The iPhone Dev team has finally released the PwnageTool 3.1.5 for the Mac which is easily the best tool to Jailbreak iPhone with OS 3.1.3 for you.
NOTE: This is for the Mac users only. If you use the blacksn0w unlock at baseband 05.11.07 you need to stay at 3.1.2. iPhone 3GS users not having SHSH Hashes must stay away from iPhone 3.1.3 firmware.
Here’s what you need to Jailbreak iPhone OS 3.1.3:
♦ Download Original iPhone 3.1.3 Firmware
Lets get this thing done then.
1. After downloading PwnageTool 3.1.5, execute it and select your device.
2. PwnageTool 3.1.5 should display the firmware you use for your iPhone/iPod Touch.
3. When you are prompted with the following, Click NO:
Do you have an iPhone contract that would activate normally through iTunes?
4. PwnageTool 3.1.5 creates the custom .ipsw file for your iPhone which is to be jailbroken.
5. Once custom ipws file is created you need to restore iPhone to this custom firmware 3.1.3 created using PwnageTool 3.1.5.
6. Click the Phone icon on the sidebar and now press and hold Alt key and click on Restore button in iTunes and then release Alt button.
7. Select the iPhone 3.1.3 firmware IPSW when prompted.
8. Your iPhone 3.1.3 should be restored by now.
9. Once installation is done your iPhone will restart automatically. Thats it! Your phone is now jailbroken!