Ok here is my next attempt at a prime number formula french celestial girlfriend poster here by the way

try something like this:

to test if 5 is prime
do 5^4 - 3 / 2
to test if 7 is prime
do 7^6 - 5 / 4
etc.

9^8 - 7 / 6

If the result is an even division then the greatest number (the first one) is prime?

etc.