Since prime numbers are very useful in secure communication, such easy-to-remember large prime numbers can be of great advantage in cryptography,
That's nonsense. I'm sure there thinking of RSA, but that needs secret prime numbers. So easy-to-remember is pretty much the opposite of one want. Also they are way to big. 2048 bit RSA needs two 300 digit prime numbers.
Yeah, I'm no expert on mathematical cryptography but I was thinking the same. Now what would be cool is... finding memorable public keys. That would solve the key exchange problem and allow for secure names without a register. But the closest I've seen is brute forced ECDSA key pairs that hash to having a vanity starting prefix.
I suppose some inspiration from brain wallets and encoding schemes could be used to transform any public key into something more memorable.