# What Is A Prime Number? Explained For Teachers

**A prime number is a number that can only be divided by itself and 1 without remainders. Here, we explain exactly what this means, give you a list of the prime numbers children need to know at elementary and middle school, and provide you with some practice prime number questions and examples.**

**What is a prime number?**

A prime number is a whole number greater than 1 with only two factors – itself and 1.

A prime number cannot be divided by any other positive integers without leaving a remainder, decimal, or fraction.

An example of a prime number is 13. Its only divisors are 1 and 13. Dividing a prime number by another natural number results in numbers leftover. For example, 13 *÷* 6 = 2 remainder 1.

15 is not an example of a prime number because it can be divided by 5 and 3 as well as by itself and 1.

15 is an example of a composite number because it has more than two factors.

Prime numbers are often seen as “building blocks” by mathematicians in number theory. The fundamental theorem of arithmetic states that a composite number can be expressed as the product of prime numbers.

**See also: **Divisibility Rules

Prime Numbers Worksheets

Test your class’ knowledge of prime numbers with 29 questions for grade 4 and 5 students, including explanatory questions and in-depth answers.

### Prime number examples

How to work out if a given number is a prime number or a composite number, based on the properties of prime numbers.

**What are the prime numbers?**

- There are 8 prime numbers under 20: 2, 3, 5, 7, 11, 13, 17 and 19.
- The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
- There are 25 prime numbers between 1 and 100.
- Prime numbers include large numbers and can continue well past 100.
- For example, 21,577 is a prime number.

**List of prime numbers 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

Notice that this list of prime numbers contains only odd numbers, with the exception of number 2.

**Smallest prime number**

2 is the smallest prime number. It is also the only even prime number – all other even numbers can at least be divided by themselves, 1, and 2, meaning they will have at least 3 factors.

**Largest prime number**

Greek mathematician Euclid (one of the most famous mathematicians of the classical era), recorded a proof that there is no largest prime number among the set of primes. However, many scientists and mathematicians are still searching to find it as part of the Great Internet Mersenne Prime Search.

The **largest known prime number** (as of November 2020) is 2^{82,589,933} − 1, a number that has 24,862,048 digits when written in base 10. Before then, the largest known prime number was 2^{77,232,917} − 1, having 23,249,425 digits.

By the time you read this, it might be even larger, but you can follow its progress on Wikipedia.

### Common FAQs about prime numbers

**What is a prime number in math?**

A prime number is a number that can only be divided by itself and 1 without remainders.

**What are the prime numbers from 1 to 100?**

The prime numbers from 1 to 100 are: 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.

**Why is 1 not a prime number?**

1 is not a prime number because it has only one factor, namely 1. Prime numbers need to have exactly two factors.

**Why is 2 a prime number?**

2 is a prime number because its only factors are 1 and itself.

**Is 51 a prime number?**

51 is not a prime number because it has 3 and 17 as divisors, as well as itself and 1. In other words, 51 has four factors.

Prime Numbers Worksheets

Test your class’ knowledge of prime numbers with 29 questions for grade 4 and 5 students, including explanatory questions and in-depth answers.

**How are prime numbers used in the real world?**

One of the most important uses for prime numbers is in cyber security – making information shared over the internet safer.

In order to encrypt (make secure) things like credit card details, medical records, and even some messaging services like WhatsApp, software engineers create algorithms using prime numbers.

By multiplying two very large prime numbers together (some companies use prime numbers that are hundreds of digits long!), we create an even larger number whose original factors (the two very large prime numbers) are only known to us. We then use this even larger number to encrypt our information.

If anyone else wants to discover what information we are sending, they have to find out what our original factors were. With prime numbers as long as the ones we have used, it could take them years or even decades of constant trial and error before they find even one. This kind of public-key cryptography ensures our information is kept safe.

**Wondering how to explain other key math vocabulary to your children? Check out our **Primary Maths Dictionary**, or try these primary math terms:**

- What Is A Cube Number: Explained For Primary Parents and Kids
- What Is The Lowest Common Multiple: Explained For Primary Parents And Kids
- What Is The Highest Common Factor: Explained For Primary Parents And Kids

**Prime number questions**

**1) A square number and a prime number have a total of 22. What are the two numbers? **

A: 9 and 13

**2) Emma thinks of two prime numbers. She adds the two numbers together. Her answer is 36. Write all the possible pairs of prime numbers Emma could be thinking of. **

A: 3 and 33; 5 and 31; 7 and 29; 13 and 23; 17 and 19

**3) Circle the two prime numbers – 29, 59, 39, 69, 29**

A: 29 and 59

**4) Write the three prime numbers which multiply to make 231.**

A: 3 x 7 x 11

**CHALLENGE QUESTION: Chen chooses a prime number. He multiplies it by 10 and then rounds it to the nearest hundred. His answer is 400. Write all the possible prime numbers Chen could have chosen. **

A: 37, 41 or 43.

**All of our resources can be found in the Third Space Maths Hub**

Every teacher (and parent) at your school can create their own free Maths Hub account to access hundreds of free resources, guides and CPD videos. Premium Maths Hub access is available through a whole-school subscription or is included at no additional cost for schools using our 1-to-1 intervention programmes. Please note, if you are using Internet Explorer you will need to switch to another browser to use the Third Space Maths Hub. Enter your details here to register for free.

### Prime number worksheets

- Ready-to-go Lessons Year 5 Multiplication & Division (Autumn Block 4) Slides & Worksheets
- Ready-to-go Lessons Year 6 4 Operations (Autumn Block 2) Slides & Worksheets
- Year 5 Worked Examples Worksheet: Multiplication & Division 1
- Year 6 Worked Examples Worksheet: Four Operations

### Prime number videos

**Do you have students who need extra support in math?**

Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor.

Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way.

Personalized one-on-one math tutoring programs are available for:

– 2nd grade

– 3rd grade

– 4th grade

– 5th grade

– 6th grade

Why not learn more about how it works?

The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.