A 27-state two value Busy Beaver can implement "Give a counter-example to Goldbach's Conjecture" - if there are none the program never halts. We can recognise that, and say "Oh dear" but it gets us no closer to an answer. Six billion isn't even in the right ballpark, our ability to understand the meaning of every self-acting machine extends maybe to six or seven bits if we're very smart.
A 27-state two value Busy Beaver can implement "Give a counter-example to Goldbach's Conjecture" - if there are none the program never halts. We can recognise that, and say "Oh dear" but it gets us no closer to an answer. Six billion isn't even in the right ballpark, our ability to understand the meaning of every self-acting machine extends maybe to six or seven bits if we're very smart.