Visualizing The Distribution of Prime Numbers

“Upon looking at these numbers, one has the feeling of being in the presence of the inexplicable secrets of creation.”
 
 
Pictures of Primes
picture of odd primes < 8192
http://www.mathematik.uni-muenchen.de/~forster/primes.html#p2_13

 
A visual representation of the primes – The author says: “This is derived from the primes, in a definite way; but is for beauty rather than information purposes
 

 

A visual Sieve for Prime Numbers
 

The well-known Ulam spiral and the variant developed by Robert Sacks, the Sacks spiral, show interesting geometric patterns in the positions of primes Number Spirals
 
 
You choose the starting integer (the mayor), and this java applet will draw the prime spiral around that point.
http://platon.lacitec.on.ca/~dmorin/applets/village/index.html
 
 
Number Spiral : A method of graphing the integers that reveals relationships between primes, factors, and products.
http://www.numberspiral.com/
 
 
Ulam’s Spiral
 
 
Ulam Spiral Visualization – The Pattern of Prime Numbers
 

 

 
Prime Number Spiral : Windows software for exploring the Ulam spiral with user-selectable central number and manner of coloring the primes, and animation of the spiral.
http://www.hermetic.ch/pns/pns.htm
 
 
Radiant Primes : Radiant generates radiant primes for you.
http://www.holygoat.co.uk/applications/radiant-primes/radiant-redirected
 
 
Representing prime numbers graphically : This page demonstrates various ways to represent prime numbers graphically.
http://yoyo.cc.monash.edu.au/~bunyip/primes/
 
 
Using the prime numbers to communicate with other civilizations
 
 
Differences between consecutive primes.
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 6, 6, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6, 4, 6, 8, 4, 2, 4, 12, 8, 4, 8, 4, 6, 12
http://oeis.org/A001223
 

 
 
 
Physics of the Riemann Hypothesis
http://arxiv.org/abs/1101.3116
 
The Riemann Zeros and Eigenvalue Asymptotics
http://jpkeating.files.wordpress.com/2010/11/32.pdf