# A mathematician takes the number line to infinity

#### Image courtesy of Princeton University.

The cover of the journal Annals of Mathematics.

Two, three, five . . . two to the fifty-seven million, eight-hundred-eighty-five thousand, one-hundred-and-sixty first?  Minus one?  What?

This is Sandra Tsing Loh with the Loh Down on Science, and the largest prime I've ever heard of.

We're talking about prime numbers—numbers that can only be divided by themselves and one.  Twin primes are prime pairs separated by two—like 3 and 5.

Math's “twin prime conjecture” says no matter how far out you go on the number line, there's an infinite number of twin primes. Maybe, but primes in general are rarer the farther out you go.  What gives?

Mathematician Yitang Zhang has the answer. He just proved there is an infinite number.  But they're not always separated by two.  The farther out you go, the bigger the gap gets.

Bottom line: there is indeed an infinite number of twin primes that are separated by a mere 70 million or less.

Which may not seem like much of a result to us, but number theorists are excited.

And bully for them.  After all that mental exertion, I myself am ready for a nap of 40 million winks.