersection of 1 PPset member from the Horizontal AXIS and 1 PPset member from the Vertical AXIS, together forming the P₁, P₂ members. The TRAIL is simply all those PPsets thus formed across a Row — or down a Column — on the bilaterally symmetrical BIM. All this is easily visible on the BIM.

That leads us to our story about the PRIMES—Fractals—Symmetry—and the intimate relationship they have with the ISL as seen on the BIM.

TPISC Media Resource Center

https://vimeo.com/413238113

Yes, a deceptively simple matrix grid square (BIM) can give us:

1. Inverse Square Law (ISL);

2. Pythagorean Triples (PTs);

3. PRIMES (P)- Goldbach Conjecture!

~~~

This is an additional supplement to the MathspeedST ebook.

Other titles include The Pythagorean-Inverse Square Connection (TPISC):

TPISC I: Basics

TPISC II: Advanced

TPISC III: Clarity and the Tree of Primitive Pythagorean Triples

TPISC IV: Details, DSEQEC and PRIMES.

PRIMES vs NO-PRIMES

PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture