Fermat primes are prime numbers that can be written in the form 2^k+1

Question

Fermat primes are prime numbers that can be written in the form  2^k+1 , where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

A. 3
B. 5
C. 17
D. 31
E. 257

Izzyjolly · Accepted Answer

Let x is a fermat prime, then  x = 2^k + 1  -->  x-1 = 2^k  -->  x-1  is a power of 2
Subtract 1 from each answer choice, only D. 31-1=30 isn't a power of 2.
Answer D.

BrentGMATPrepNow · Answer

GIVEN: k is an integer and a power of 2  
Some powers of 2 are:  1  (since 2⁰ = 1),  2  (since 2¹ = 2) ,  4 ,  8 ,  16 , .... etc

So, the Fermat primes are as follows: 
2^k + 1 = 2^ 1  + 1 = 2 + 1 = 3 (eliminate A)
2^k + 1 = 2^ 2  + 1 = 4 + 1 = 5 (eliminate B)
2^k + 1 = 2^ 4  + 1 = 16 + 1 = 17 (eliminate C)
2^k + 1 = 2^ 8  + 1 = 256 + 1 = 257 (eliminate E)

By the process of elimination (POE), the correct answer is D

Cheers,
Brent

Archit3110 · Answer

Fermat primes are prime numbers that can be written in the form 2k+12k+1, where k is an integer and a power of 2. Which of the following is NOT a Fermat prime

A. 3
B. 5
C. 17
D. 31
E. 257

option D ; check for all values k 0,1,2,3, so on.. only D does not matches.

rahulms94 · Answer

Someone please clarify.
k is a power of 2
==> k = 2,4,8,16.... isn't that what the qs says?

Lowpoint · Answer

Yeah, I made the same mistake.

But the question is actually asking:
Among the answer choices given, which cannot be expressed in the form 2^k + 1.

Fermat primes are prime numbers that can be written in the form 2^k+1

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Fermat primes are prime numbers that can be written in the form 2^k+1

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