FOM: twin primes vs. Goldbach conjecture

[Peter Schuster]

>The problem with using Goldbach's conjecture as an example of a possibly 
>indeterminate statement is that it is hard to imagine how it could be both 
>false and unknowable, because a counterexample can be finitely verified.  
>This asymmetry obscures the relationship between "unknowable" and 
>"indeterminate" that I was trying to illustrate.

Couldn't also the falsehood of "there are infinitely many twin primes" 
be finitely veryfied by exhibiting the greatest pair and by giving a proof 
that it is so? Such a proof might even be simpler than all the calculations 
necessary for demonstrating that some large even integer is not sum of two 
prime numbers. 

Peter Schuster.