Don't forget that untethered jailbreak 7.1.3 mean you will not have to connect your iPhone, iPad or iPod Touch for rejailbreak. After jailbreak via pangu utility, you can reboot your idevice without PC or Mac. It's untethered jb method for all, who want install cydia tweaks for iOS 7.1.3.
Pangu jailbreak teaml has updated for from jb 7.1.2 to jb 7.1.3. :) If you have iOS 8 beta 3 - you can jb new iOS 8 on yours confirmed idevice. :)