On the Number of Primes Less Than a Given Magnitude
Okay kiddo, let's talk about numbers and primes. You know how we count numbers, right? We start with 1, then 2, then 3, and keep going. But some numbers are special, they are called primes.
Primes are numbers that can only be divided by 1 and themselves. So 2 is a prime number because it can only be divided by 1 and 2. But 4 is not a prime because it can be divided by 1, 2, and 4.
Now, imagine we have a big number, like 100. How many prime numbers are there that are less than 100? Well, we can start counting and checking if each number is prime, but that would take a very long time.
Thankfully, some smart grown-ups have already figured out a formula to help us know the number of primes less than a given number! It's called the Prime Number Theorem.
The Prime Number Theorem tells us that the number of primes less than a given number N is about N/ln(N). Don't worry, the ln(N) part just means the natural logarithm of N, which is another fancy math thing.
So if we take 100 as our N, then the number of primes less than 100 would be about 100/ln(100), which is about 25.94. That means there are about 26 prime numbers less than 100.
Pretty cool, huh? So now you know that there's a formula to help us figure out how many primes there are, without having to count them one by one. And remember, stay curious and keep learning!
Primes are numbers that can only be divided by 1 and themselves. So 2 is a prime number because it can only be divided by 1 and 2. But 4 is not a prime because it can be divided by 1, 2, and 4.
Now, imagine we have a big number, like 100. How many prime numbers are there that are less than 100? Well, we can start counting and checking if each number is prime, but that would take a very long time.
Thankfully, some smart grown-ups have already figured out a formula to help us know the number of primes less than a given number! It's called the Prime Number Theorem.
The Prime Number Theorem tells us that the number of primes less than a given number N is about N/ln(N). Don't worry, the ln(N) part just means the natural logarithm of N, which is another fancy math thing.
So if we take 100 as our N, then the number of primes less than 100 would be about 100/ln(100), which is about 25.94. That means there are about 26 prime numbers less than 100.
Pretty cool, huh? So now you know that there's a formula to help us figure out how many primes there are, without having to count them one by one. And remember, stay curious and keep learning!