iOS 6.1.3 Jailbreak: Read If You Want Jailbreak 6.1.3

Don't Upgrade To iOS 6.1.3 If You Want Untethered Jailbreak. Wait. 
To Be continued ....

..... Wang tells me that he's analyzed the 6.1.3 beta 2 update and found that it patches at least one of the five bugs the jailbreak tools, namely a flaw in the operating system's time zone settings. The beta update likely signals the end of using evasi0n to jb new or updated devices after the update is released to users, says Wang, who says he's still testing the patch to see which other tools by the jailbreak might no longer exist in the new operating system.