Two Apart

There are others climbing up the side of the waterfall in Butterfly Valley.

Bunny, Steve and Arthur wait their turn.

Now they are climbing up a rope ladder.

It's repetitive, climbing up a rope ladder, so they converse.

Steve tells Bunny, who is below him on the ladder, more about the twin prime conjecture.

What it is, says Steve, is this. Prime numbers two apart, like three and five, eleven and thirteen, and so on, continue to appear indefinitely. That's the conjecture.

Oh, says Bunny. And do they?

Yes, says Arthur, from several rungs below.

Correct, Arthur, says Steve.

What a show off! Bunny decides to pay proper attention.

So this guy has proved that prime numbers two apart continue to appear indefinitely? asks Bunny.

Not exactly, says Steve.

Bunny sighs. This is just like maths at school.

What then? asks Bunny.

He proved that there are infinitely many prime numbers separated by less than seventy million, says Steve.

It's a start, says Arthur.

Exactly, Arthur, says Steve.

Bunny kicks Arthur lightly in the head.

Soon they reach the top of the waterfall.

Wow. An awesome view. They sit and gaze at it.

Three Tiger Butterflies flutter past in the sunshine. Then two more, eleven, thirteen..........

They may do so indefinitely.

But it is time for Steve, Bunny and Arthur to climb down.