Aesthetics of the Prime Numbers Sequence
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Aesthetics
of the Prime Sequence

This page is created, copyrighted
and maintained by:
Turpel Armand
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Last-modified: 1/3/1999

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My approach to the Prime-numbers is more intuitive than mathematical, but may worth to have a look. For a more mathematical view of Primes, visite Chris Caldwell's excellent Prime Page.

Book Bestsellers list at amazon.com

Introduction

Primality Testing Applet and more

Translation from Prime Numbers to Music Notes

Translation from Prime Numbers to Nucleotide Bases

Prime Graphics

Prime Numbers expressed by Lyapunov Exponents

Idiot Savants or is 65748756543542343631 Prime?

Test your sensitiveness about Prime-Numbers

Primes-to-Ascii program

Algomath is a small mathematical functions collection of fast C routines

Visualize of nucleotide sequences

Copyrights notice

Related Links

Introduction

A prime number is a number that is only divisible by 1 and itself.Why is it so fascinating, some people may ask? Throughout the history human beings tried to understand the environment. It was (is) important for the evolution. Often the environment was too complex to understand in its entirety. Humans were forced to compress information and still be able to tackle it. Sometimes they were successful and somtimes they failed.

A formula to produce prime numbers dosent exist. They can not (yet?) be reduced to something smaller than itself. They are the basic numbers which all other numbers are build from. Every non-prime is divisible by a prime. This characteristic is important in cryptography. Some species of insects even use primes in reproduce time as an advantage against predators. (primes are not only a human fantasy). Which leads to the question: If the billion year evolution use the advantage of non-compressibility of the primes to produce organisms, is then man capable to prove the opposite of this characteristic?

Translation from Prime Numbers to Music Notes

The Idea

Prime numbers have the characteristic that they extract themselves from each regularity. Since they expand however in the infinite, theoretically meaningful information must arise sometime. The difficulty consists in, to break down this result that it is available in an understandable form. Music is a form under many possibilities. The music midi files below, may not contains any particularly valuable informations, than aestheticalies. However it represent the spirit of this reflection.

This midi file is created, using the basic algorithm (see below), from the first 18000 primenumbers, start at the 4'th primenumber 7.
This midifile take part in Phil Thompson's Fractal Music CD

Some other examples of prime midi files
(different algorithms):

Quartet	Walking	Gong	Christmas
Rain	Halo	Kato	Sonami

Download MAKE-PRIME-MUSIC (release 1.1.3.2)

Description of the Midifile (basic algorithm)

With exception of 2 and 5, any prime number modulo 5 have as results 1, 2, 3 or 4. Around now the definite Midi note to be received, the modulo results of three successive prime numbers are selected and to a number, on base 4, compound. 64 possible combinations result.

Notice:
In each case three basic pairs, in the molecular biological language for special purposes as "codon" designated, stand for an amino acid. Ex: CAG = Glutamin. However, only 20 amino acids are formed from the 64 possible combinations. There are several combination suits for the same amino acid.

How to calculate the three first midi notes?

Prime Number	Modulo 5	Digit Base 4	Number Base 4	Midi Note (Decimal)
				No. 1
7	2	2 - 1 = 1
11	1	1 - 1 = 0	102	18
13	3	3 - 1 = 2
				No. 2
17	2	2 - 1 = 1
19	4	4 - 1 = 3	132	30
23	3	3 - 1 = 2
				No. 3
29	4	4 - 1 = 3
31	1	1 - 1 = 0	301	49
37	2	2 - 1 = 1

The three first prime numbers 7. 11. 13 modulo 5 results in 2. 1. 3. In the four-calculating-system this number represent 2-1=1, 1-1=0, 3-1=2 >> 102. In the decimal system this results in 1*4^2+0*4^1+2*4^0=18. The midi note become 18.

The Midi file has the following characteristics

Off course, the prime numbers 2 and 5 make no sense in the characteristic described here, so the prime number 7 is the first possible number to be considered.
These notes are divided in to 4 voices/tracks.

voice 1 contains the notes between 000 and 033
voice 2 contains the notes between 100 and 133
voice 3 contains the notes between 200 and 233
voice 4contains the notes between 300 and 333

In each voice the note continue until the next note in this voice arise.

Prime-to Ascii

This program write a list of prime numbers of your choice in a .txt file (ascii format). You can edit this file in a text editor and print it out.

Algomath is a small mathematical functions collection of fast C routines

Download the library v.1.0.3 beta 12.1998

Short description:
int am_sumdigits(int n); return the sum of the digits of the number n
int am_sumdigitsalt(int n); return the alternating sum of the digits of the number n
int am_rotate(int n, int x); rotate the digits of a number n, x times, in base 10
int am_sumdivisors(int n); return the sum of all possible divisors of the number n, n not included
int am_sortdigits(int n); sort the digits of a number n
int am_primetest(int n); return 1 if n is prime else -1
int am_gcd(int a, int b); return the greatest common divisor of two numbers a and b
void am_primearray (int p, n, int* Array ); store prime numbers to an array
void am_factorize(int n, int* Array); factorize a number n and stores its factors in array[]
int am_goldbach(int a,int *p); Goldbach's Conjecture

Next Project in work ........

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Copyrights Notice

You are free to do anything you desire with this material, as long as you give credit where credit is due... . In all cases the programms and the midifiles are NOT free for commercial use.

For commercial use contact me

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created 8/1997

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Aestheticsof the Prime Sequence

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