Three-part video introduction:

Is not the number one (1) the ultimate "fractal?"

While not technically a prime, it is only divisible by itself and 1.

If we loosen our definition of what a fractal is to include that which forms a larger whole simply by doubling itself and each sum/product thereafter: 1--2--4--8--16--32--64--....

We can also write that as exponentials of 2:

2^0^--2^{1}--2^{2}--2^{3}--2^{4}--2^{5}--2^{6}--..., respectively.

A careful look at the four images above of the first four **MPS** reveals that just such a simple definition of fractal is in play here.

Once you can see how the "big" forms of the **MPS** are formed from the smaller forms by this simple fractal of one, you will have one of the keys that unlock how ALL the forms of the **MPS** are formed! And it is quite amazing!

While these simple fractal forms that become the AREAS that define the three generations of AREAS that make up each and every **MPS**, as can be seen on any common grid layout, it is not until one reveals the same on the **BIM** that the true details can be seen!

Our method will be to put each **MPS** on the **BIM** and then highlight their individual details -- profiles, really -- and then proceed to show how such a **Number Pattern Sequence** (**NPS**) is fractal repeated in each successive **MPS**.

We will start with the simpler universal grid and then proceed to the details as seen in the **MPS** on the **BIM** (**BIM** + **MPS** = **BIMMPS**).

Before we get started, let's just get an overview by looking again at the four images above. The comments below will apply as a **NPS** across to ALL **MPS**.

The

**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).The EVEN is the Perfect Number (

**PN**) and the ODD is the ODD Complement (**OC**).The

**PN**has rectangular bands of a single color that meets up with the last multi-colored band.This last, polychromatic band sits right on the center line of the

**MPS**.The large rectangles on either side are equal. That's right, the colorful rectangle to the left = the gray rectangle to the right.

This central, polychromatic band is ALWAYS composed of a sequence of 1-2-4-... fractals and it ALWAYS ends with an EVEN.

Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that =

**Mp**=**z**.The

**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.**Mp**=**z**.So the difference (∆) between the

**PN**and**OC**is this**Mp**=**z**.The number of fractals in this

__central__, vertical band =**p**, where**p**= prime.The total number of the colorful

__vertical__bands, with the central band counted as one, within the**PN**also =**p**.Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the

**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor.The

**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

That's it -- for now! Every **MPS** follows this **NPS**!

Let's go over some of the MPS in detail using the above NPS overview as a starting point.

- The
**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).

- The EVEN is the Perfect Number (
**PN**) and the ODD is the ODD Complement (**OC**).

- The
**PN**has rectangular bands of a single color that meets up with the last multi-colored band.

- This last, polychromatic band sits right on the center line of the
**MPS**.

- The large rectangles on either side are equal. That's right, the colorful rectangle to the left = the gray rectangle to the right.

- This central, polychromatic band is ALWAYS composed of a sequence of 1-2-4-... fractals and it ALWAYS ends with an EVEN.

- Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that = Mp = z.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x,**and**x**+**y**=**z**.

- So the difference (∆) between the
**PN**and**OC**is this**Mp**=**z**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**, also =**p**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**, also =**p**.

- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the
**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor.

- The
**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

- The
**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray). - The EVEN is the Perfect Number (
**PN**) and the ODD is the ODD Complement (**OC**). - The PN has rectangular bands of a single color that meets up with the last multi-colored band.
- This last, polychromatic band sits right on the center line of the
**MPS**. - The large rectangles on either side are equal. That's right, the colorful rectangle to the left = the gray rectangle to the right.
- This central, polychromatic band is ALWAYS composed of a sequence of 1-2-4-... fractals and it ALWAYS ends with an EVEN.
- Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that =
**Mp**=**z**. - The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.**Mp**=**z**. - So the difference (∆) between the
**PN**and**OC**is this**Mp**=**z.** - The number of fractals in this
__central__, vertical band =**p**, where**p**= prime. - The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**also =**p**. - Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the
**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor. - The
**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

As described earlier, there are three generations -- grandparent-parent-grandchild-- that inform each **MPS**. The "grandparent" is of course the **MPS** itself. The "parent" is the generation layered below. Most of the above #1-13 **NPS**s above describe this generation.

