Primality Testing for Beginners

Lasse Rempe-Gillen · Rebecca Waldecker

2013년 12월 · Student Mathematical Library 70권 · American Mathematical Soc.

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How can you tell whether a number is prime? What
if the number has hundreds or thousands of digits? This question may
seem abstract or irrelevant, but in fact, primality tests are performed
every time we make a secure online transaction. In 2002, Agrawal,
Kayal, and Saxena answered a long-standing open question in this
context by presenting a deterministic test (the AKS algorithm) with
polynomial running time that checks whether a number is prime or not.
What is more, their methods are essentially elementary, providing us
with a unique opportunity to give a complete explanation of a current
mathematical breakthrough to a wide audience.

Rempe-Gillen and
Waldecker introduce the aspects of number theory, algorithm theory, and
cryptography that are relevant for the AKS algorithm and explain in
detail why and how this test works. This book is specifically designed
to make the reader familiar with the background that is necessary to
appreciate the AKS algorithm and begins at a level that is suitable for
secondary school students, teachers, and interested amateurs.
Throughout the book, the reader becomes involved in the topic by means
of numerous exercises.