Natural prime numbers

[Epsilon=One]

Natural prime numbers

Natural prime numbers are Natural integers (www.101123.com/NI) generated by any Natural integer (www.101123.com/NI) value for the perigee, "p," of an obtuse Brunardot Ellipse (www.101123.com/BE) for it's hypotenuse, "h."

The formula for any Natural prime number where "p," is any Natural integer (www.101123.com/NI) is:Square root of (4p^4 – 8p³ + 8p² – 4p +1). Thus, the Natural prime numbers are uniformily distributed because they can be mapped to any Natural integer (www.11101123.com/NI).

Natural prime numbers can be considered as the units of Nature's scale. This explains why the scale of Reality (subatomic scales, anthropic scale, and Cosmic scales) is exponential.

Natural prime numbers are not the same set of numbers as conventional prime numbers that seem to have random distribution, and are uniformly grouped, and often appear paired.

The inexplicable distribution of conventional prime numbers is a result of the combination of several sets of numbers, which includes the set of Natural prime numbers.

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[ste]

When substituting natural integers above 2 for p in the following equation: sqrt(4p^4 - 8p^3 + 8p^2 - 4p + 1), a remainder of 1 is always returned. Therefore, all of the numbers returned are par1 numbers, and are neither in the number set par or par3.

[Epsilon=One]

When substituting natural integers above 2 for p in the following equation: sqrt(4p^4 - 8p^3 + 8p^2 - 4p + 1), a remainder of 1 is always returned. Therefore, all of the numbers returned are par1 numbers, and are neither in the number set par or par3.You are correct.

You will also notice that you get the same Par1 number set of Natural integers when “p” = 0 or is set to any negative Natural integer in said formula.

The formula √(4p − 8p + 8p − 4p + 1) is that of the hypotenuse, "h," of a Conceptual Ellipse (www.CQthus.com/PT/CE) (CE) expressed in the perigee, “p” (or Cosmic Pulse, “P”).

When “p” is a Natural integer, it is one of the sets that comprise Natural prime numbers, which are found among the structural parts and cycles of the CE.

Conventional prime numbers are derived by subtracting sets from the set of Natural Prime Numbers.

Note that the hypotenuse and radius of the nuclear CE always differ by a doubled Elliptical Constant (www.CQthus.com/PT/EC). ( h = v² + ε; r = v² – ε ) Such is the basis for “paired” prime numbers. And, also be aware that base 10 is a contrivance that is unknown to Nature.

[ste]

Natural prime numbers can be considered as the units of Nature's scale. This explains why the scale of Reality (subatomic scales, anthropic scale, and Cosmic scales) is exponential.
It seems that the natural prime numbers (at least the set you describe through hypotenuse length) are defined by a degree 2 polynomial (2x^2+2x+1, where x is the key). Why should the scale be exponential?

When “p” is a Natural integer, it is one of the sets that comprise Natural prime numbers, which are found among the structural parts and cycles of the CE.
If the values for h make up only one set that comprises natural prime numbers, which other structural parts make up the other sets (i.e. par3 numbers)? How would you define them other than the hypotenuse length in a CE? Are there any other interesting charactaristics to natural prime numbers?


Conventional prime numbers are derived by subtracting sets from the set of Natural Prime Numbers.
Which sets? When are they subtracted? Is there any apparent pattern?

[Epsilon=One]

It seems that the natural prime numbers (at least the set you describe through hypotenuse length) are defined by a degree 2 polynomial (2x^2+2x+1, where x is the key). Why should the scale be exponential?For an inertial Conceptual Ellipse (CE) the hypotenuse equation is:

h = √(4P – 8P + 8P – 4P + 1),

where the Pulse = P. When P is an integer, h is an integer.

For a nuclear CE the hypotenuse equation is:

h = √(4P + 2P + 1) or h = P + 1.

If the values for h make up only one set that comprises natural prime numbers, which other structural parts make up the other sets (i.e. par3 numbers)? How would you define them other than the hypotenuse length in a CE?The answer to that question will get you, at the least, a million dollar prize.

Are there any other interesting charactaristics to natural prime numbers?I find their distribution within various bases as interesting. And, of course, the integer value of the hypotenuse when the Pulse is an integer is not only the epitome of elegance; but, a necessity for existence.

Which sets? When are they subtracted? Is there any apparent pattern?The pattern is easily seen by most all good mathematicians. For the other questions, see the above answer concerning a prize.