Number Choosing Contest.

2^57,885,161 : (Largest known prime +1)

4000

202

18

1388741444313152705354935065649 : Largest number I could find that should pass 3 and 5.

2^57,885,161
Rule 1: Computational resources not enough. Effective failure.
Rule 2: Breaks.
Rule 3: Breaks.
Rule 4: Passes.
Rule 5: Breaks.

4000: Breaks
2 3 5 R U

202: Breaks
2 3 5 R U

18: Breaks
1 2 3 5 R U

1388741444313152705354935065649:
Rule 1: Passes.
Rule 2: Passes.
Rule 3: Passes.
Rule 4: Passes.
Rule 5: Passes.
Breaks R U