The Maria Number Matrix of the 33-Summation-Tier

[abraxasinas]

http://tonyb.freeyellow.com/id197.html (as I have not yet figured out IF and how this browser here would print indices (exponents) some of the mathematical detail below is basically unreadable - I apologize for this A.)

The 'Perennial Philosophy' or the 'Wisdom of the Ancients' often points to what is commonly termed as 'Sacred Geometry', based on the Platonic Solids (of five regular polyhedra: Tetrahedron, Cube; Octahedron; Dodecahedron and Icosahedron) and the Tetraktys of Pythagoras (for the minimum mathematical points to define the four dimensions of 0D=1 Point; 1D=2 Points for a Line; 2D=3 Points for a Plane and 3D= 4 Points for a Space).
Also invoked is the pentagonal supersymmetry of quasiperiodicity as 'Nature's Preferred maximisation of 'packing efficiency' known as the Fibonacci Series and the 'Perfect Numbers' of Euclid and the 'Harmony of Numbers and the Spheres' of Pythagoras, Leonardo da Vinci and Kepler.

In Pythagoraen Numerology, the 'masternumbers' 11, 22 and 33 are often emphasised and this post shall introduce some relatively rigorous number theory (of the so called 'pure' mathematics) to validate the significance of the 'masternumbers' from frst principles.
The alphanumeracy of the Arabic-Hebrew semiotiks then is bounded in say 22 or 26 letters of alphabets, which can attain numerical values in the decad of three triplicities:
Round or Curved 'Mental Numbers' {3-6-9} characterised by masternumber 33;
Mixed or Discontinuous 'Emotional Numbers' {2-5-8} characterised by masternumber 22 and
Linear or Straight 'Physical Numbers' {1-4-7} characterised by masternumber 11.


The Maria-Code in the Riemann Analysis specifies the partitioning of the decimal monad around the primary Maria-Number and SEps-Constant '11'.
This generates the Prime Number Algorithm: +1+11+10+11 as 33-tiered segments, which transform the mechanics of SEps into the 64-codex of the DNA/RNA code for its eventual quadrupling as the 256-codex incorporative of dormant intron/intein codings.

The Maria-Code is based on the distribution of the Maria-Numbers (MN)given by:
M(p)+99=M(p+12); n=[√(264k+1)-1]/2 by n2+n-66k=0.
Maria Numbers are those IntegerCounts, which contain all previously counted integers as mod33.
Example: 1+2+3+4+5+6+7+8+9+10+11=66 = 2x33 → '11' is MN#1 for k=2 11love65use110love164use209love263use......Archety pe 2 (rootreductive) 21use66love120use165love219use264love......Archety pe 3 (rootreductive) 32use77love131use176love230use275love......Archety pe 5 (rootreductive) 33love87use132love186use231love285use......Archety pe 6 (rootreductive) 44love98use143love197use242love296use......Archety pe 8 (rootreductive) 54use99love153use198love252use297love......Archety pe 9 (rootreductive) 65use110love164use209love263use308love....Archetyp e 2*... ... ... ...

Archetypes 2+3+5+6+8+9=33 and Archetypes 1+4+7+0=12 then define the imaginary time-dimensions as the archetypes not in the Sequence for Eps=1/e* Coefficients used in the application of the seven fundamental principalities to define the F-Space.
We have used the (Hebrew-Isaac-encoding): 54=LOVE=12+15+22+5 with 45=USE=21+19+5; USELOVE=99 as the Maria-Code connectors.
The first 10 MN's are: 11, 21, 32, 33, 44, 54, 65, 66, 77 and 87.
One can use the Maria-Code to establish a redefinition of infinity by defining a transfinite mapping Aleph-All from 12D-Omnispace as Cantorian transform of Cardinality Aleph-Null.
Limit (T(n)) for n→Infinity = Infinity {Cantor Cardinality Aleph-Null}
Limit (T(n)) for n→X = 1 {Cantor Cardinality Aleph-All}

This maps the Riemann pole about z=1 in the Functional-Riemann-Bound (FRB=-1/2) in the gaussian universal wavefunction B(n)=(2e/hA).exp(-Alpha.T(n)), T(n)=n(n+1) as the Feynman-Path-Integral. This becomes the Riemann-Euler-Harmonic, defining the Gamma-Function geometrically in its nth Term T and nth Sum S and mapping the factotrial function onto the positive integer count: Tk(En) = nk.Tk(En-1) + [(n-1)!]k and Sk(En) = Tk(En)/(n!)k
This uses the Harmonic Series in the Zeta-Function ζ(z) with constant p.
The Sum (1 to Infinity) Σ(1/np)= 1/1p+1/2p+1/3p+...+1/np and converges for any p>1, since for even terms: 2.2-p ≥ 2-p+3-p, with geometric series 11-p+21-p+41-p+...summing to
(1-2[1-p]^n)/(1-21-p)=1/[1-21-p] in the limit for n→Infinity.

