I'm assuming the *keys* nextP and prevP in the Integer menu work for you, but *typing* in these names yields just 'nextP' and 'prevP' on the stack.
The function names behind the nextP and prevP key caps are NEXTPRIME and PREVPRIME (in line with HP 50g naming). If you type these, you'll be ok.
Normally the full function name appears as key cap, but extra long function names may be shortened so the key caps read better. There's only a few instances of key cap and function name not matching. You found two of them.
In order to see the true function name, start an expression with the ' expresssion-name key and tap the function key in question. That will display 'NEXTPRIME( and 'PREVPRIME(.
(Similarly, if you start an RPL program with ≪, that will write out NEXTPRIME and PREVPRIME, respectively.)
Does this help?
P.S. I double-checked the documentation, and under Functions by Menu | Integer nextP and prevP are listed alongside NEXTPRIME and PREVPRIME. I realize that's misleading, and I shall either add a qualifier to make clear that these words refer to key-caps only, or make these two words aliases to NEXTPRIME and PREVPRIME (which are a handful to write with the iOS keyboard...), as you expected. Thanks for reporting.