Below the "parent" is the "grandchild" generation. The **PN** and **OC** Rectangles of the "parent" generation are simply further divided into the Perfect Number Square (**PNS**) and remaining Complement Rectangle (**CR**) of the **PN**, and, the ODD Complement Square (**OCS**) and the identical **CR** of the **OC**. The next three (#14, 15, and 16) **NPS** describe the **PNS**, **OCS** and **CR**.

- The Complement Rectangle (
**CR**) =**xy**, appears twice in the “grandchild” generation as 2**CR**=2**xy**=**OC**+**y**=**yz**+**y**= gray(**OC**)+all the central bands except the last EVEN=**PN**- the central band last EVEN, e.i., 24=21+3=28-4. - While the Perfect Number Square (
**PNS**) =**x²**appears just once and as double its value as 2**PNS**=2**x²**=2(**x*****x**) =**PN**+**x**=**xz**+**x**= color(**PN**)+central band last EVEN, e.i., 32=28+4. - While the ODD Complement Square (
**OCS**) =**y²**appears just once and as double its value as 2**OCS**=**2y²**=2(**y*****y**)=**OC**-**y**=**yz**-**y**=gray(**OC**) - all the central bands except the last EVEN, e.i., 18=21-3.

The #17 **NPS** describes something special: the sum (**∑**) of the **PNS** + **OCS** Areas.

- The sum (
**∑**) of the**PNS**+**OCS**Areas =**∑(x²**+**y²**)=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+**x**, e.i., 16 + 9 =25 =28-3=21+4.

(See next size up for images and examples.)

`xxxxxxxxxx`

- The
**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).

- The EVEN is the Perfect Number (
**PN**) and the ODD is the ODD Complement (**OC**).

- The
**PN**has rectangular bands of a single color that meets up with the last multi-colored band.

- This last, polychromatic band sits right on the center line of the
**MPS**.

- Because it has ALL EVENS + the ODD #1, it sums (
**∑**) up to an ODD that =**Mp**=**z**.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- So the difference (∆) between the
**PN**and**OC**is this**Mp**=**z**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**, also =**p**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**, also =**p**.

- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the
**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor.

- The
**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

- The MPS Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).
- The EVEN is the Perfect Number (PN) and the ODD is the ODD Complement (OC).
- The PN has rectangular bands of a single color that meets up with the last multi-colored band.
- This last, polychromatic band sits right on the center line of the MPS Square.
- Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that = Mp = z.
- The ∑ of ALL the fractals, up to but not including the last ending EVEN, = y, as the last, ending EVEN itself = x, and x+y=z. Mp=z.
- So the difference (∆) between the PN and OC is this Mp=z.
- The number of fractals in this
central, vertical band = p, where p = prime.- The total number of the colorful
verticalbands, with the central band counted as one, within the PN also = p.- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the z=Mp to give the remaining AREAS of the PN, each one successively doubling its predecessor.
- The ∑ of these AREAS = the OC, and, when added to the AREA of the central band = PN.

As described earlier, there are three generations -- grandparent-parent-grandchild-- that inform each **MPS**. The "grandparent" is of course the **MPS** itself. The "parent" is the generation layered below. Most of the above #1-13 **NPS**s above describe this generation.

Below the "parent" is the "grandchild" generation. The **PN** and **OC** Rectangles of the "parent" generation are simply further divided into the Perfect Number Square (**PNS**) and remaining Complement Rectangle (**CR**) of the **PN**, and, the ODD Complement Square (**OCS**) and the identical **CR** of the **OC**. The next three (#14, 15, and 16) **NPS** describe the **PNS**, **OCS** and **CR**.

- The Complement Rectangle (
**CR**) =**xy**, appears twice in the “grandchild” generation as 2**CR**=2**xy**=**OC**+**y**=**yz**+**y**= gray(**OC**)+all the central bands except the last EVEN=**PN**- the central band last EVEN, e.i., 24=21+3=28-4.

- While the Perfect Number Square (
**PNS**) =**x²**appears just once and as double its value as 2**PNS**=2**x²**=2(**x*****x**) =**PN**+**x**=**xz**+**x**= color(**PN**)+central band last EVEN, e.i., 32=28+4.

- While the ODD Complement Square (
**OCS**) =**y²**appears just once and as double its value as 2**OCS**=2**y²**=2(**y*****y**)=**OC**-**y**=**yz**-**y**=gray(**OC**) - all the central bands except the last EVEN, e.i., 18=21-3.

