# Twin Primes and Brun's Constant

1. Feb 21, 2008

### 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?

2. Feb 22, 2008

### 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.

3. Feb 22, 2008

### 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.