What happens if I send bitcoins to my private key instead of my actual bitcoin address? I recently used the website https://www.bitbrothersllc.com/Bitbrothersllc/Welcome.html to obtain my bitcoins, but when I was asked what address to send my coins to, I accidentally put down my wallet's private key, not my bitcoin address.

I'm wondering if the coins are lost forever now, or if they will still appear in my wallet because the private key is attached to my address.  I'm really hoping they are not lost forever, and I would greatly appreciate any assistance anyone could provide.
A private key can be encoded in a number of different formats:


51 characters base58, starts with a '5' 
(for example: 5JrnhhNpRNsC6xPUhLfc4yJEviuRxMcvpcB4pc1opgHTSVi64aP)
64 characters [0-9A-F] hexadecimal format, 
for example: 89609C6B52AE0061FB8FFE3AF83528AC24AC637A386FE61D2822128ABE80162F
44 characters base64,
for example: iWCca1KuAGH7j/46+DUorCSsY3o4b+YdKCISir6AFi8=
52 characters base58, WIF Compressed, starts with a 'K' or 'L', 
for example: L1pkidDJJbWY1HUDF3oPnXV6U7xR9L1aZ8FRs7YZfSPdh5NPzRB5


A bitcoin address, which is a hash of the public key, is 25-34 characters, typically 34 characters,
for example: 1A5QMFw4vXVwLF1zZMSvAYJStuVMcjSqAa

Maybe a bitcoin address could be encoded in some other format, but 25-34 characters of base58 is the standard.

I don't know what kind of validations are in place at bitbrothersllc, but they should easily be able to see that you entered 51, 64, 44, or 52 characters instead of the 25-34 characters that would make up a valid bitcoin address.  

Contact them.  If they are legit, you'll get your funds back.  Good luck!