If you are not comfortable carrying your medical card with your Social Security number on it, some health insurance companies will assign you a card with a different number. Call them and ask. Explain that you are trying to protect yourself from identity theft.
If you cannot get the card number changed, then carry the card only on those days when you really need it (e.g., when you are visiting a doctor or having lab work done). At all other times, carry a copy of the card with the Social Security number deleted. If you forget to bring your card when it is needed, it is likely that your doctor and hospital will have your card number on file.
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