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The government doesn't use SQL
(programming.dev)
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So they’ve issued almost half the possible numbers, current US population is actively using 1/3rd of them. I think unless there is a major drop in birth rates “several generations” is two. Either my great grandkids will be reusing dead people SSNs or there will be 10 digit numbers which is going to be a problem for any systems that coded it as char(9).
Ongoing trends would indicate a significant drop in birth rate is extremely likely. Major cities will most likely be facing population shrinkage by the end of the century