C-u with mouse event is ignored?

[Drew Adams]

I'm probably missing something simple, but it looks like C-u followed by a
mouse event is ignored.

1) Is this by design or a bug?
2) If by design, shouldn't this be mentioned somewhere (e.g. node Prefix
Command Arguments of Emacs manual)?

Example:

(global-set-key [S-mouse-1] 'test)
(global-set-key [S-down-mouse-1] 'ignore) ; Get rid of `mouse-set-font'.

(defun test (arg) (interactive "P") (message "pref: %s" arg))

C-u followed by S-mouse-1 shows "arg: nil".