6.1.3 iOS version is Jailbreakable!
As we always say, first make sure that the iOS version you are planning to upgrade to is jailbreakable, then save your SHSH blobs and finally proceed with the iOS upgrade. By skipping one of these steps, you may end up with an unjailbreakable device and you will most likely lose your Software Unlock (If you have one). 6.1.3 iOS version is jailbreakable for only the A4 chip devices, so if you own an iPhone 4S/5 or the latest iPad models and iPod Touch DO NOT UPGRADE TO 6.1.3 iOS version!
How to jailbreak 6.1.3 iOS version for your iPhone 4?
The procedure is very similar to the jailbreaking procedure for iOS 6.1.2. The software you need to use is the Redsn0w 0.9.15b3 jailbreaking tool and it will provide you a tethered jailbreak of 6.1.3 iOS version.
You can perform an 6.1.3 iOS version jailbreak to the following devices:
And Windows and Mac operating systems are supported by Redsn0w 0.9.15b3 version.
By downloading and running the Redsn0w jailbreaking tool, the only thing you need to do is to follow the instructions step by step.
Special untethered jailbreak of 6.1.3 iOS version for iPhone 3GS!
iPhone 3GS is a very special occasion because its bootrom can be an old or new version. The new version can be jailbroken tetheredly but the old bootrom can be jailbroken untetheredly. The iPhone 3GS with old bootrom users were always the lucky ones, because not only they can jailbreak 6.1.3 iOS version untetheredly, they can also proceed with a software unlock!