The maths behind the numbers
Short, friendly explanations of everything you see on 2357.rocks — from primes and factorisation to the spirals and perfect numbers.
Prime numbers
A prime number is a whole number bigger than 1 that can only be split evenly by 1 and itself.
Prime factorisation
Every whole number above 1 is built from prime numbers in exactly one way, and that single fact holds up most of number theory.
Divisors
A number's divisors are everything that divides it evenly, and two simple functions let you count them and add them up straight from the prime factorisation.
Perfect, abundant and deficient numbers
Add up everything that divides a number except itself — if the total lands exactly on the number, it's perfect.
Twin primes
Twin primes are two primes that sit just 2 apart, like 11 and 13 — and whether they go on forever is one of math's most famous open questions.
Mersenne primes
Mersenne primes are primes that sit exactly one below a power of two — the simple shape behind the largest primes humanity has ever found.
The Ulam spiral
Write the whole numbers on a square spiral, light up the primes, and they snap onto surprising diagonal lines.
The polar prime spiral
Place every number at radius n and angle n radians, light up the primes, and watch spiral arms and straight rays appear out of nowhere.