The Strongest Matthew For Whenever Options

[Dr Strum]

Back for it's third iteration, and still longer than any other.
You know what to do. Just post about stuff. Your life, your insanity, or even your favorite cardinal direction.

[Raijinili]

Well, the thing is that p being prime doesn't necessarily mean that q will be prime as well. Playing with the factorials shows that. Although its only a few examples, I did try a few numbers, thinking that "Well, I wonder...what if the factorial was so huge that the chances of any sort of prime being a part of the number is nullified?" Thats not true either, since there's infinitely many primes, and numbers all have sort of unique prime "sets" (Like, 900=9*2*5*2*5), so the factorial would have to be infinitely huge too, so that doesn't help..

I'm starting to reconsider keeping 1! and sets of 2 and 3. The 1! because its odd. So there's a ridiculously high chance you can have something like 1!+t! (as in, you hit an even number that can be represented by a factorial). So its safer to say n>=2. Anyways, tomorrow i'll be going over with it with my professor and see what he thinks about it.

I think I'm still missing something.

Never using a smaller factorial than I've used before:
3=1!+2
5=2!+3
7=2!+5
11=3!+5 (first one I can't use 2! with)
13=3!+7
17=3!+11
19=3!+13
23=3!+17
29=3!+23
31=4!+7 (first one I can't use 3! with)
37=4!+13
41=4!+17
43=4!+19
47=4!+23
53=4!+29
59 (first one I can't use 4! with, but 5! is too big)