So what exactly is the prime number theorem? Well, it basically says that as you get further out into the realm of big numbers, there are roughly an equal number of primes for every given interval. For example, if we look at all the numbers between 1 and 20 (inclusive), we’ll find that there are 7 prime numbers in this range: 2, 3, 5, 7, 11, 13, and 17. If we then move out to a larger interval say, from 1 to 100 we should expect to see roughly the same number of primes (around 66), since they’re spread pretty evenly throughout all those numbers.

Now, you might be wondering: “Why is this important? Who cares if there are a bunch of prime numbers or not?” Well, for one thing, it turns out that understanding how many primes there are can help us solve other math problems (like figuring out the number of ways to arrange a set of objects). But more importantly, it’s just really cool and fascinating!

So how did mathematicians figure this all out? Well, one guy named Newman came up with a pretty clever method for proving the prime number theorem. Basically, he used some fancy calculus tricks to show that if you take a bunch of numbers (like 1, 2, 3, etc.) and multiply them together, then divide by another set of numbers (like all the primes less than or equal to each individual number), you’ll end up with something pretty close to the actual value of pi.

Now, I know what you’re thinking: “Wait a minute isn’t pi that weird-looking number that goes on forever and never repeats?” And yes, you’d be right! But as it turns out, there are some interesting connections between pi and prime numbers (which is why mathematicians like to study them both).

So if all this math talk has left your head spinning, don’t worry just remember that the prime number theorem is basically a fancy way of saying “there are roughly an equal number of primes for every given interval.” And who knows? Maybe someday you’ll be able to use it to solve some really cool math problems (or at least impress your friends with your newfound knowledge).