Abstract
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.
“It is recorded that all God’s works were completed in six days, because six is a perfect number. ... For this is the first number made up of divisors, a sixth, a third, and a half, respectively, one, two, and three, totaling six.”
- St. Augustine of Hippo (The City of God)
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References
D. H. Lehmer, “An extended theory of Lucas functions,” Ann. Math., 31(1930), 419–448.
Edouard Lucas, “Théorie des fonctions numériques simplement périodiques,” Amer. J. Math., 1(1878), 184–240, 289-321.
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© 1989 Springer-Verlag New York, Inc.
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Bressoud, D.M. (1989). Primes and Perfect Numbers. In: Factorization and Primality Testing. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4544-5_2
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DOI: https://doi.org/10.1007/978-1-4612-4544-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8871-8
Online ISBN: 978-1-4612-4544-5
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