### To start with, what are odd and even numbers?

Right. Let’s start off with some definitions, then.

- What is an
**odd number?**Any number that**cannot be divided by 2.** - What is an
**even number?**Any number that can be**divided by 2.**

### What is a factor?

A **factor is** any number that can **divide another number without a remainder**.

So, for example,

- 4/2 = 2. No remainder.
- 9/3 = 3. No remainder.
- 11/1 = 1. No remainder. But, there’s a hint here…

### What is a composite number?

**A composite number is** any number that can be **divided by at least one other number (a factor) other than itself. **

- In other words, composite numbers
**always have more than 2 factors**(1, the number, any other factors). - Examples? Oh, that’s easy.
- 4 = 2 x 2. So, 4 has 3 factors – 1, 2, and 2.
- 6 = 3 x 2. So, 6 has 3 factors – 1, 2, and 3.

### Now, finally – what are prime numbers?

Prime numbers are the exact opposite of composite numbers.

- They are only divisible by the number 1 and themselves.
- In other words, a prime number can only have 2 factors.

### So, 1 is a prime number then?

Aaahh, good question! No – 1 is a very special kind of number. It doesn’t even have 2 factors. *It only has itself.* So, nope – 1 is not a prime number.

### So, which ones are the prime numbers then?

Let’s go through a quick exercise to find the first 25 prime numbers. Look below at the table with the first 100 numbers, 1 to 100.

**Step 1 – We already know our friend, 1, is too special to be prime.**

**Step 2 – Composite factors of 2.**

**Step 3 – Composite factors of 3 (that are not already composite factors of 2).**

**Step 4 – Composite factors of 5 (that are not already composite factors of 2 and 3).**

**Step 5 – Composite factors of 7 (that are not already composite factors of 2, 3 and 5).**

** Let’s blank out all the composite numbers and now we have the first 25 prime numbers!**

### Is that it? That’s not too bad – I could memorize this list pretty fast!

Uhhhhh, no, not really! Here’s a list of the first 50 million primes, in blocks of 1 million. More fun to memorize!

### What’s the largest known prime today?

As of January 2018, the largest known prime number is 2^{77,232,917} − 1, a number with **23,249,425** digits. It was found by the Great Internet Mersenne Prime Search (GIMPS). Here’s a wiki article on it.

### And, in some “prime” news….

A Mathematical Breakthrough: Yitang Zhang and the Twin Prime Conjecture