Primality test
Okay kiddo, so you know how numbers are either even or odd, right? Well, some numbers are special because they can only be divided by 1 and themselves without any leftovers. Those numbers are called prime numbers!
Now, imagine we have a really big number, like a hundred digits long. We want to know if it's a prime number or not, but checking all the possible divisors would take forever! So instead, we use something called a primality test.
There are different kinds of primality tests, but let's talk about one called the Miller-Rabin test. Basically, it uses some math to quickly check if the number is likely to be prime or not.
First, the test picks a random number between 2 and the big number minus 1. Let's call this random number "a".
Then it does some fancy calculations with "a" and the big number to see if they follow some special rules. For example, if "a" raised to the power of the big number minus 1, and then divided by the big number, leaves a remainder of 1, then the big number is probably prime.
If the test doesn't find any violations of these special rules after trying a bunch of different random "a" numbers, then the big number is probably prime! But if it does find a violation, then it's definitely not prime.
And that's how we can use a primality test to quickly determine if a really big number is a prime number or not, without having to check all the possible divisors one by one. Cool, huh?
Now, imagine we have a really big number, like a hundred digits long. We want to know if it's a prime number or not, but checking all the possible divisors would take forever! So instead, we use something called a primality test.
There are different kinds of primality tests, but let's talk about one called the Miller-Rabin test. Basically, it uses some math to quickly check if the number is likely to be prime or not.
First, the test picks a random number between 2 and the big number minus 1. Let's call this random number "a".
Then it does some fancy calculations with "a" and the big number to see if they follow some special rules. For example, if "a" raised to the power of the big number minus 1, and then divided by the big number, leaves a remainder of 1, then the big number is probably prime.
If the test doesn't find any violations of these special rules after trying a bunch of different random "a" numbers, then the big number is probably prime! But if it does find a violation, then it's definitely not prime.
And that's how we can use a primality test to quickly determine if a really big number is a prime number or not, without having to check all the possible divisors one by one. Cool, huh?