I have an even easier one: any prime number can be written as n.But I agree ... any prime number can be written as 6n+/-1.

My argument is ... any prime number can be written as 2n+1.

Actually, mine is easier in that you don't need to consider two cases -- 6n+1 and 6n-1.

Unfortunately I can't complete the proof.

Musings ...

The proof works for any (3p-1); I wonder why the puzzle writer chose 26.

299999 (300000-1) might be discouraging? -1 trivial? ["prime = n" works there.]