Gilbreath's conjecture

Okay kiddo, let's talk about Gilbreath's Conjecture!

First, do you know what a number sequence is? It's when you have a set of numbers that follow a pattern, like 1, 2, 3, 4, 5... and so on.

Well, Gilbreath's Conjecture is about a special kind of number sequence called the "prime gap sequence". This means it's a sequence of numbers where each number represents the difference between two consecutive prime numbers.

For example, the first few numbers in the prime gap sequence are: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2... and so on.

Now, Gilbreath's Conjecture says that if you take that sequence and create a new sequence by subtracting each number from the next one, then the resulting sequence will have a lot of zeros near the beginning.

So basically, you'd start with the prime gap sequence (which gives you the differences between consecutive prime numbers), and then subtract each of those numbers from the next one to create a new sequence. And Gilbreath's Conjecture says that this new sequence will have lots of zeros early on.

Now, it's important to note that Gilbreath's Conjecture is only a "conjecture" - which basically means it's an idea that people think might be true, but they haven't proven it yet. So even though lots of people think Gilbreath's Conjecture is probably true, nobody knows for sure!