Since every Maria Number contains all numbers before it as a sum, it is given that all the prime numbers must eventually crystallise out of the Maria Count.
Define a general number count n and a 'Mersenne-Count' 8n-1=M*.
For a number to be prime this number must be born in the Maria Code.
M* is either a prime or a product of primes in the immediate neighbourhood of the count # or its mapping to M*, which in a sense 'counts' the primes it generates.
This is the finestructure as octaves derived from integer n.
To test a number for primeness, so amounts to a testing for Marianess.
If the number is a member of the Maria-Matrix, then it must be denumerable in the form of M*.

This is the meaning behind the Mersenne-Code (for n prime) M(p)=2p-1 and the Fermat-Code F(n)=22^n+1 and the 'Perfect Numbers' depicted as the Mersenne Numbers (Mp), as a subset of M*.
For the Mersenne Numbers, the exponent p is defined to be prime.
M2=22-1=3; M3=23-1=7; M5=25-1=31; M7=27-1=127; M11=211-1=2047=23x89 and so is not a Mersenne Prime - yet M13=213-1=8191; M17=217-1=131,071;
M19=219-1=524,287 are prime and M23=223-1=8,388,607=47x178,481 and
M29=229-1=536,870,911=233x1103x2089 are not and M31=231-1=2,147,483,647 is prime again in the 33-tier count.

The 'uniqueness' of the prime number 11 (and esoteric masternumber) recrystallizes in Mersenne primes as the (first) 'odd one out'.
But it gets better. First we notice that there are just five 'perfect Fermat Primes'.
F0=21+1=3; F1=22+1=5; F2=24+1=17; F3=28+1=257 and F4=216+1=65,537 are all 'perfect' Fermat Primes, but F5=232+1=4,294,967,297=641x6,700,417 and following are not. Only these five Fermat primes are known to date.


From wiki:
Euclid discovered that the first four perfect numbers are generated by the formula 2p-1(2p - 1):
for p = 2: 21(22 - 1) = 6 for p = 3: 22(23 - 1) = 28 for p = 5: 24(25 - 1) = 496 for p = 7: 26(27 - 1) = 8128. Noticing that 2p - 1 is a prime number in each instance, Euclid proved that the formula 2p-1(2p - 1) gives an even perfect number whenever 2p - 1 is prime (Euclid, Prop. IX.36).


Ancient mathematicians made many assumptions about perfect numbers based on the four they knew, but most of those assumptions would later prove to be incorrect. One of these assumptions was that since 2, 3, 5, and 7 are precisely the first four primes, the fifth perfect number would be obtained when p = 11, the fifth prime. However, 211 - 1 = 2047 = 23 × 89 is not prime and therefore p = 11 does not yield a perfect number. Two other wrong assumptions were:

• The fifth perfect number would have five digits in base 10 since the first four had 1, 2, 3, and 4 digits respectively.
• The perfect numbers' final digits would go 6, 8, 6, 8, alternately.

The fifth perfect number (33550336 = 212(213 - 1)) has 8 digits, thus refuting the first assumption. For the second assumption, the fifth perfect number indeed ends with a 6. However, the sixth (8 589 869 056) also ends in a 6. It is straightforward to show that the last digit of any even perfect number must be 6 (when p = 2 or 4k+1) or 8 (when p = 4k-1).
In order for 2p - 1 to be prime, it is necessary but not sufficient that p should be prime. Prime numbers of the form 2p - 1 are known as Mersenne primes, after the seventeenth-century monk Marin Mersenne, who studied number theory and perfect numbers."(end wiki)

The 'Perfect Numbers' relate (for prime p) as 2p-1.Mp :
P2=21.(22-1)=6=1+2+3=1x2x3;
P3=22.(23-1)=28=1+2+3+4+5+6+7=[7x8]/2=4x7=13+33=1+27;
P5=24.(25-1)=496=1+2+3+...+30+31=[31x32]/2 =16x31=13+33+53+73=1+27+125+343;
P6=26.(27-1)=8128=1+2+3+...+126+127=[127x128]/2=13+33+53+73+93+113+133+153

All 'Perfect Numbers' so are EVEN (it is hitherto unknown if any ODD 'Perfect Numbers' exist); and EXCEPT the basic 'First Perfect Number' 6=1+2+3=1x2x3, they all are the sums of the ODD NUMBERS CUBED.

Abraxasinas