The SSN is nine digits long. That means there are 1,000,000,000 possible values. It used to be that there were some structure, the first three digits were an area code but this was abandoned in 2011. There are still some rules, such as SSN not starting with 9, no group should be all 0’s, and it does not start with 666. The first of these rules are most significant on the number as it brings it down to 900 million but it is also something which can easily change in the future if we need more numbers.
So far over 450 million numbers have been issued, so just over half the numbers. But also note that this does not directly correspond with the number of people born in the US. Not everyone have a SSN, most notably the Amish, and not all kids have a SSN. In addition people who move to the US to work all need a SSN, even if only temporary. You can also get a new SSN if you need this for various reasons. So at the moment there are about 5.5 million SSN issued per year. By that rate it would take 90 years to exhaust the remaining available SSNs.
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