#perfectsquare

Mersenne Prime Squares ————April-Mersenne

digital, #4-29, 2021, Reginald Brooks

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Prime Squares —————-April-Mersenne

digital, #4-25, 2021, Reginald Brooks

It is interesting that if one knows either “x” or “y” one can reconstruct the entire Mersenne Prime Square (MPS) family tree:

MPS

PN

PNS

CR

OC

OCS

CR

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Primes Square ————April-Mersenne

digital, #4-24, 2021, Reginald Brooks

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Prime Squares ————-April-Mersenne

digital, #4-27, 2021, Reginald Brooks

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Primes Squares ————————- April-Mersenne

digital, #4-30, 2021, Reginald Brooks

See the White Paper — Mersenne Prime Squares — for the full story and updates, here.

Knowing the value of just one number — “x” or “y” — one can reconstruct the entire MPS!

I might add: the MPS is kind of like “Russian Dolls” in that within are more geometric areas, and within those, more areas. The big difference — other than the math — is the math!

In this 2D Euclidean space, the MPS occupies a Square AREA. Subdivide this into 2 RECTANGLES to give the Perfect Number (PN) and ODD Complement (OC). Now sub-divide each RECTANGLE into a SQUARE and another RECTANGLE, the Perfect Number Square (PNS) and its Complement Rectangle (CR) in the former, and the ODD Complement Square (OCS) and its CR (identical to the other CR), in the latter. The “x” is the side of the PNS and the “y” is the side of the OCS. They are also the sides of the CR. It all fits!

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Prime Squares ————————April-Mersenne

digital, #4-28, 2021, Reginald Brooks

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LINKS:

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Prime Squares ————-April-Mersenne

digital, #4-17, 2021, Reginald Brooks

See how the Perfect Number area encompasses the factors 1–2–3 that add up to 6. ALL PNs follow a geometry pattern like this.

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LINKS:

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

http://brooksdesign-ps.net/reginald_brooks/code/html/netarti5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number

Mersenne Prime Squares —————April-Mersenne

digital, #4-16, 2021, Reginald Brooks

EXAMPLE: In the bottom image, Mp=3 with a Perfect Number of 6. Embedded in the PN is a Perfect Square (PNS) 2x2=4. Another Perfect Square (OCS=1x1=1) is embedded in the ODD Complement (OC) rectangle. If you overlay the PNS to the top left corner of the grid with the OCS, the number 3 is found kitty-corner just below. 3=Mp=Mersenne Prime. The Mersenne Prime Square of ALL Mersenne Primes follows this pattern. There are currently 51 known Mersenne Primes, along with their 51 matching Perfect Numbers. This is the new geometry.

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LINKS:

http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/porfoli5.htm

https://en.wikipedia.org/wiki/Mersenne_prime

https://en.wikipedia.org/wiki/Perfect_number