- The Complement Rectangle (CR) =xy, appears twice in the “grandchild” generation as 2CR=2xy=OC+y=yz+y= gray(OC)+all the central bands except the last EVEN=PN - the central band last EVEN, e.i., 24=21+3=28-4.
- While the Perfect Number Square (PNS) = x² appears just once and as double its value as 2PNS=2x² =2(x*x) = PN + x = xz+x = color(PN)+central band last EVEN, e.i., 32=28+4.
- While the ODD Complement Square (OCS) = y² appears just once and as double its value as 2OCS=2y² =2(y*y)=OC-y=yz-y=gray(OC) - all the central bands except the last EVEN, e.i., 18=21-3.

The #17 **NPS** describes something special: the sum (**∑**) of the **PNS** + **OCS** Areas.

- The sum (∑) of the
**PNS**+**OCS**Areas =**∑(x²**+**y²**)=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+**x**, e.i., 16 + 9 =25 =28-3=21+4.

- The sum (
**∑**) of the**PNS**+**OCS**Areas =**∑(x²**+**y²**)=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+**x**, e.i., 16 + 9 =25 =28-3=21+4.

x

- The
**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).

- The EVEN is the Perfect Number (
**PN**) and the ODD is the ODD Complement (**OC**).

- The
**PN**has rectangular bands of a single color that meets up with the last multi-colored band.

- This last, polychromatic band sits right on the center line of the
**MPS**.

- Because it has ALL EVENS + the ODD #1, it sums (
**∑**) up to an ODD that =**Mp**=**z**.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- The
**∑**of ALL the fractals, up to but not including the last ending EVEN, =**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- So the difference (∆) between the
**PN**and**OC**is this**Mp**=**z**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**also =**p**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**also =**p**.

- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the
**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor.

- The
**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

- The MPS Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).
- The EVEN is the Perfect Number (PN) and the ODD is the ODD Complement (OC).
- The PN has rectangular bands of a single color that meets up with the last multi-colored band.
- This last, polychromatic band sits right on the center line of the MPS Square.
- Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that = Mp = z.
- The ∑ of ALL the fractals, up to but not including the last ending EVEN, = y, as the last, ending EVEN itself = x, and x+y=z. Mp=z.
- So the difference (∆) between the PN and OC is this Mp=z.
- The number of fractals in this
central, vertical band = p, where p = prime.- The total number of the colorful
verticalbands, with the central band counted as one, within the PN also = p.- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the z=Mp to give the remaining AREAS of the PN, each one successively doubling its predecessor.
- The ∑ of these AREAS = the OC, and, when added to the AREA of the central band = PN.

As described earlier, there are three generations -- grandparent-parent-grandchild-- that inform each MPS. The "grandparent" is of course the **MPS** itself. The "parent" is the generation layered below. Most of the above #1-13 **NPS**s above describe this generation.

Below the "parent" is the "grandchild" generation. The **PN** and **OC** Rectangles of the "parent" generation are simply further divided into the Perfect Number Square (**PNS**) and remaining Complement Rectangle (**CR**) of the **PN**, and, the ODD Complement Square (**OCS**) and the identical **CR** of the OC. The next three (#14, 15, and 16) **NPS** describe the **PNS**, **OCS** and **CR**.

- The Complement Rectangle (
**CR**) =**xy**, appears twice in the “grandchild” generation as 2**CR**=2**xy**=**OC**+**y**=**yz**+**y**= gray(**OC**)+all the central bands except the last EVEN=**PN**- the central band last EVEN, e.i., 24=21+3=28-4.

- While the Perfect Number Square (
**PNS**) =**x²**appears just once and as double its value as 2**PNS**=2**x²**=2(**x*****x**) =**PN**+**x**=**xz**+**x**= color(**PN**)+central band last EVEN, e.i., 32=28+4.

- While the ODD Complement Square (
**OCS**) =**y²**appears just once and as double its value as 2**OCS**=2**y²**=2(**y*****y**)=**OC**-**y**=**yz**-**y**=gray(**OC**) - all the central bands except the last EVEN, e.i., 18=21-3.

