Elements in $X = \{2^n +1$ | $n$ is a positive integer and $2^n + 1$ is prime$\}$ Are $3, 5, 17$ and $257$ the first four elements in the set $X$? When I first wrote it out I thought it would be $1, 2, 4$ and $8$, but that doesn't seem right. I'm relatively new to set notation. Thank you.

Yes, $2^n+1$ is to the left of the vertical bar, so these are the numbers in the set.  You might read it as "numbers of the form $2^n+1$ that are prime"
