Are there infinitely many pairs of primes exactly two apart?
3 and 5, 11 and 13, 17 and 19, 29 and 31: pairs of prime numbers separated by exactly two keep turning up as you count higher, even as primes generally become rarer. The twin prime conjecture claims this never stops, that infinitely many such pairs exist, no matter how far out you look.
Reveal the answer
Still unproven, over a century after being formalized. The closest anyone has come is a 2013 breakthrough by Yitang Zhang, previously an obscure lecturer, who proved infinitely many prime pairs exist within some bounded gap, then just 70 million; collaborative work quickly shrank that gap to 246. Whether the gap can be brought all the way down to 2, proving the original conjecture, remains open.
— Yitang Zhang, Bounded gaps between primes — Annals of Mathematics, 2014