Concept
Divisibility — where it appears
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
There is no last prime
Euclid's argument is often described as producing a new prime from any finite list. It does not, and the number it builds is frequently composite — which makes the proof more interesting rather than less.
One way to factor, and no other
Every number breaks into primes in exactly one way. That is so familiar it is hard to see as a claim at all — until it is put beside an arithmetic where it is false, and where six has two different factorisations that cannot be reconciled.
Named alongside it
The objects these essays reach for when they reach for this one.
PrimesProof by contradictionCompositeCounting argumentCounting two waysEuclidEuclid lemmaExistence proofGreatest common divisorHarmonic seriesIrreducibleNorm