A round, memorable number with no registration behind it — pure convention when you find it in use.
IANA does not assign 35500, and Nmap has no service name for it, recording it open on roughly 0.08% of scanned hosts. Round numbers like this get picked by hand for internal services precisely because they are easy to remember, which is the usual reason one is listening. The number is also inside Linux's default ephemeral range, so not every open socket here is a server.
Expose with care
A hand-picked port often means a hand-rolled service; confirm what it is and whether it authenticates before it faces anything untrusted.
$ nmap -sV -Pn -p 35500 TARGETSeen 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.