Search notes:

/var/run/sudo/ts

/var/run/sudo/ts is the default directory where sudo stores timestamp files.
These files are used to cache a user's password so that he does not have to re-enter it again when executing another command with sudo.
By default, the password is cached for 15 minutes.

See also

sudo -k invalidates a timestamp file, sudo -K removes it and sudo -v updates it without running a command.

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