Is there a working 6.1.3 untethered jailbreak?

I have an iPhone 3GS and I want to know If there's an untethered jailbreak for it?

Can't say anything surely about that, though there are rumors that a hacker has a binary that untethers 6.1.3… So nothing's clear by now.

Not at the moment. Winocm (twitter: @winocm) is a developer that is allegedly working on an untethered jailbreak for 6.1.3, but it is not out yet and so the only jailbreak currently is a tethered one. There's no release date or ETA for the untethered 6.1.3, and with IOS 7 arriving in a few short days, there might already be an IOS 7 jailbreak before that.

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