Concept
Density
How thinly a set is spread through the whole numbers, measured as the fraction of them it occupies up to a bound.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
The primes on a spiral, and a pattern nobody ordered
Wind the whole numbers outward in a square spiral, mark the primes, and they line up on diagonals. The observation is a hundred years old and there is still no proof it means anything.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
PrimesCompositeConjectureCounting two waysCramér's modelParityPrime counting functionPrime gapsPrime number theoremQuadratic polynomialsSieve of eratosthenesSmallest prime factor