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Finally found a fix how to stop firefox downloading each PDF to your local drive
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The problem is not that it gives a download prompt, but rather that it tosses the PDF file into your downloads folder unrequested.
It opens the PDF in the internal PDF viewer as well, but that is not the thing people are having issues with.
NONE of the files i tested it on triggered the download prompt, populated the download status of the browser, or appeared in my default downloads location during their 'viewing' or after.
Great that it seems to work for you, but I've been experiencing this bug for months now if not longer.
I made the changes OP suggested, and now it seems to work correctly.