- The Complement Rectangle (CR) =xy, appears twice in the “grandchild” generation as 2CR=2xy=OC+y=yz+y= gray(OC)+all the central bands except the last EVEN=PN - the central band last EVEN, e.i., 24=21+3=28-4.
- While the Perfect Number Square (PNS) = x² appears just once and as double its value as 2PNS=2x² =2(x*x) = PN + x = xz+x = color(PN)+central band last EVEN, e.i., 32=28+4.
- While the ODD Complement Square (OCS) = y² appears just once and as double its value as 2OCS=2y² =2(y*y)=OC-y=yz-y=gray(OC) - all the central bands except the last EVEN, e.i., 18=21-3.

The #17 **NPS** describes something special: the sum (**∑**) of the **PNS** + **OCS** Areas.

- The sum (
**∑**) of the**PNS**+**OCS**Areas =**∑(x²**+**y²**)=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+**x**, e.i., 16 + 9 =25 =28-3=21+4.

- The sum (
**∑**) of the**PNS**+**OCS**Areas =**∑(x²**+**y²)**=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+x, e.i., 16 + 9 =25 =28-3=21+4.

`xxxxxxxxxx`

- The
**MPS**Square Area is divided into two parts - rectangles - one that is EVEN (colors) and slightly larger, the other ODD (gray).

- The EVEN is the Perfect Number (
**PN**) and the ODD is the ODD Complement (**OC**).

- The
**PN**has rectangular bands of a single color that meets up with the last multi-colored band.

- This last, polychromatic band sits right on the center line of the
**MPS**.

- Because it has ALL EVENS + the ODD #1, it sums (
**∑**) up to an ODD that =**Mp**=**z**.

- The ∑ of ALL the fractals, up to but not including the last ending EVEN, =
**y**, as the last, ending EVEN itself =**x**, and**x**+**y**=**z**.

- The ∑ of ALL the fractals, up to but not including the last ending EVEN, =
**y**, as the last, ending EVEN itself =**x,**and**x**+**y**=**z**.

- So the difference (∆) between the
**PN**and**OC**is this**Mp**=**z**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**also =**p**.

- The total number of the colorful
__vertical__bands, with the central band counted as one, within the**PN**also =**p**.

- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the
**z**=**Mp**to give the remaining AREAS of the**PN**, each one successively doubling its predecessor.

- The
**∑**of these AREAS = the**OC**, and, when added to the AREA of the central band =**PN**.

- The EVEN is the Perfect Number (PN) and the ODD is the ODD Complement (OC).
- The PN has rectangular bands of a single color that meets up with the last multi-colored band.
- This last, polychromatic band sits right on the center line of the MPS Square.
- Because it has ALL EVENS + the ODD #1, it sums (∑) up to an ODD that = Mp = z.
- The ∑ of ALL the fractals, up to but not including the last ending EVEN, = y, as the last, ending EVEN itself = x, and x+y=z. Mp=z.
- So the difference (∆) between the PN and OC is this Mp=z.
- The number of fractals in this
central, vertical band = p, where p = prime.- The total number of the colorful
verticalbands, with the central band counted as one, within the PN also = p.- Not counting the central band, the remaining bands are exponential powers of 2 fractals that multiply with the z=Mp to give the remaining AREAS of the PN, each one successively doubling its predecessor.
- The ∑ of these AREAS = the OC, and, when added to the AREA of the central band = PN.

As described earlier, there are three generations -- grandparent-parent-grandchild-- that inform each **MPS**. The "grandparent" is of course the **MPS** itself. The "parent" is the generation layered below. Most of the above #1-13 **NPS**s above describe this generation.

Below the "parent" is the "grandchild" generation. The **PN** and **OC** Rectangles of the "parent" generation are simply further divided into the Perfect Number Square (**PNS**) and remaining Complement Rectangle (**CR**) of the **PN**, and, the ODD Complement Square (**OCS**) and the identical **CR** of the **OC**. The next three (#14, 15, and 16) **NPS** describe the **PNS**, **OCS** and **CR**.

- The Complement Rectangle (
**CR**) =**xy**, appears twice in the “grandchild” generation as 2**CR**=2**xy**=**OC**+**y**=**yz**+**y**= gray(**OC**)+all the central bands except the last EVEN=**PN**- the central band last EVEN, e.i., 24=21+3=28-4.

