Mersenne Primes Squares ββββββββ- April-Mersenne
digital, #4-30, 2021, Reginald Brooks
See the White Paper β Mersenne Prime Squares β for the full story and updates, here.
Knowing the value of just one number β βxβ or βyβ β one can reconstruct the entire MPS!
I might add: the MPS is kind of like βRussian Dollsβ in that within are more geometric areas, and within those, more areas. The big difference β other than the math β 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 βxβ is the side of the PNS and the βyβ is the side of the OCS. They are also the sides of the CR. It all fits!
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
https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem