RSA quickrundown

p and q are primes that are randomly chosen and used to create public and private key
e1 private key
e2 public key

p=7 q=11 generates keys: e1=13 e2=37
n = pq = 77 (gets used at encryption and decryption as [mod n])

necessary verification assuring that encryption and decryption will work with this two primes and two keys
(7-1)(11-1)=60 (gets used at verification as [mod 60] that has to be 1)
13 mod 60 x 37 mod 60 = 481 mod 60 = 1

Example:
decrypted message: 2
encrypted message: 30

encryption: e1   2^13 = 30 mod 77 = 30
decryption: e2   30^37 = 2 mod 77 = 2



RSA calculator (key creation and encryption)
https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html