When it comes to explaining what prime numbers are, it is pretty simple. Prime numbers have only two factors (numbers that multiply to make the number) – the number itself and 1.
This means that prime numbers can only be divided by themselves and by one without any remainders. So if a number can be divided by more numbers than itself and 1, it is not a prime number and is called a “composite number.”
The number 1 is not a prime number because one can only be divided by 1, so it does not have two factors. As such, prime numbers are numbers greater than 1.
Would the number 21 be a prime number? What do you think?
The number 21 is also not a prime number because 21 can be divided by 7 and 3, as well as by itself and 1, giving it more than two factors and making it a composite number.
Examples of prime numbers
The number 17 is an example of a prime number.
Seventeen can only be divided by itself and by 1. any other number cannot separate 17 without leaving remainders, a fraction, or a decimal. A quick way we can tell this is that it doesn’t appear in any of our multiplication families.
Let’s look at another example. 43. Instantly, you know it won’t appear in the 2, 5, 9, 10, or 11 times tables as it doesn’t fit the pattens from those times table families. Similarly, its odd number status removes it from the 4, 6, 8, and 12 times tables. So that leaves the 3 and 7 times tables as possibilities.
43 divided by three would give you 14.33 – so 43 is not a multiple of 3.
43 divided by seven would give you 6.14 – so 43 is not a multiple of 7.
That means that 43 is another example of a prime number. Divisible only by itself and 1.
What are the prime numbers from 1 to 100?
If you don’t fancy working the prime numbers out for yourself but are wondering, ‘what are the prime numbers from 1 to 100?’ here is a list of prime numbers from 1 to 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
What is a prime number used for?
Now you’ve seen examples of prime numbers; you should be able to answer the question: ‘what is a prime number?’ Let’s have a look at how they are essential.
Prime numbers are handy in keeping digital information safe. They are used for encryption keys. As prime numbers are more complex than other numbers to reverse engineer, these codes are much harder to crack. So if you are ever shopping online or sharing private data, this will be safely encrypted thanks to prime numbers!
They are also important in mathematics as they are the building blocks for other numbers. A number is either a prime number or can be created by multiplying prime numbers together. For example:
70 = 7 x 5 x 2
But it’s not a prime number, as it can be divided by numbers other than one and itself (70). This is important for mathematical theory.
How to identify prime numbers:
So we know that prime numbers do not appear in any multiplication family other than their own and that of 1. We also know that they must be greater than 1. Does this give us all the information we need to identify prime numbers?
Let’s take a look at an example and find the answer together, to identify what are prime numbers and which are composite numbers.
Let’s take the numbers 2, 7, 12, 17, 21, 29, 32, 41, 67, and 82.
Remember that prime numbers can only be divided by the number itself and by 1. Otherwise, they are composite numbers.
Using the numbers above, our answer is:
Prime Numbers: 2, 7, 17, 29, 41, 67
Composite Numbers: 12, 21, 32, 82
The Sieve of Eratosthenes is an ancient mathematical method used to help identify prime numbers. This method allows us to remove all numbers that are not prime numbers (up to 100).
- Start with a hundred squares, or write the numbers 1–100.
- Cross out the number 1. We already know this isn’t a prime number, as it is not larger than 1.
- Move to the following number (2) and circle it to identify it as a prime number.
- Cross out all of 2’s multiples. They cannot be prime numbers, as they’re in the two-times table.
- Move to the following number not crossed out (3) and circle it to identify it as a prime number.
- Cross out all of the 3’s multiples. This is because they cannot be prime numbers, as they’re in the three times tables.
- Move to the number not crossed out (5) and circle it to identify it as a prime number.
- Cross out all of 5’s multiples. They cannot be prime numbers, as they’re in the five times tables.
- Move to the number not crossed out (7) and circle it to identify it as a prime number.
- Cross out all of 7’s multiples. They cannot be prime numbers, as they’re in the seven times tables.
- Repeat this process of moving on to the following number, identifying it as prime, and removing any multiples of that number from your hundred square/number list.
By following this method, you can quickly identify prime numbers.
