Does it make sense to have a 4000 bit long key? My question is about the key length of a asymetric algorithm. How is it possible to memorize or remember a key that is about 4000 bits long?
A 4000-bit RSA key is reasonable (more precisely, that would be the bit size of the public modulus; and 4096-bit would be more common). But it is not reasonable to memorize it (or, more precisely, that the owner try to memorize the corresponding private key); and that's practically never done.

One does not ask normal users to memorize or remember a key, or other information, with more than perhaps 50 bits worth of entropy (say as 8 characters among 77, or 2 phones numbers); even that is hard, and XKCD's method is probably more reasonable.

Long asymmetric private keys are usually


Stored encrypted by way of a symmetric algorithm using a stretched password/phrase as key, and stored on disk as a file; that's what PGP, GPG, and many other programs do.
Not stored, but rather re-generated at each use, from a passphrase combined with stretching seeding a CSPRNG used by the key generator; advantage is that the passphrase entirely replaces the private key in normal usage; but that makes safe passphrase change impossible; and requires a lot of stretching and a long passphrase to be secure.
Stored (and while we are at it used) inside a Smart Card protected by PIN with error counter (locking the card after 3 consecutive errors).