What is Goldbach, Vinogradov theorem?

Goldbach and Vinogradov are about how numbers can be broken down into smaller parts, kind of like splitting up your toys to share with friends.

Imagine you have a big pile of blocks, say 10 blocks. Goldbach says that if the number is even (like 10), it might always be possible to split it into two smaller piles, both made of prime numbers (numbers like 3 or 5, which can't be divided evenly except by 1 and themselves). So, for example, 10 could be broken into 7 and 3.

But what if the number is odd? That's where Vinogradov steps in. He showed that any big enough odd number (like 15 or 21) can be made by adding together three prime numbers, like 3 + 5 + 7 = 15.

So, Goldbach and Vinogradov are like two friends who help you understand how even and odd numbers can always be broken down into smaller parts, especially primes, no matter how big they get. It's a bit like having a recipe for splitting up any number of candies with your friends!