Periodic Table Of PRIMES (PTOP) & the Goldbach ConjecturePPsets That = EVENS: Form Isosceles RightTriangles, reflecting a symmetrical pattern to the PRIMES whose sums equal a given EVEN.
By: Reginald Brooks 2019 Reginald Brooks ~~~ Gather the EVENS STEPS are P_{2}  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 BBSISL Matrix (BIM):
PTs are the Pythagorean Triples, PPTs are the Primitive Pythagorean Triples. They have been extensively covered in the TPISC (The Pythagorean The PRIMES vs NOPRIMES (2019) was covered earlier. The original MathspeedST (200913) work, Brooks (Base) Square (200911), 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 1^{st} Parallel Diagonal (containing ALL the ODDs (≥3), there are NO PRIMES on the BIM. This is the basis of the PRIMES vs NOPRIMES work. Yet, convert that same 1^{st} 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° Rightangled, isosceles triangle so formed lies on a straight line path from the EVEN/2 to the given EVEN # located on that converted 1^{st} Parallel Diagonal. This relationship is geometrically true and easily seen on the BIM. Extracting those PRIMEPair 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 2^{nd} column on the PTOP — acting like a bifurcation point — a "Trail" of PPsets forms a zigzagging 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 fractallike addition of one new, additional PRIME Sequence PPset to each subsequent "Trail" formed results in the overlapping trails growing at a rate that 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 https://vimeo.com/ 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 TPISC I: Basics TPISC II: Advanced TPISC III: Clarity and the Tree of Primitive Pythagorean Triples TPISC IV: Details, DSEQEC and PRIMES. PRIMES vs NOPRIMES End
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