what's a prime number?
An integer greater than 1 with no positive integer divisors other than 1 and itself; example, 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers.
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number is only divisible by 1 and itself, and it cannot be formed by multiplying two smaller natural numbers.
To determine if a number is prime, you can follow these steps:
1. Start with the number you want to check.
2. Take the square root of that number, and round it down to the nearest whole number. Let's call this rounded square root "n".
3. Starting from 2, check if the number is divisible by any integer up to "n". If it is divisible by any number, other than 1 and itself, then it is not prime. If it is not divisible by any number up to "n", then it is prime.
For example, let's check if 11 is a prime number:
1. Take the square root of 11, which is approximately 3.316. The rounded square root is 3.
2. Check if 11 is divisible by any integer up to 3. It is not divisible by 2 or 3.
3. Since 11 is not divisible by any number other than 1 and itself, it is prime.
Therefore, 11 is a prime number.
It's worth mentioning that 2 is the only even prime number, and all other even numbers greater than 2 are not prime. Prime numbers have many interesting properties and are fundamental in number theory and cryptography.