[AT&T Samsung Galaxy S 4 General] jortex:
HOWTO:

Use a card reader to format the micro SD card to exFAT (FAT32 or other formats does not work) in Windows. I haven't tried Linux or MacOS X, so they may not work.

Download the attached file (Root_for_ATTSG4_FM3.rar) and extract it into the root of your EXTERNAL microSD card using the card reader in Windows. (You can do the extraction using WinRAR or 7-zip).

Put the SD card back to the phone and download the Android Terminal Emulator app.

Open the Terminal Emulator app and run below 3 commands:

cd /mnt/extSdCard
./pwn
./script.sh

Then, open SuperSU and check everything looks good.

Then open a root app and it should be working properly.

Reboot your device once to confirm root is still working after reboot.

Come back to the post and press the THANKS button :)

Notes:

I uploaded a screenshot from the Terminal screen where the instructions are entered. Yours should be the same except you don't need to enter the "ls -l" command. It's just to show what files I have on the SD card. Ignore LOST.DIR directory.

Remove any SuperSU apps from your phone before following the above steps. script.sh installs it automatically.

You can use adb shell instead of a terminal app which is more convenient but requires Android SDK. Follow these steps only if you are about to use adb:

Download and install all Samsung Galaxy S 4 drivers from here.

Activate Developer options -> USB Debugging mode. To have the phone show the Developer options, go to Settings -> More -> About device. Tap on "Build number" 6 times.

You have to use an external SD card. No other alternative have been found yet. Using the device storage, i.e. /mnt/sdcard, or /data/local/tmp, DOES NOT work.

Warning (suggested by rushi.1986): "We have root for MF3 but we neither have a working recovery, nor an ODIN back to stock package. Be very careful what you do with your root. At this point, there is no way to recover even from a soft brick. (unless you know exactly what caused the soft brick and can correct it using adb)"

For those who do not know how to format an SD card on Windows (thanks to jee'sgalaxy):

Insert the micro SD into the computer (may have to use a reader or a micro SD adapter).

Go to "My Computer".

Right click on your SD card that showed up.

Click Format.

Choose exFAT as the format.

Click "OK".

Stopping AT&T Auto Software Update

Since AT&T just rolled out the new update (4.3), I add this short guide on how to stop it before it becomes late! Note that these steps require root, so you should follow the rooting steps first.

Download and install "App Quarantine ROOT/FREEZE" from Play Store.

Open the app and go to settings by tapping on the wrench icon at the top right of the screen.

Uncheck the "Hide system services" option.

Go back to the app and select "AT&T Software update".

Tap on the lock icon on the top right of the screen.

It may ask you to enable the USB debugging.

Feel safe from AT&T's new attack :D

How to get MK2 without losing root

I have tested this approach and it worked for myself. You should consider the risk of losing the root access and follow these steps on your on risk:

Root your MF3 phone using the approach described earlier in this post.

Stop AT&T from pushing the update as described above.

Install Super SU Pro. Note that this is not a free app and it is an add-on for Super SU.

Run Super SU. Go to Settings and check the "Survival Mode". If you don't have this option, probably you don't have the Pro version.

Disable your guard against the AT&T update by enabling "AT&T Software update".

Let the device update itself and hope for the best.

Don't forget to press the THANKS button. :)

Credits:

***Exploit adapted for AT&T by Jortex***

***Original Guide by Open1Your1Eyes0 for Verizon Galaxy S 4***

***Original Exploit by DooMLoRD***