Latest iOS 6.1.3 Jailbreak is released by Evad3rs
http://www.evasion-jailbreak.com/

Apple Software Update iOS 6.1.3 Compatibility:

iPhone 5
iPhone 4S
iPhone 3GS
iPhone 4GSM Model
iPod Touch 3rd generation
iPod Touch 4th generation
iPad
iPad 2
iPad 3

The following steps will help you jailbreak your device on Apple iOS 6.1.3
Step 1: Go to apple.com and Download latest iTune v 10.2.1 and Update your device to Software Update 6.1.3
Step 2: Then go to http://www.evasion-jailbreak.com/ and Download evasion iOS 6.1.3 Jailbreak for Mac or Windows
Step 3: Save the evasion iOS 6.1.3 Jailbreak Tool on desktop and Run as Administrator
Step 4: Select your device and click on install button.
Step 5: Let the application do its work and wait for the app to show "Jailbreak Complete!" message.
Step 6. At this point, wait for the device to automatically reboot otherwise Reboot it according to the messesge.
Step 7: Finish! You should now have a fully jailbroken iPhone & iPad & iPad firmware iOS 6.1.3

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