Properties of Prime Numbers

  • Paul Erdős
  • János Surányi
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

We have seen two proofs in Chapter 2 showing the uniqueness of prime decompositions of integers (Theorem 1.8). The consequences of that theorem there and also in following chapters make it clear why Theorem 1.8 is called the fundamental theorem. The prime numbers mentioned in that theorem are distributed among the integers in a very peculiar way. One can get a feel for this by looking at the sequence of primes less than 150. We list these primes, writing the differences between consecutive primes below them, and writing those differences that are larger than all the previous differences in boldface.

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Paul Erdős
  • János Surányi
    • 1
  1. 1.Department of Algebra and Number TheoryEõtvõs Loránd UniversityBudapestHungary

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