Nice! That’s very interesting.
My solution is also fully deterministic and passes 100% of the test cases. I also rely on two different mathematical operations.
What really caught my attention is the probabilistic angle you mentioned - I’m genuinely curious: how would you even introduce randomness into this puzzle in a meaningful way?
With some probability (lets say 2%) output a solution that just prints “prime”, otherwise (in the remaining 98%) print your standard solution.
Thanks, but I have to confirm to you that I’m definitely not doing better math than you or @bamilan in this puzzle, I only use comparisons in my solution. I’m genuinely curious about what you’ve done to get a 3.9K solution with 100%
So yes, there is something I know that you don’t, yet 
(the 3rd step I named long ago)
And the reverse is true. I may try to come up with some of those automated searches of solutions in the future, I have some simple optimization codes but mostly to find local improvements with specific calculations, and in my 100% solution I only had place for 1 of those math tricks that would improve my solution, but that was still at 4616 steps with 100%…
There is some “art” to optimizing luck too but it’s also a totally different game, in theory you could get the absolute minimum by randomly printing either option, but that’s impossible in practice. In my case, I was once close to getting less than 2.4K (I think), but I stopped trying long ago…
Once upon a time, I was first on this puzzle …. it seems so far away 
Still have no idea about how you can do that.
For the record, my best deterministic solution is 3875. I’m not going to submit any probabilistic solutions because it’s boring (for me) to spam submissions. 
My result of 3877 is deterministic.
