The Messages app on the iPhone, like other apps, can provide you with a notification when you have a new message. Use the Notifications section of the Settings app to control what types of notifications you get, including, as we all know, a red badge on the app itself to show you the number of unread messages.
Sometimes my app shows me that I have a few unread messages. I suppose at some point over the years I may have had as many as a dozen or so unread messages, but I don't think I've ever seen more than that.
My daughter recently spent about two weeks at summer camp. When we picked her up at camp (in another state), I brought her iPhone because I figured that she would be eager to catch up on text messages etc. in the car ride home. But what I did not expect to see was this:
How is it even possible to have 1,800 unread messages? I'm not sure that I have ever received that many messages in my entire life. My daughter informed me that most of it was from large group texts where there can be dozens of new texts every minute. When I told her that I cannot even imagine taking the time to catch up on that many messages, she told me that all she would need to do is a quick skim to get a sense of whether she missed anything important.
So anyway, my public service announcement for today is that—in case you were curious—yes, the Messages notifications badge does support numbers that are four digits long. I hope that I never have a reason to see that it can support five digits too.