What application

Nearly anything.

"I'd like to buy an operating system name."

In other words, ports 63000+ are perfectly normal for some operating systems but relatively unusual in others. There are bittorrent clients for a number of very different operating systems, so we can guess that you -might- be talking about some Windows version or other, but with all of the possibilities, it isn't worth our time to list off all of the potential OSs and describe the behaviour of each of them.

The Software Update service does not prevent client computers from accessing Apple's Software Update servers directly; it just mirrors updates provided by Apple. If you want to block users from accessing Apple's servers, then you must block client access to port 63000 on your network's main firewall.

That's nice, but the original poster asked about port 63000 "and >" meaning ports 63001, 63002, etc.. The peachpit article deals only with port 63000 *exactly*.

And we still don't have any idea which operating system the original poster is using.