The Map of Numbers
Every number from 1 to 10,000, coloured by how interesting it is — a count of the distinguishing properties each one carries. Cool grey numbers are plain; hot red ones sit in many named sequences at once. Hover any cell to see exactly which properties it has, or click through to its full page.
Look for the pale vertical streaks. They run under every number ending in 25 or 75 — the odd multiples of 25, which can never be prime and are never squarefree, so they miss two of the most common properties at once (3.6 properties on average, against 5.6 across the whole map).
The opposite tilt is there too, though too gentle to pick out of the grid by eye: past the single digits only numbers ending in 1, 3, 7 or 9 can be prime, and a prime collects a cluster of named properties at once. Averaged by last digit:
It also cools with magnitude, from an average 3.9 stars across the first thousand to about 3.1 by the last. That is honest rather than an artefact of the scoring: small numbers genuinely belong to more named families, because they are the early terms of nearly every sequence anyone has bothered to define.
Standouts, thousand by thousand
A plain "top 60" would just be 1, 2, 3, 4, 5… — small numbers sit in nearly every sequence, so they win every time. These are the richest numbers of each thousand instead, which is where the map actually gets interesting.