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Ulams Prime Number Spiral

By Dmitry Brant Free

Developer's Description

There is an infinite number of prime numbers, and yet the prime numbers themselves do not display any apparent pattern, nor does any formula exist that generates prime numbers. In fact, Legendre proved that there cannot be an algebraic function which always gives primes.

It was first noticed by the physicist StanisÃ??aw Ulam in 1963, when he got bored in a meeting and started doodling spirals of numbers. He noticed that, if he makes a spiral of consecutive integers, and circles only the prime numbers, strange diagonal "lines" of prime numbers emerge. This is quite surprising, since we would intuitively expect a random distribution of prime numbers. However, these diagonal segments occur on an impressively large scale, and arbitrarily far from the center of the spiral. The following image is a spiral containing about 4000 primes, and next to it is the same image with some of the diagonal paths highlighted. To explore this phenomenon on a large scale, Ulams Prime Number Spiral generates arbitrarily large spirals, with configurable coloring and other options.

Full Specifications

What's new in version 1.0

General

Release July 17, 2010
Date Added January 5, 2007
Version 1.0

Operating Systems

Operating Systems Windows 2000, Windows Vista, Windows 98, Windows Me, Windows, Windows NT, Windows 7, Windows XP
Additional Requirements None

Popularity

Total Downloads 91
Downloads Last Week 0
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