Primes and Perfect Numbers

  • David M. Bressoud
Part of the Undergraduate Texts in Mathematics book series (UTM)


With this chapter we begin the process of finding the primes and factoring the composite integers. The first question that arises is whether or not the list of primes is finite. If it were then we could, at least in theory, publish a book containing all the prime numbers and anyone wanting to determine whether an integer were prime would only have to look it up. Unfortunately, there is no limit to the number of primes, a fact which was known to Euclid.


Prime Divisor Factor Number Large Prime Factor Proper Divisor Perfect Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. D. H. Lehmer, “An extended theory of Lucas functions,” Ann. Math., 31(1930), 419–448.MathSciNetMATHCrossRefGoogle Scholar
  2. Edouard Lucas, “Théorie des fonctions numériques simplement périodiques,” Amer. J. Math., 1(1878), 184–240, 289-321.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1989

Authors and Affiliations

  • David M. Bressoud
    • 1
  1. 1.Mathematics and Computer Science DepartmentMacalester CollegeSaint PaulUSA

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