Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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"

share|improve this question
    
(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
add comment

1 Answer

Both problems are open. For the first, see the Wikipedia article; amazingly, it is also unknown whether or not there are an infinite number of Mersenne composites. For the second, see this question and the reference to the Prime Pages; however, it is known that every even integer is the difference between a prime and a number which is either a prime or a semi-prime.

share|improve this answer
    
! could you prove the (2). –  vmrfdu123456 Nov 16 '12 at 7:59
    
No, but someday a good mathematician might prove it, or produce a counterexample to refute it. That is what an "open problem" means: nobody knows. –  Dan Brumleve Nov 16 '12 at 8:00
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.