how to find every prime up to 120 in 4 passes
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
The figure in the circle is the smallest prime factor of the number, that is, the pass that struck it out. The number 1 is neither prime nor composite: it has only one divisor.
Every prime after 3 stands in the 6k − 1 or 6k + 1 column, right next to a multiple of six. Every number in the other four columns is divisible by 2 or by 3 — apart from 2 and 3 themselves, there is no room there for a prime.
The converse does not hold: up to 120, the same two columns hold 11 composites — 25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119. Every one of them has the factor 5 or 7, which is why only the last two passes strike them out.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 8 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
the IWF colour code and the plate count: from target weight to each side of the bar, no calculator
why a “yes” from a test that is right 99 times in 100 is wrong more than nine times in ten when one in a thousand has the thing
the first digit of a number: why a one turns up more than six times as often as a nine, and in which sets that is true
how many people it takes for two of them to share a birthday — and the same count for codes and fingerprints