*One thing that I think is pretty neat is that somebody has written a program for a 47 state Turing machine that will halt if and only if it finds an even number that is not the sum of two primes, in other words it will halt only if Goldbach's Conjecture is false. If we knew what the 47th Busy Beaver number is (a very big if) and we ran the program until it reached BB(47) and it had not halted then we would know it would never halt, and thus Goldbach's Conjecture must be true. The only trouble is it's almost certainly impossible to calculate BB(47), we know for a fact it's impossible to calculate BB(745) and I wouldn't be surprised if it's impossible to calculate BB(6).*

*Goldbach Turing machine with 47 states* <https://gist.github.com/jms137/cbb66fb58dde067b0bece12873fadc76> John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> nn6 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv1WiDW3Y2kghxRDtsYoacNVR2ky%2Bi_Sa8zCGw%3Dbfk9mgQ%40mail.gmail.com.