If your old mobile number is linked to your Facebook account, then delete it immediately.

That's because if your old number is allotted to a person, then he can log in to your Facebook from that number. You will not have any such notifications as well.

A website called Bug Finder said that Facebook does not have any solution to this matter. 

An independent programmer, James Martindell, was getting details of someone else's Facebook login after their new phone number (which was the number one before), after which they found this bug. He has given information to this matter to Facebook.

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