Would a number half as long as that not be sufficient?

That number is the value Google currently uses to identify accounts. 100001702987293 (Facebook’s) is still too long.

And in either case, someone will end up with huge, unwieldy numbers. By using ascii identifiers, they’ll be 3 times shorter, though. Facebook’s number is just "WvN1+8Yd" in base64.

And at that point, why not allow people to choose identifiers? John.Doe.123 is still much more readable than 100001702987293

I wonder what happens if you still get to choose a username, but the service appends at least 3 digits (randomly; the first doesn't get 001; in fact let's say nobody gets a number below 101), and does some mangling especially for really short usernames (appends something or prepends something).

This gives every 'username' an effectively unlimited space of identifiers via the number suffix, and it trains users to realize that 'person who controls the account with username X' is not necessarily the same person as 'person who I know on other sites as username X'.

Discord (and I believe Blizzard/Battle.net) does this. Your site-wide username would be something like Example#5436 but on individual servers you can be tagged with @example

When Google introduced account names in G+ (separate from gmail account names), they started by doing this. But I suspect it was a fairly big turn-off for people who are used to getting their usernames.

Alternatively, the service provider could implement a procedural jingle generation system to produce a short, catchy customized song to help them recall the number.

0118999881999119725....3

12 digits would be more than enough.