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



Within the inverse square law

PPset entry

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


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



PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture

Excerpt From: Reginald Brooks. PRIMES on the BIM (POB) and the Goldbach Conjecture.” eBook.

Apple Books Store Link

Platforms: This is a multi-touch, interactive ebook made with iBooks Author and published in the Apple Books. Currently, it requires an iPad, or OS X running on a Mac, and the free iBooks app to download and read.

Most of the same content is found online here on my website in the form of white papers and multi-media. HERE is the Media Center link.

Selected SCREENSHOTS for PRIMES on the BIM (POB) and the Goldbach Conjecture

(NOTE: eBooks are available for reading on your Mac or iOS device.)

Artist Link in iTunes Apple Books Store: Reginald Brooks    



TPISC I: Basics The Pythagorean — Inverse Square Connection ©2015, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

TPISC II: Advanced The Pythagorean — Inverse Square Connection ©2015, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

TPISC III: Clarity Tree of Primitive Pythagorean Triples (ToPPT) ©2017, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

MathspeedST: Leapfrogging LightspeedST FASTER than The Speed of Light ©2013, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to return to the home page.

LightspeedST: Leapfrogging @ The Speed of Light ©2013, Reginald Brooks, Brooks Design. All rights reserved.

click HOME to go to the LightspeedST ebook home page.

~ MathspeedST: The Ubiquitous Information of Numbers white paper
~ LightspeedST: Leapfrogging @ The Speed of Light
T H E   U B I Q U I T O U S   I N F O R M A T I O N    O F    N U M B E R S new media net.art project
~ MathspeedST: Leapfrogging Lightspeed FASTER than The Speed of Light MOVIES
The contents of MathspeedST and LightspeedST, as well as most of the TPISC Series, can be viewed as White Papers in the Art Theory 101 links below.

Relevant White Papers by the Author


titles and topics:

LightspeedST: The Complete New Media net.art project (HOME)

  • Page 60:     PTOP: Periodic Table Of PRIMES and the Goldbach Conjecture: How to Make with Fractals

  • Page 61:     PRIMES on the BIM

  • Page 62:     PRIMES on the BIM ebook

  • TOP ]

    POB, PRIMES on the BIM, PTOP, Periodic Table Of PRIMES, PRIMES,NO-PRIMES, BIM, algebraic, algebraic geometry, Active Row Sets, AR, ARS, NON-Active Row, Number Pattern Sequence, NPS, TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability,LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number.

    Art Theory 101 / White Papers Index
    PIN: Pattern in Number...from primes to DNA. | PIN: Butterfly Primes...let the beauty seep in. | PIN: Butterfly Prime Directive...metamorphosis. | PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~. | GoDNA: the Geometry of DNA (axial view) revealed. | SCoDNA: the Structure and Chemistry of DNA (axial view). | The LUFE Matrix | The LUFE Matrix Supplement | The LUFE Matrix: Infinite Dimensions | The LUFE Matrix: E=mc2 | Dark Matter=Dark Energy | The History of the Universe in Scalar Graphics | The History of the Universe_update: The Big Void | Quantum Gravity ...by the book | The Conservation of SpaceTime | LUFE: The Layman's Unified Field Expose` | GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I | Brooks (Base) Square (BBS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series
    net.art index | netart01: RealSurReal...aClone, 2001 | netart02: Hey!Ufunk'n with my DNA? | netart03: 9-11_remembered | netart04: Naughty Physics (a.k.a. The LUFE Matrix) | netart05: Your sFace or Mine? | netart06: Butterfly Primes | netart07: Music-Color-ISL | netart08: BBS-ISL matrix | netart09: BBS-interactive (I) | netart10: Sunspots and Solar Flares | netart11: Music-Color-ISL (II-III) | Art Theory 101: PIN, DNA, LUFE Matrix, GoMAS, BBS index | home
     Copyright 2020, Reginald Brooks, Brooks Design. All rights reserved.

     iTunes, iTunes Store, Apple Books, iBooks, iBooks Store, iBooks Author, Mac OS are registered® trademarks of Apple Inc. and their use on this webpage does not reflect endorsement by Apple Inc.