The 8000th Busy Beaver number eludes ZF set theory (2016)
>   You’d certainly never run across such a program by chance—not even if you had a computer the size of the observable universe, trying one random program after another for billions of years in a “primordial soup”!<p>This is a remarkable claim, given that we <i>did</i> encounter this program by random chance, and it only took about 10 billion years (the estimated age of the universe) give or take a few billion years.