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

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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?

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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