Latest iOS 6.1.3 Jailbreak Released Visit This http://www.evad3rsteam.net/

Today 16th May 2013 Evad3rs 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.

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