#divisors

"DMT_119," digital + acrylic, July 29, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

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"DMT_90," digital + acrylic, June 30, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

June bloom

Never too soon

Twenty eight

Don't be late

"tDMT-#3," digital, Sept. 2024, Reginald Brooks

The original DMT (Divisor Matrix Table) reveals ALL natural numbers and their divisors.

The truncated DMT -- tDMT -- is based on the original DMT, only filtered to reveal just those ODDs in Column 1 that are the Running Sums (∑) of the Row 1, i.e. 1-3-7-15-31-...

Why? The tDMT reveals ONLY those Rows that are "container" Rows -- i.e. based on the ∑s of the Exponential Power of 2 (seen as the Butterfly Fractal 1 sequence in Row 1 -- and these contain ALL possible Mersenne Prime-Perfect Number (Mp-PN) candidates.

Yes, that's a lot to swallow up front. One is simply taking the DMT and redacting out every Row except those beginning with 1-3-7-15-31-...

Why, again? The tDMT gives a simpler view of the key numbers informing the Mp-PNs!

The Mp-PNs are the rarest gems of the Primes!

Here, Perfect Numbers (PN) 6, 28, 496, 8128 and 33550336 are shown as they are presented by Mersenne Primes (Mp) 3, 7, 31, 127 and 8191, respectively.

"DMT_87," digital + acrylic, June 27, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

The Running Sums (∑) -- coming up -- specifically cull out those Exponential Power of 2 "containers" that hold all the Mersenne Prime - Perfect Number pairings.



"DMT_91," digital + acrylic, July 1, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

Jully

So high

With flowered skies

Twenty eight

Don't be late

"DMT_56," digital + acrylic, May 28, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

The BIM (BBS-ISL Matrix), is basically a subset of the DMT. Unlike the DMT that contains ALL the natural numbers, the BIM's Inner Grid only contains EVENs ÷4 and ODDs that are Non-Primes.

However, for any given Mersenne Prime-Perfect Number pairing, all 10 of its defining parameters can be located on the BIM, so it is not all that surprising that they can also be found on the DMT!

x, x², y, y², z, z², xy, xz, yz, p

Except for p=Prime, all the other algebraic parameters have a geometric counterpart. And as they are all inter-related parts of that geometry as well as being related by strict algebraic calculation, knowing any one parameter immediately lets you know (calculate/geometrically draw) any and all of the other parameters.

The key difference is that on the DMT, one must include the Running Sums (∑) along with the tables proper values to see all 10 of the parameters.

Is it no wonder that the Universe(s) is/are an entangled fractal that is self-aware!