Back when the Evad3rs team came through with the untethered jailbreak for iOS devices up to and including iOS 6.1.x, it was later stated by those behind it that a jailbreak for iOS 6.1.3 would not be pursued because exploits would instead be saved for the more pressing issue of iOS 7. This hasn’t stopped other well-known developers from trying to find a solution, and developer Winocm has just thrown out a tweet suggesting he is getting there.
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Untethered iOS 6.1.3 Jailbreak Found, Needs Some Work