The company gives the computer number, how to get a social security card yourself

As long as you pay social security, you will have a social security computer number, and there is no conflict with whether or not to get a card. According to your above, there is no social security card, and you now have no work unit, and naturally no contributions, then the social security card is not useful to you. (You are not entitled to medical treatment during the period of suspension of contributions, and you can't enjoy it if you have only paid for one month

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Secondly, for the first time you should apply for a social security card by the enterprise, and you can't apply for it by an individual (in most cities).

Extended reading: insurance how to buy, which is good, hand to teach you to avoid the insurance of these "pits"