0.0120130150170111011301170119012301290131013701410143... (no encoded zeros in this example.)
Then you wouldn't have to brute-force word boundaries... You could also put the ordinality of the prime number between 08...09 tags, then you could know exactly whether you're looking at the millionth prime or the million and second one.
But yeah other than not encoding boundaries you are right, it's quite akin to the real number you provided. I like your explanation - thanks.
EDIT: also, as I show above, the program to get a prime back out can seem complicated. What's remarkable about mill's constant is that the program is simple: just raise Mill's constant to 3^n (and apply the floor function). seems so simple. What's remarkable is not just that such a constant exists - that will give you a prime for any n - but that there is a smallest such constant and we already know it:
1.3063778838630806904686144926...
I find that remarkable. raise that to any 3^n and you get a prime and change. wow.
EDIT2: Your argument also didn't address one thing I'm curious about - why a similar number can't exist for 2^n instead of 3^n... thanks for any thoughts.
So heuristically, the existence of Mills' constant is really just saying that primes grow at a relatively consistent rate, which is something that the prime number theorem formalises.
You can think of Mills' constant as being akin to this real number[1]:
You could write a program to extract primes from that number, but the existence of the constant, or the program, is not surprising in the least.[1]: https://en.wikipedia.org/wiki/Copeland%E2%80%93Erd%C5%91s_co...