# Goldbach conjecture and primes

I need some clarification on (1) Is there any proof to say Mersenne primes $M_p$ are finite or infinite? if there, could you share here.. (2) If Goldbach is conjecture is true, how you can justify the statement" For all finite positive integer 2n can be written as the difference between TWO primes"

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(1) No. (2) What have you tried? – Benjamin Dickman Nov 16 '12 at 6:39
@B.D! for (1) I do not have any idea and I am looking for proof, if there. For (2), I guessed the statement by trail and error. I am not sure, how far I am true. I am looking justification for (2), if possible please share. – vmrfdu123456 Nov 16 '12 at 7:06