1. 2 521 2 1 is a Mersenne prime. Find the perfect number associated with this number. Write your answer using exponents with a base of 2. 2. In RSA encryption, if the public key is 35, what is the...

1. 2⁵²¹
2 1 is a Mersenne prime. Find the perfect number associated with this number. Write your answer using exponents with a base of 2.

2. In RSA encryption, if the public key is 35, what is the private key?

3. In RSA encryption, if the public key is 51, what is the private key?

4. In RSA encryption, if the public key is 143, what is the private key?

5. In RSA encryption, if the public key is 221, what is the private key?

6. a. Rewrite the first four perfect numbers with the binary system.

b. Describe the pattern or patterns you see in the result of part (a).