Over time, and as the platform scaled to require multiple and parallel backend services, a system that consistently generated unique IDs across servers and datastores was needed - so, Twitter developed Snowflake, which is a service and method for doing just that.1
That's how we end up with those long ID numbers - but what if you only have a Tweet ID, and you want to see the original Tweet on the website? You don't know which Twitter user originally Tweeted it, so you don't have the username, and can't make a URL from it easily...
Well, if the Tweet is available (that means, it has not been deleted and is not a protected Tweet belonging to an account you do not follow), there's a trick that you can use here.
Let's pick a recent Tweet with ID 1234903157580296192, for example.
The long way to do this would be to use the official Twitter API, and pull back the Tweet object and associated user information. Then, we'd pick out the screen name of the user that posted the Tweet from the JSON response, and do something like this, in pseudo-code:
URL = "https://twitter.com/[screen name]/status/[Tweet ID]"
"... oh! But I don't have a Twitter Developer Account / I don't want to build an app just to do this simple thing"
No problem! There's a handy trick, and you can even use it to generate embedded Tweets via markup from publish.twitter.com (or, if you do have an app, you can also grab the HTML markup directly from the oEmbed API endpoint, without ever having to know the user's original screen name)
Here's the secret...
Each Tweet ID is already unique, so you don't need to know the user that posted it! It turns out, you can add any username to the URL, and Twitter will work it out for you. I always like to use twitter itself, because that one is likely to be around for a while.
So now, with our previous example:
URL = "https://twitter.com/twitter/status/1234903157580296192"