PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture:
A NEW Pattern reveals how every EVEN is made of 2 PRIMES
~A MathspeedST Supplement~


Gather the EVENS

Steps are P2-A

A=half E

Here’s the thing. Amongst a myriad of other connections, there exists an intimate connection between three number systems on the BBS-ISL Matrix (BIM):

  1. The Inverse Square Law (ISL) as laid out in the BIM;
  2. PTs — and most especially PPTs — as laid out on the BIM;
  3. The PRIME numbers — PRIMES — as laid out on the BIM.

The BIM is the FIXED GRID numerical array of the ISL.

PTs are the Pythagorean Triples and PPTs are the Primitive Pythagorean Triples. They have been extensively covered in the TPISC (The Pythagorean-Inverse Square Connection) series as: TPISC I Basics, TPISC II Advanced, TPISC III Clarity, TPISC IV Details. (See links at bottom.)

The PRIMES vs NO-PRIMES (2019) was covered earlier.

The original MathspeedST (2009-13) work, Brooks (Base) Square** **(2009-11), that started this journey, was divided in to two sections:

I. TAOST (The Architecture Of SpaceTime);

II. TCAOP (The Conspicuous Absence Of PRIMES).

You see, other than the natural whole numbers that form the BIM Axis’ and the standard 1st Parallel Diagonal (containing ALL the ODDs (≥3), there are NO PRIMES on the BIM.

This is the basis of the PRIMES vs NO-PRIMES work.

Yet, convert that same 1st Parallel Diagonal to ALL EVENS (≥4, by adding 1 to each former ODD), and now the BIM reveals the stealthily hidden PRIMES relationship in forming symmetrical pairs of PRIMES that are ALWAYS equal distance (STEPS) from ANY given EVEN # divided by two.

All this occurs on the BIM Axis. The apex of the 90° Right-angled, isosceles triangle so formed lies on a straight line path from the EVEN/2 to the given EVEN # located on that converted 1st Parallel Diagonal. This relationship is geometrically true and easily seen on the BIM.

Extracting those PRIME-Pair sets (PPsets) for each given EVEN forms the basis for the PTOP — Periodic Table Of PRIMES.

While “hidden” on the BIM, it clearly forms a definitive pattern on the PTOP: for EVERY 3+PRIME PPset that forms the 2nd column on the PTOP — acting like a bifurcation point — a “Trail” of PPsets forms a zig-zagging diagonal pointing down and to the right.

These are ALWAYS — much like a fractal — added with the SAME PRIME Sequence (3,5,7,11,13,17,19,23,29,31,37,...).

When you read a given horizontal line from left to right across the PTOP, you see that each given PPset that was contributed by a PPset Trail, adds up — composes — its respective EVEN. The sum (∑) number of PPsets that form its EVEN is totaled in the last column.

The fractal-like addition of one new, additional PRIME Sequence PPset to each subsequent “Trail” formed results in the overlapping trails growing at a rate that far, far exceeds the growth and incidence of the PRIME Gaps. This ensures that there will always be at least one PPset that will be present to compose ANY EVEN.

The Goldbach Conjecture has been satisfied and a new PRIME pattern has been found.

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



Excerpt From: Reginald Brooks. “PTOP (Periodic Table Of PRIMES) 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 PTOP (Periodic Table Of PRIMES) and the Goldbach Conjecture

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

Artist Link in iTunes iBookstore: 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 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 project (HOME)

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 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 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 2019-20, 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.