An interesting prime number spiral was discovered in 1963 by Stanislaw M. Ulam, and is now called "the Ulam spiral". It reveals a strange property of the prime numbers.
A positive integer (1, 2, 3, ... ) greater than 1 is called prime if its only divisors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, ... The series is infinite, since there is no largest prime number. The proof of this goes back to the ancient Greek mathematician Euclid.
The Ulam spiral is constructed as follows: Consider a rectangular grid. We start with the central point and arrange the positive integers in a spiral fashion (anticlockwise) as at below left. The prime numbers are then marked (here with blue boxes). There is a tendency for the prime numbers to form diagonal lines. This can be seen more clearly in the image below right, in which each of the 70,255 pixels marks a position in the number sequence and the primes are marked by white pixels.
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This Prime Number Spiral software is a tool for exploring the Ulam spiral. Here is a typical screen:
The remainder of the user manual is here:
Languages: Prime Number Spiral is bilingual: English and German.
Demo version: A copy of the Prime Number Spiral installation program can be downloaded from this website for the purpose of evaluation. Click on the following link for further information:
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Refund: A refund will be provided promptly up to 30 days after purchase if the software does not perform satisfactorily.
Updates: Purchasers of a user license for this software are entitled to an update to any later version at no additional cost.
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