What is the twin prime conjecture?
Mel Nathanson, City University of New York Well, a twin prime conjecture is a beautiful conjecture. People have noticed for a long time that very often two consecutive odd numbers are both primes. You can’t have two consecutive numbers that are primes because one will be even and one will be odd. And the even one certainly is not a prime. But you can have 17 and 19. Or 41 and 43. You just notice that the closest together two primes can be is two. Forget two and three. That’s just an abnormality at the beginning. The closest together would be two. And whenever you have a pair of primes that differ by two, that’s called a twin prime. And if you get a big piece of paper and start writing down the primes and looking for twin primes, or you get a big computer or the world’s biggest computer and you run it looking for twin primes, you keep finding them. And everyone believes there are infinitely many pairs of twin primes, but no one’s been able to prove it.
