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Yes, you most likelly do if you just bought it brand new.

You need to look at either the serial number, or better yet the actual bootrom version to determine "old vs new". Newer bootrom version means that you can jailbreak but it will be a "tethered" jailbreak, requiring you to connect to a computer whenever you reboot or turn the phone back on from being completely off.

Good luck. Search the forum, all the details are there.
 
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