FOM: twin primes vs. Goldbach conjecture

Peter Schuster pschust at
Mon Jun 19 10:30:04 EDT 2000

>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. 

More information about the FOM mailing list