n is a positive integer, 2^n -1 is a prime number? 1) n is a

Question

n is a positive integer, 2^n -1 is a prime number? 
1) n is a prime number 
2) n≥7

game over · Answer

E. 

Prime numbers that fulfill the property -1+2^p (p prime) are called Mersenne prime numbers, but not every number that fulfills this property is a prime. Counterexample -1+2^11=2048-1=2047 is divisible by 23 (2300-253):23 = (100-9). 

Unfortunately, I don't know how to solve these type of questions in an appropriate time, if you don't know the result.

Raghavender · Answer

Hey, I have never come across ur explanation in any gmat buk...I guess ur too gud in ur math

Anyway, i tried it by substituting numbers...n got the option .E

freetheking · Answer

OA is E.. Thanks :cool

gmatmathguru · Answer

Yes, indeed.

Actually, 2^n - 1 is prime for the following n

n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107 and 127.

For n >=7, to arrive at answer E, you need one example of each. at n = 7, 2^n-1 = 127, which is a prime number.

at n = 11, 2^n-1 = 2047 which is not a prime number as described by the earlier post.

-mathguru
https://www.askmathguru.com

Raghavender · Answer

Hey wat was the solution given in the book??

freetheking · Answer

It's actually real q. I heard it from my friend.
I'm not sure those numbers are accurate but it makes sense anyway.

jaynayak · Answer

E.

Putting values we can see that 2^n - 1 can be a prime as well as composite for both cond 1 and cond 2

Hence E

n is a positive integer, 2^n -1 is a prime number? 1) n is a

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