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Twin Primes and Brun's Constant

  1. Feb 21, 2008 #1
    If one could show that Brun's constant is irrational, would that imply that there are an infinite number of primes?

    I think it would since Brun's constant is the sum of a bunch of fractions, and the sum of a finite number of fractions must be rational. Thus is the sum is irrational there must not be a finite number of fractions...

    Is my thinking correct?
  2. jcsd
  3. Feb 22, 2008 #2

    Gib Z

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    Yes, if Brun's constant were to be shown irrational, then there are an infinite number of twin primes, and hence primes. Yes your thinking is correct.
  4. Feb 22, 2008 #3
    Unless you find some equivalent expression that doesn't use the infinite sum of reciprocals of twin primes which computes Brun's constant B, it will be more difficult to show that B is irrational than it is to show that twin primes are infinite, I think.
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