Thanks for putting up your question on Just Answer.
Phantom pain is when you feel pain in teeth that are no longer there. You just had the 4th tooth extracted today, so i wouldn't diagnose it as phantom pain right away.
If, after a month or so, you feel that those 4 or any of those 4 teeth are still hurting, then that diagnosis can be considered.
I would just put it down to bad luck, that you have had 4 failed root canals followed by extractions. Root canals are blind procedures, and therefore carry a success rate of about 90-95%. What this means is, that in every 5-10 out of 100 cases, the root canal has to be done again. The main reason for this is that some amount of pulp tissue that was supposed to be removed in the first attempt, gets left behind. This happens because teeth have a lot of variation in their anatomy, all of which cannot be seen on X rays.
This has happened to you with 4 consecutive teeth, which is really rare. Maybe you need to change your dentist?
Please dont lose hope, this could be the last tooth you get pulled in decades!
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Good Luck !