- While the Perfect Number Square (
**PNS**) =**x²**appears just once and as double its value as 2**PNS**=2**x²**=2(**x*****x**) =**PN**+**x**=**xz**+**x**= color(**PN**)+central band last EVEN, e.i., 32=28+4.

- While the ODD Complement Square (
**OCS**) =**y²**appears just once and as double its value as 2**OCS**=2**y²**=2(**y*****y**)=**OC**-**y**=**yz**-**y**=gray(**OC**) - all the central bands except the last EVEN, e.i., 18=21-3.

- The Complement Rectangle (CR) =xy, appears twice in the “grandchild” generation as 2CR=2xy=OC+y=yz+y= gray(OC)+all the central bands except the last EVEN=PN - the central band last EVEN, e.i., 24=21+3=28-4.
- While the Perfect Number Square (PNS) = x² appears just once as double its value as 2PNS=2x² =2(x*x) = PN + x = xz+x = color(PN)+central band last EVEN, e.i., 32=28+4.
- While the ODD Complement Square (OCS) = y² appears just once as double its value as 2OCS=2y² =2(y*y)=OC-y=yz-y=gray(OC) - all the central bands except the last EVEN, e.i., 18=21-3.

The #17 **NPS** describes something special: the sum (**∑**) of the **PNS** + **OCS** Areas.

- The sum (∑) of the
**PNS**+**OCS**Areas =**∑(x²**+**y²)**=**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+x, e.i., 16 + 9 =25 =28-3=21+4.

- The sum (
**∑**) of the**PNS**+**OCS**Areas =**∑(x²**+**y²**) =**PN**-**y**= color(**PN**) - all central bands except the last EVEN = gray(**OC**)+x, e.i., 16 + 9 =25 =28-3=21+4.

`xxxxxxxxxx`

As one can see, the color bands that make up the **PN** can form all three "generations" withing the **MPS** space. They do so in a completely fractal manner, based on the exponential power of 2. They do so in a repeating **NPS** template that is exactly the same for each **MPS**, with only the relative numbers being different.

BIM-MPS-PN-1--1.mp4

BIM-MPS-PN-1--1.gif

Now let's go back and look at the opening statement:

Is not the number one (1) the ultimate "fractal?"

While not technically a prime, it is only divisible by itself and 1.

If we loosen our definition of what a fractal is to include that which forms a larger whole simply by doubling itself and each sum/product thereafter: 1--2--4--8--16--32--64--....

We can also write that as exponentials of 2:

2

^{0}--2^{1}--2^{2}--2^{3}--2^{4}--2^{5}--2^{6}--..., respectively.

Letting the **Fractal "1"** (**F~1~**) simply double itself and then let the result double itself, and that result double itself -- a successive doubling -- generates a bi-lateral mirror-symmetric fractal pattern whose mirrored sides exactly repeat the pattern of the "whole!" The resulting image is aptly called the "* Butterfly Fractal~1~*" and not only does it more than suggest the patterns of butterflies and moths, it also generates the key values within the

Reginald Brooks

Brooks Design

Portland, OR

brooksdesign-ps.net

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~

NEXT: MPS Master Tables

LINKS:

Mersenne Prime Squares (Part I) the Introductory white paper.

Mersenne Prime Squares (Part II) 3 Simple Intros.

Mersenne Prime Squares (Part III) the Advanced white paper.

The MPS Project The Mersenne Prime Squares Project.

MathspeedST: TPISC Media Center

Artist Link in iTunes Apple Books Store: Reginald Brooks

Back to Part I of the BIM-Goldbach_Conjecture.

Back to Part III of the BIM-Goldbach_Conjecture.

BACK: ---> PRIMES Index on a separate White Paper BACK: ---> Periodic Table Of PRIMES (PTOP) and the Goldbach Conjecture on a separate White Paper (REFERENCES found here.) BACK: ---> Periodic Table Of PRIMES (PTOP) - Goldbach Conjecture ebook on a separate White Paper BACK: ---> Simple Path BIM to PRIMES on a separate White Paper BACK: ---> PRIMES vs NO-PRIMES on a separate White Paper BACK: ---> TPISC_IV: Details_BIM+PTs+PRIMES on a separate White Paper BACK: ---> PRIME GAPS on a separate White PaperReginald Brooks

Brooks Design

Portland, OR

brooksdesign-ps.net

Art Theory 101 / White Papers Index