This was my first chance at testing this, and it did
work.  How, I'm not sure though.
Specifically:

What do you call the "PRIMES:" and "__END___" syntax? 
I'll look up what it's purpose is, I just don't know
it's name.

Next, I don't quite understand the for loops.  I
understand that you created two scalars,
$possible_prime and $test within the scope of the for
loops, and I assume you did that because they are not
needed outside of the for loops, right?  That part I
understand.  However, I don't understand this part of
the line:
for my $possible_prime (@primelist)
If I were to write it, I'd declare $possible_prime at
the top where all of my variables are declared.  And
then I'd write it like this:
foreach (@primelist)
Would that be a correct representation?

I'm also not sure how $possible_prime gets a value for
the range operator to work on it in the second for
loop.  How does it get a value?

The other constructs that are confusing me are next
and unless.  I've read about them, I've just not used
them.  I remember reading that unless can be used in
place of while, where the block of code is before
using unless, instead of after like in while.  That's
correct, right?  I'll have to look up next.  I know
when I first read about it, I didn't understand it, so
I've avoided attempting to use it.

Thanks for the help.

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