Yeah, that’s the shift function / number of steps. I’m talking about the length of the contents on the tape when the machine enters a halt state. The notation “BB” is a bit overloaded in the literature.
If we think of the nth prime as the output of a Turing machine that computes the prime numbers where n is on the input tape, then if people are saying the output aloud of such a machine, it would make sense to do so similarly here as well.
Ultimately, it doesn’t really matter. All these functions basically grow at the same rate asymptotically.