Primes that differ by exactly 2 — like (11, 13) or (41, 43). Are there infinitely many? Nobody knows.
Twin Prime Conjecture: There are infinitely many pairs of primes (p, p+2).
In 2013, Yitang Zhang proved there are infinitely many prime pairs within a gap of 70 million — later reduced to 246. But gap = 2 remains open.
The dots below highlight twin primes on the number line. The bar chart shows how twin pairs thin out in each interval.