New iOS 6.1.3 Jailbreak Released for Apple devices http://www.evasionjailbreak.net/
Evasi0n Just released their new version that can jailbreak ios 6.1.3 untethered!
This untethered jailbreak 6.1.3 finds a certain vunlerabilty in the settings kernel that apple didn't fix correctly.
How to jailbreak 6.1.3 Tutorial:
Download the evasi0n tool for ios 6.1.3 jailbreak untethered.
Open the evasi0n jailbreak 6.1.3 tool
First connect your iDevice to our pc/laptop windows or mac
Make sure your iTunes is closed before proceding.
Hit the jailbreak button and wait a few minutes.
After iDevices is turned up you can check cydia is working and also restart your iDevice to check the 6.1.3 jailbreak is really untethered.