Investigate correctness of RSA example

[syreal17]

https://discord.com/channels/575006934089072650/759508515403726858/1337172891883671674

Hello! I guess, I found a mistake in the CTF Primer, section 6.5 Modern Cryptography. In the first point of RSA key generation algorithm says "Generate two large co-prime numbers, p and q.". But it's incorrect because we need to generate two large prime numbers, otherwise the Euler's totient function won't be equal (p-1)(q-1) in general, because p or q if they are just co-prime may not be prime. And further in the example we have p = 13 and q = 9. Since q isn't a prime number the Euler's totient function in the example is wrong calculated and algorithm don't work in some cases. For example if we try to encode number 105, we will get 27. If we try to decode it, we will get 27 again (not 105 as expected).