Exploration of the Ulam Spiral

Overview

Objectives/Goals The Ulam Spiral is a way of visually displaying the prime numbers which shows some of the sequence relationships which exist across the whole set of natural numbers. My project focused on whether the patterns observed in the original Ulam Spiral would be seen in variant forms and most especially when the spiral became much larger than when it is typically displayed on a single page. Methods/Materials Windows PC loaded with a version of the Python Programming language which has the matplotlib package installed. Results My discovery was that patterns seen early within small versions of the Ulam spiral continue to exist even when the Ulam Spiral gets to be very large. Spiral sizes in excess of five million required hours for my computer to produce but could then be sampled to see the patterns continue to exist. These large spirals could then be searched by computer to find the areas of the spiral where the patterns were the longest and most frequently seen. Conclusions/Discussion My project showed that Ulam's discovery of the prime number spiral could be extended to a very large set and could possibly be mined to provide pattern areas which might be generalized to predict the existence of large prime numbers.

Competition history

• CSEF 2015 Mathematics & Software · Entry J1406

Resources

• CSEF project summary ↗

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