Question

Suppose 2 to the power of n is a prime number. What must be the value of n? Explain how you know.

Answer 1

Hmm well I guess we can start by saying that we know what n CANNOT be.
n cannot be an integer greater than 0.

2 raised to any (positive integer) will result in an even number.
All even numbers larger than 2 are not prime.

So where do we go from there? Hmmmmm...

Answer 2

Also, 2^0 = 1
1 is not a prime number, so then n also cannot equal 0.

Hmmmm.

Answer 3

If we are looking for integer solutions, then that will rule out all fractional exponents.
and all negative exponents as well.

I think that leaves us with one possible value for n! :D
And I made a mistake on my first post.

It looks like n would have to be 1.
2^1 = 2
2 is a prime number.

So in my first post I shouldn't said, n>1 is excluded.

Ok hope that helps! :)

Answer 4

thanks