Using the prime p=2621 and encryption key e=7, encrypt the message SWEET DREAMS using modular exponentiation.
This is what I came up with. Not sure if it's right though?
Your goal is to encrypt the message SWEET DREAMS and creating the ciphertext. If you convert SWEET DREAMS into numerical equivalents and then create 4-digit blocks, you’d have: 1822 0404 1903 1704 0012. Now you have to raise each one of these 4-digit blocks to the 7th power and reducing modulo 2621 would give you 0394 1679 01804 0755 01177 as your ciphertext.
If you want to be a mathematician and/or a computer scientist, you need to be precise. Your question lacks precision. Presumably, the only characters allowed in a message to be encrypted are capital letters. But what is the numerical equivalent of a capital letter? By inference only, 'A' is 0, 'B' is 1, ... 'Z' is 25.
Your encryption scheme is not very good, even for upper case letters. No spaces allowed and the number of letters in your message must be even!
In direct answer to your question, your encryptions are correct except 01177 should be 0117.
An encryption method is worthless unless you can decrypt a message. How do you decrypt a message? In particular, suppose the encrypted message is 2223 2203 1492 2071 2226, what was the message?