Prime factorisation
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
How many primes a typical number has
A typical number near N has about log log N different prime factors, and the count is spread around that in a bell curve whose variance is log log N as well. Both facts are theorems. Neither is visible at any size anyone can count: up to ten million the average is right and the spread is less than half what the limit says.
Euclid's proof run as a machine
Euclid proved there is no last prime by multiplying the primes on any list, adding one, and noting that the result has a prime factor not on the list. Run the proof as a machine — start from 2, and each time take the smallest prime factor of one more than the product so far — and it produces 2, 3, 7, 43, 13, 53, 5, 6221671, … a sequence that never repeats, that reaches small primes late and large ones early, and that nobody can prove reaches every prime.
Named alongside it
The objects these essays reach for when they reach for this one.
Central limit theoremExhaustive searchFactorisationMertens constantModular arithmeticNormal orderOpen problemPrimality testPrimesSieveSquarefree