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

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Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes
n is a positive integer, 2^n -1 is a prime number? 1) n is a [#permalink]

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15 Jul 2006, 08:44
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n is a positive integer, 2^n -1 is a prime number?
1) n is a prime number
2) n≥7
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The only thing that matters is what you believe.

Manager
Joined: 04 Jul 2006
Posts: 57

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15 Jul 2006, 09:43
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.

[But I must admit that I haven't seen any (in)official GMAT preparation material yet. ]
Manager
Joined: 11 Jan 2006
Posts: 230
Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing

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15 Jul 2006, 10:09
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
Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes

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15 Jul 2006, 18:44
game over wrote:
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.

[But I must admit that I haven't seen any (in)official GMAT preparation material yet. ]

OA is E.. Thanks
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The only thing that matters is what you believe.

Intern
Joined: 17 Jul 2006
Posts: 26

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17 Jul 2006, 13:14
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
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Manager
Joined: 11 Jan 2006
Posts: 230
Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing
Re: DS : prime number [#permalink]

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17 Jul 2006, 19:22
freetheking wrote:
n is a positive integer, 2^n -1 is a prime number?
1) n is a prime number
2) n≥7

Hey wat was the solution given in the book??
Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes

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17 Jul 2006, 19:24
It's actually real q. I heard it from my friend.
I'm not sure those numbers are accurate but it makes sense anyway.
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The only thing that matters is what you believe.

SVP
Joined: 30 Mar 2006
Posts: 1728

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19 Jul 2006, 02:38
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
19 Jul 2006, 02:38
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