# Everything you ever wanted to know about prime numbers! And more!

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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?

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 277,232,917 − 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

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As a 7th grader, Divya has a million ideas running through her head at any single moment. She's a creative force, and is the official design guru for STEAMism.com, designing the infographics and digital art you see on the website. She loves reading, has been a blogger and prolific writer since Kindergarten and is an expert on Greek Mythology. She's also learning the art of video and audio design and editing. Checkout her STEAMism videos on YouTube!