User blog comment:Pellucidar12/Idea for a function (Hyperprime counting functions)/@comment-30754445-20170723221034

It's a very interesting idea, in terms of number theory.

It doesn't grow very fast, though. The hyperprime sequence will begin:

2,3,5,7,11,23,29,41,43,47,61,83,101,113,131,137,151,173,191,223,227,241,263,281,311,313,317,331,353,421,443,461,599,641,797,821,887,911,977...

That's not fast at all.

Of-course, recursing it will make it stronger, but that's due to the recursion rather than the function HP itself.

(now I'm really curious: What is the exact growth rate of HP(x)? It's not a googological question really, but it is a very interesting question nevertheless)

Fun fact: The number composed of 317 1's is a hyperprime.