Properties of Prime Numbers

[Guest]

We know that a prime number is an integer divisible by one and itself. We exclude one as prime in the multiplicative case so that the Fundamental Theorem of Arithmetic will work...

Some Properties of Prime Numbers:

0) They generate all composites.

1) All but one prime number is odd.

2) All have size.

3) There are infinitely many prime numbers.

4) They are 'optimal', and therefore, they are unique.

5) They have 'particle-wave duality' properties...

6) They are generally the sum of other primes.

...
Please share your thoughts or comments. Please make a contribution. Thanks!

[Guest]

We know that a prime number is an integer divisible by one and itself. We exclude one as prime in the multiplicative case so that the Fundamental Theorem of Arithmetic will work...

Some Properties of Prime Numbers:

0) They generate all composites.

1) All but one prime number is odd.

2) All have size.

3) There are infinitely many prime numbers.

4) They are 'optimal', and therefore, they are unique.

5) They have 'particle-wave duality' properties...

6) They are generally the sum of other primes.

...
Please share your thoughts or comments. Please make a contribution. Thanks!

Some Reference links:

http://phillipmfeldman.org/mathematics/primes.html
(Prime Numbers and Their Statistical Properties by Dr. Phillip M. Feldman)

http://betterexplained.com/articles/ano ... e-numbers/
(Another Look at Prime Numbers by Kalid Azad )

[Guest]

Some More Reference Links:

http://file.scirp.org/Html/2-5300861_55360.htm
(The Harmonic Neutron Hypothesis: Prime Number Factor Patterns and Their Relationship to the Hierarchy of the Fundamental Particles and Bosons)

http://complex.ffn.ub.es/~mbogunya/archivos_cms/files/PhysRevE.90.022806.pdf
(Complex architecture of primes and natural numbers)

[Guest]

At present, both number theory and physics are stuck in the limits of predictability with regards to prime numbers (see my topic on Uncertainty Principle for Prime Numbers), and the *discovery of essential macroscopic properties of matter from microscopic properties of matter, respectively. Godel Incompleteness Theorems rear their heads here. Our current technology and understanding are lacking...

But there's hope, artificial intelligence or a major breakthrough may save the day. So, keep the faith (hope and effort). Good results will come...

*Reference link:

http://www.sciencedaily.com/releases/2015/12/151209142727.htm?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+sciencedaily%2Fcomputers_math%2Fmathematics+%28Mathematics+News+--+ScienceDaily%29

[Guest]

At present, both number theory and physics are stuck in the limits of predictability with regards to prime numbers (see my topic on Uncertainty Principle for Prime Numbers), and the *discovery of essential macroscopic properties of matter from microscopic properties of matter, respectively. Godel Incompleteness Theorems rear their heads here. Our current technology and understanding are lacking...

But there's hope, artificial intelligence or a major breakthrough may save the day. So, keep the faith (hope and effort). Good results will come...

*Reference link:

http://www.sciencedaily.com/releases/2015/12/151209142727.htm?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+sciencedaily%2Fcomputers_math%2Fmathematics+%28Mathematics+News+--+ScienceDaily%29

"

Please read, 'Out of Chaos' by llya Prigogine (the late great scientist) and Isabelle Stengers at the following link:

https://deterritorialinvestigations.files.wordpress.com/2015/03/ilya_prigogine_isabelle_stengers_alvin_tofflerbookfi-org.pdf

[Guest]

One More Excellent Reference:

'Physics of the Riemann Hypothesis'
by Daniel Schumayer
and David A. W. Hutchinson
at Jack Dodd Centre for Quantum Technology,
Department of Physics,
University of Otago, Dunedin, New Zealand:

Please read the paper at the following link:
http://arxiv.org/pdf/1101.3116v1.pdf

[Guest]

Dimensions of State Space--Complexity and Change

Keywords: State Space, Network Theory, Artificial Intelligence, Fundamental Theorem of Arithmetic, Prime Number Theorem, the sound Polignac Conjecture, the sound Riemann Hypothesis, the Harmonic Series, the sound Goldbach Conjecture, the Prime Parity Law, Multiplication (Factorization) and Addition Operations.

In both prime number theory and physics (especially quantum theory and cosmology), state space description of system at hand is important. For example, the generation of prime numbers (particles) requires knowledge of the prime gap (the space between two consecutive primes), and the generation of composites (superposition of waves of particles due to their spatial quality) requires knowledge of the prime gap as well. And since prime numbers are optimal, we have three key components or metrics of the prime gap: repetition, growth, and primality. These metrics determine the generation of primes and the generation composites according to the Fundamental Theorem of Arithmetic and Prime Number Theorem, and according to the sound Goldbach Conjecture and the Prime Parity Law.

Fundamental Theorem of Arithmetic is great because of its uniqueness quality of factorization, and the sound Goldbach Conjecture is great because of its elegance (simplicity and efficiency) of addition.

[leesajohnson]

Thanks for sharing the properties of prime numbers.