Twin primes are pairs of primes that differ by two, such as eleven and thirteen or seventeen and nineteen.

The longer version

Pair two primes that sit two apart and the number between them must be a multiple of six, once you move past three and five. The reason is modular: among any three consecutive odd candidates, one is divisible by three, so the survivors have to straddle a multiple of six. That framing turns a search into a narrow sieve.

Pairs like eleven and thirteen or seventeen and nineteen keep appearing, and whether they ever stop is one of the oldest open questions in mathematics. Computational projects have turned up enormous examples, some with hundreds of thousands of digits, but no argument yet rules out a final pair. Near-miss cousins, such as primes four apart, face the same uncertainty.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.