You're still not being specific enough. You seem to be saying that

Code:

(x^mersenne[i]-1)-(x^mersenne[i-1]-1)

is 4 mod 6 when x is 2 mod 3 and i = 2, but is 0 mod 6 otherwise. But what is mersenne[i]? A000043? A000668? Something else?

You really can't expect other people to do the work for you when you're asking them to check your conjectures!