Prime numbers

The concept

There is one remarkable thing about randomness: Its existence is neither proved nor disproved it even appears everyday in science and in our everyday lives. Random walk is interesting for people who want to know more about the mystic character of this invisible companion.

This diploma thesis was created at the University of Applied Sciences in Mainz, Germany by Daniel A. Becker in 2009 and was supervised by Prof. Johannes Bergerhausen.

The visualizations

All visualizations of physical mathematical phenomena are not just illustrated representations; they are actually simulated with the help of „proce55ing“. True chaos and order within randomness has been demonstrated by the use of pure numerical data and software simulations. Therefore, the software not only presents the visualizations but it also uses the graphics to prove the phenomenon of randomness.

Prime numbers

A prime number is a natural number which has exactly two distinct natural divisors: 1 and itself. Within the natural numbers from 0 to 1,000,000 there are exactly 78,498 prime numbers. Their distribution is chaotic – it cannot be predicted whether any subsequent number will be prime or not. Each number has to be checked precisely. However, the density of prime numbers decreases in the higher number ranges. In the range from 1 to 1,000 there are 168 prime numbers, whereas between 999,000 and 1,000,000 there are just 53.

The visualization shows lines in a circle each representing 400 natural numbers. The more prime numbers there are within each package of 400 numbers, the longer the line grows towards the center of the circle. There is no regularity within the different lengths of the lines – the number of primes is randomly distributed in each package. However, in the long term a spiral is generated suggesting a decrease of the density of prime numbers in higher number ranges.

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