Type 25–50 numbers that look like real data — invoice totals, say. Don't think about it too hard. That's the point.
Take the population of every city on earth, the length of every river, every number printed in today's newspaper, the file size of everything on your hard drive. Look only at the first digit. You'd expect each of 1–9 to show up about 11% of the time. They don't. The distribution is this:
Discovered by the astronomer Simon Newcomb in 1881, who noticed the early pages of shared logarithm tables were grubbier than the later ones. Rediscovered and popularised by physicist Frank Benford in 1938, who checked it against 20,229 numbers from river areas to baseball statistics to street addresses.
Because real quantities grow multiplicatively, not by addition. A town of 1,000 people has to grow 100% to reach 2,000, but a town of 9,000 needs only 11% to tick over to 10,000 — and then it's back to leading with a 1 again. Anything spread evenly on a logarithmic scale spends far more of its life in the "1" zone. Watch the powers of 2 fill in: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 — count how many start with 1.
Humans inventing "random-looking" numbers spread their first digits far too evenly, and lean toward the middle: 4, 5, 6, 7. Forensic accountants run Benford's test on expense claims, tax returns and election tallies as a first-pass smell test. It has been used in real casework — and it flagged irregularities in the Greek economic data reported before the 2010 debt crisis.
A warning worth stating: failing Benford's test is evidence, not proof. Plenty of honest data doesn't follow it — anything with a fixed range (heights in cm, exam scores out of 100, dice rolls) or an artificial floor. Try Random 1–999 and Sum of 3 dice to see honest data fail badly.