Concept
Composite — where it appears
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
The primes are what is left over
Eratosthenes' sieve does not find the primes. It removes everything else, one prime at a time, and whatever survives is prime by default — which is a strange way to reach the most studied objects in arithmetic.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
PrimesCounting argumentCounting two waysDensityDivisibilityEuclidExistence proofHarmonic seriesPrime counting functionPrime gapsPrime number theoremPrimorial