Only the lessons of Bitcoin. The finitude of all real measurable states caps the number of possible primes. Only when mathematics enters an ungrounded domain like the mind can infinity persist.
Seems like a waste of time to chase proofs around infinity when only things mathematically finite can be measurable by definition.
sorry, wait a minute, are you saying there are finitely many primes?
Yes/No. Any real, meaningful, and measurable system must be finitely bound, which means the set of twin primes available to any physically instantiated system is necessarily finite.
Mathematics extends toward infinity only in the mind because that branch of math is not grounded in any physical structure. Yet it derives all meaning from our finite experience of the world. That’s the paradox: infinity is thinkable, but never observable; definable, but never instantiated.
