I had a working root after JB update, but I lost it after factory reset. I still have /system/bin/su, /system/app/Superuser.apk and /system/xbin/busybox with correct permissions. I don't have a copy or link of busybox in /system/bin, though.
If I try to run su from a terminal directly on the Prime, it says "Permission denied". However, I can run su through adb and have # prompt. The version reported by su is 188.8.131.52.
Before I proceed with OP's method I have a few quesions:
1. I'm a bit worried about versions of files you have provided. They have all different sizes and dates than files on my Prime:
- su my: = 22364, 2012/09/28, yours = 380532, 29/02/2008
- busybox: my = 2005736, 2012/03/06, yours = 1085140, 9/08/2012
- Superuser.apk: my = 843503, 6/03/2012, yours = 1468798, 29/02/2008
Where did you get these files from? Are they appropriated for my system? In particular, your su seems to be 4 years old, unless date was changed on purpose. On the other hand, your su, when executed with -v options reports version 3.1.1.
2. Just of curiosity, why do you use
dd if=/data/local/tmp/Superuser.apk of=/system/app/Superuser.apk
instead of simply
cp /data/local/tmp/Superuser.apk /system/app/Superuser.apk
busybox rm /system/bin/su
busybox cp /data/local/tmp/su /system/bin
cp /data/local/tmp/su /system/bin
I only guess that the last command is necessary because I'm running the su shell that needs replacing, is it correct?