Firefox is up to version 17 and it works fine with XP. - http://www.mozilla.org/en-US/firefox/new/
If you really only want Firefox 13 it can be downloaded via this link -
http://mozillafirefoxfreedownload.in/mozilla-firefox-13-free-download-best-browser/
or you can get Firefox 14 here -
http://www.mozilas.com/download/firefox-14-download.htm
Be aware that the older versions, while available, are lacking security patches and bug patches but the choice is yours.
I'm using XP Home 32-bit, Compaq Presario 2002, love it, do not want to upgrade, just download Firefox 13, which I had once before but must have accidentally deleted. Firefox 12 doesn't seem to be working. I want it mostly for Facebook and default browser. TIA.

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