Earlier quoted context omitted.
That's gonna be a nice storage bill!
Let's see...2^241 or so possible 256 bit numbers, so that's 256 * 2^241, so that's....10^50 yottabytes. Obviously we're gonna need cloud storage for all this, so let's say that's about 2 cents per gigabyte/month, so that's...2.2614 × 10^63 dollars per month? Actually, why does the site list the odds as ~1 in 5.27 × 10⁷²? That's 2^241, but it's picking random 256 bit numbers. Is it because there are so many valid hits…
You can keep a comprehensive list of "all 256-bit numbers tried so far" in 256 bits of storage.