Jailbreak 6.1.3 iOS version cannot only be achieved by Redsn0w, because the latest update of Sn0wbreeze tool is also more than capable to jailbreak it!
Now that Evasi0n tool is out of the picture (Unless an update arises soon!), redsn0w had to do the “dirty” job for us again. Redsn0w is able to Jailbreak 6.1.3 iOS version but it still has the same restrictions as it had with the iOS 6 version.
Many users updated to 6.1.3 iOS version and evasi0n cannot help them with an untethered jailbreak. The final Redsn0w version, 0.9.15b3 is able to jailbreak 6.1.3 iOS version, but for the moment this is not possible for all the A5 chip and above devices.