On UNIX (not Windows), the accepted socket uses a file descriptor, so the limit is the number of open file descriptors allowed. The number of open file descriptors is the limit for each process with a hard and soft limit. See ulimit (2) for more information.
Note that if you close the socket, you will release the file descriptor so that it can be used again. The ulimit limit applies only to the number of simultaneous open file descriptors.
To specifically answer your question, there is no limit on the number of sockets a port can accept, only on the number that the process that is listening on the port can be opened at the same time. If there was a limit, web servers that listen on port 80 would need to be restarted more often.
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