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.
What makes a pair twins
A prime is a number bigger than 1 whose only divisors are 1 and itself. Twin primes are two primes that differ by exactly 2 — as close as two odd numbers can ever be.
The first few pairs are (3, 5), (5, 7), (11, 13), (17, 19), and (29, 31). So 11 sits next to its twin 13, with nothing dividing either one. Apart from (3, 5), there's always a multiple of 3 hiding between the twins (like 12 between 11 and 13), which is why twins can't get any closer.
The conjecture nobody can crack
Primes thin out as numbers grow larger — they get rarer and more spread out. So you might expect twins to eventually run out. But every time mathematicians look further, more pairs keep turning up.
The Twin Prime Conjecture says they never stop: there are infinitely many twin primes. It sounds simple, and most mathematicians believe it's true. Yet after more than 150 years, nobody has been able to prove it. It's one of the great unsolved problems in mathematics.
Zhang's breakthrough
In 2013, a little-known mathematician named Yitang Zhang stunned the field. He couldn't prove the gap of 2 stays forever, but he proved something almost as striking: there are infinitely many pairs of primes that are at most a fixed distance apart.
His first bound was 70 million — far from 2, but the point was revolutionary. For the first time, someone had nailed down a finite gap that recurs forever. A worldwide effort soon pushed that bound down to 246. Closing it all the way to 2 would finally settle the Twin Prime Conjecture.