For some reason, I'm finding this fascinating. The Zone Improvement Plan "ZIP" codes to expedite postal shipment on addresses in the United States was first proposed in 1944 by postal worker Robert Moon. It was put into voluntary effect in 1963, and became mandatory in 1967.
The 10000 ZIP codes begin in the heart of New York City at 10001, and presumably spiral more or less outward from there.
The 20000 ZIP codes begin in the heart of Washington, DC (though, oddly, not at the White House or the Capital Building).
The 30000s in Atlanta, Georgia, though starting at 30002; there is no 30001.
That all makes pretty logical sense, but here's where it gets interesting.
The 40000s begin in Louisville, Kentucky at 40003.
The 50000s in Des Moines, Iowa.
The 60000s in Chicago.
The 70000s in New Orleans.
The 80000s in Denver, Colorado at 80002.
And the 90000s start in Los Angeles.
The lowest numerical ZIP code is 00501, but that's for an Internal Revenue Service facility located there. Adjuntas, Puerto Rico is also quite low at 00601, but since Puerto Rico is an unincorporated territory of the United States, this was likely a wild card like the IRS location.
Following the logic above, the 00000 ZIP codes should probably be considered to begin in Springfield, Massachusetts--strangely, not Boston--at 01001.