Gaps & Twins

Deserts and pairs

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $n! + 2, \dots, n! + n$ shows that prime gaps can be arbitrarily long.
• Twin primes differ by 2. Whether there are infinitely many is unknown.
• Since 2013, we know some gap of at most 246 occurs infinitely often.

Steps

1. Prime deserts
2. A run of composites
3. Never too far
4. The first gap of 14
5. Gaps among the primes
6. Twin primes