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if 2^n-1 is prime
prove that n is prime
prove that n is prime
if 2^n-1 is prime
prove that n is prime
The idea behind this problem is not setting 2^(n) - 1 (not 2^(n-1) like you have) equal to a prime in solving for n, (in virtually every problem in number theory n is limited to the natural numbers so for most cases this is an exercise in futility). The point here is, for example, 2^3 - 1 = 7 thus 3 is prime.
you interpreted 2^n-1 as "2 raised to the (n-1) power". The ordinary precedence (and what everybody else has understood the problem was) asks you to interpret it as "2^n, and then subtract 1".2^n-1=3
(n-1)ln2=ln3
actually its not 2^n-1 its (2^n)-1
C3H5N3O9 points out that if n is not a natural number it is not prime. For instance there is an irrational number n such that [tex]2^{n}-1[/tex] is equal to 13 which is prime but since n is irrational, it can't be prime. I don't know why C3H5N309 used the example of 3 and the logic there is not correct but the idea that one must specify that n is a natrual number is correct. Usually one write n to signify an integer an not an irrational number so the original poster obviously meant n to be an integer, but C3H5N309 apparently wants more care taken to specify what is meant.Riddhish, we understood you, no need to clarify.
As Dodo said, most people would take 2^n -1 to be (2^n) - 1, I am not sure why C3H5N3O9 thought otherwise.
C3H5N3O9 points out that if n is not a natural number it is not prime. For instance there is an irrational number n such that [tex]2^{n}-1[/tex] is equal to 13 which is prime but since n is irrational, it can't be prime. I don't know why C3H5N309 used the example of 3 and the logic there is not correct but the idea that one must specify that n is a natrual number is correct. Usually one write n to signify an integer an not an irrational number so the original poster obviously meant n to be an integer, but C3H5N309 apparently wants more care taken to specify what is meant.Riddhish, we understood you, no need to clarify.
As Dodo said, most people would take 2^n -1 to be (2^n) - 1, I am not sure why C3H5N3O9 thought otherwise.
Well is 97513144621 prime? All of the lists I checked do not have prime numbers listed that high.
Well is 97513144621 prime? All of the lists I checked do not have prime numbers listed that high.
if 2^n-1 is prime
prove that n is prime