Registered as "distinct", but in practice the most common ad-hoc admin or alternate-HTTP port above 9000.
IANA registers 9999 as distinct, assigned to Distinct Corporation, with 9998 as distinct32 — a registration you will not meet in the field. What actually answers on 9999 is an HTTP service someone parked on a memorable number: Nmap's database labels it abyss, the Abyss Web Server's remote management console, and the port is a perennial favourite for debug endpoints, appliance UIs, and second web servers. At roughly 0.44% of scanned hosts, it is by far the busiest port in this range.
Expose with care
Because it is almost always an ad-hoc HTTP surface rather than a standard protocol, assume it is a management interface until proven otherwise — and a management interface on a public IP is a never.
$ curl -sSI http://TARGET:9999/Seen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.