To make what everybody else said already, more explicit:
Your exponent 283243137 is divisible by 3. So 283243137 = 3*N.
Then the number you propose, namely 2^283243137  1, is equal to 2^(3*N)  1 = (2^3)^N  1. And that will be divisible by 2^3  1 = 7. So the number you suggest, is divisible by 7 (because your exponent is divisible by 3).
/JeppeSN
