| Congruences, prime numbers, and primality testing are major topics of elementary number theory. Crandall, Richard, and Carl Pomerance, Prime Numbers: A Computational Perspective , New York: Springer-Verlag, 2001.
This book discusses the theoretical and computational aspects of prime numbers. Crandall and Pomerance cover primality testing in Chapter 4. Gardner, Martin, "The Remarkable Lore of Prime Numbers." In Mathematics: An Introduction to Its Spirit and Use , edited by M. Kline, San Francisco: W.H. Freeman and Company, 1979.
This is an article about patterns in prime numbers when numbers are arranged in a spiral. Herkommer, Mark, Number Theory: A Programmer's Guide , New York: McGraw-Hill, 1999.
This book on number theory emphasizes computer programming. Chapter 8 discusses both the Lucas test and the Miller-Rabin test, and it includes programs written in C that implement these tests. Koshy, Thomas, Elementary Number Theory with Applications , San Diego: Harcourt Academic Press, 2002.
This is an excellent introduction to number theory. The textbook covers congruences in Chapter 4, Fermat's Little Theorem in Chapter 7, and primality testing in Chapter 10. Some of the necessary background for understanding the Lucas-Lehmer test is in Chapter 11. Ribenboim, Paulo, The New Book of Prime Number Records , New York: Springer-Verlag, 1996.
This book also discusses the theoretical and computational aspects of prime numbers. Ribenboim covers primality testing in Chapter 2 and prime-generating polynomials in Chapter 3. The Web is a good place to search for information on primality testing. For example, http:// mathworld .wolfram.com/Lucas-LehmerTest.html has a good explanation of the Lucas-Lehmer test, and it includes links to related topics. |
