The first thing I did when I pulled the Kindle Paperwhite out of its box was to turn it on and check the firmware version on it, I wasted no time getting to work on jailbreaking this thing.
The Paperwhite (PW) version 3 black is the one that I ordered and it shipped with firmware version 5.7.3.1 so the first order of buisness was downgrading to a version that was vulnerable to the known jailbreaking methods for this device. The version the was reccomended was 5.6.5 so I found the manual "upgrade" package for that version, I found it at ( https://www.mobileread.com/forums/showthread.php?t=265675 ) I connected the Kindle to my computer using the USB cable that came with it, it automatically mounted as an external USB hard drive. I uploaded the upgrade file to the root of that "drive" and ejected the Kindel, I then told the Kindel to install the upgrade. I would like to have given more detail on this process but I did not document this durring the jail breaking process. This however was an indispencible wiki page with basically every bit of critical information you could want about the Kindle.
https://wiki.mobileread.com/wiki/Kindle_Touch_Hacking