Can I jailbreak my iPhone on ios 6.1.3?

I have an iPhone 3GS, running ios 6.1.3. I know there's a jailbreak for 6.1.2, but I really can't be bothered downgrading to 6.1.2, I was just wanted to know if there's any way I can jailbreak my phone without downgrading?

There's, use redsnow or green poison, I personally used redsnow first as my first one however it took far too redsnow to get the job done in my opinion however I found Evasi0n, which was great quick and easy i didn't even have to do much just have iTunes installed and Evasi0n as well then hook the device up and the grayed out button will show " Jailbreak Me " or something Simalair to that I haven't used it in months so I can't remember the exact words, however once its done with the process you unlock the device and press the app it tells you to I believe it was Cydia or a pineapple sign ( I really don't remember ) never the less it's much easier an quicker than the others in my opinion, it could also work on 7.0 and below last I checked you can see the type of firmwares it works on, by looking at their site if you google Evasi0n, I'm running 5.1.1, I'm not going to upgrade at all and it's an iPhone 4S, because upgrading means a lot of things don't work because they are not optimized for the upgraded firm ware, so usually the older firm ware is better, good luck

Sorry but there's no jailbreak whatsoever for iOS 6.1.3 You would just need to downgrade to 6.1.2