ELI5: Explain Like I'm 5

Bombieri–Vinogradov theorem

The Bombieri-Vinogradov Theorem is like a math magic trick that helps us understand prime numbers. Prime numbers are special numbers that can't be split evenly into smaller parts. For example, 2, 3, 5, 7, and 11 are all prime numbers.

The Bombieri-Vinogradov Theorem helps us figure out how many prime numbers there are between two big numbers. It shows us that we can estimate this number using some math rules without needing to check each and every number between those two big numbers.

Imagine you have two big numbers. One is 1,000 and the other is 10,000. That's a lot of numbers to count! But with the Bombieri-Vinogradov Theorem, we can make a good guess as to how many prime numbers are between these two large numbers without having to count them all.

The theorem is like a special formula that tells us how many prime numbers to expect in a certain range. It's based on some complicated math rules, but if we follow the formula, we can get a pretty good estimate of the number of prime numbers in that range.

So basically, the Bombieri-Vinogradov Theorem is like a math shortcut that helps us estimate how many prime numbers there are between two big numbers, without having to painstakingly check each number one by one.