Twin Primes and Brun's Constant

[Diffy]

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?

 

[Gib Z]

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.

 

[Dragonfall]

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.