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Yes, you can remove the crashed remote DP from the primary site by going to Administration - Site Configuration - Servers and Site System Roles, right-clicking on the server in question, and selecting Delete. This will remove the server's entries in the primary site, DB, and distributed packages references.
However, it's important to note that if the remote DP was also a site system server, you will need to remove any site system roles associated with it before deleting the server.
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