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\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\tWhat Is A Prime Number? Explained For Teachers\t\t\t\t\t\t
\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tSophie Bartlett\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tA 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.
\n\n\n\nWhat is a prime number?
\n\n\n\nA prime number is a whole number greater than 1 with only two factors \u2013 itself and 1.
\n\n\n\nA prime number cannot be divided by any other positive integers without leaving a remainder, decimal, or fraction.
\n\n\n\nAn 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 \u00f7 6 = 2 remainder 1.
\n\n\n\n15 is not an example of a prime number because it can be divided by 5 and 3 as well as by itself and 1.
\n\n\n\n15 is an example of a composite number because it has more than two factors.
\n\n\n\nPrime numbers are often seen as \u201cbuilding blocks\u201d by mathematicians in number theory. The fundamental theorem of arithmetic states that a composite number can be expressed as the product of prime numbers.
\n\n\n\nSee also: Divisibility Rules
\n\n\n\n\t\t\t\n\t\t\t\t\t\t\t\tPrime Numbers Worksheets\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tTest your class\u2019 knowledge of prime numbers with 29 questions for grade 4 and 5 students, including explanatory questions and in-depth answers.\t\t\t\t\t\t\t
\n\t\t\t\t\t\tPrime number examples
\n\n\n\nHow to work out if a given number is a prime number or a composite number, based on the properties of prime numbers.
\n\n\n\n![\"Prime](\"https://thirdspacelearning.com/wp-content/uploads/2019/11/How-do-prime-numbers-work.png\")
What are the prime numbers?
\n\n\n\n- \n
- There are 8 prime numbers under 20: 2, 3, 5, 7, 11, 13, 17 and 19. \n\n\n\n
- The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. \n\n\n\n
- There are 25 prime numbers between 1 and 100. \n\n\n\n
- Prime numbers include large numbers and can continue well past 100. \n\n\n\n
- For example, 21,577 is a prime number. \n
List of prime numbers to 100
\n\n\n\n2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
\n\n\n\nNotice that this list of prime numbers contains only odd numbers, with the exception of number 2.
\n\n\n\nSmallest prime number
\n\n\n\n2 is the smallest prime number. It is also the only even prime number \u2013 all other even numbers can at least be divided by themselves, 1, and 2, meaning they will have at least 3 factors.
\n\n\n\nLargest prime number
\n\n\n\nGreek 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.
\n\n\n\nThe largest known prime number (as of November 2020) is 282,589,933 \u2212 1, a number that has 24,862,048 digits when written in base 10. Before then, the largest known prime number was 277,232,917 \u2212 1, having 23,249,425 digits.
\n\n\n\nBy the time you read this, it might be even larger, but you can follow its progress on Wikipedia.
\n\n\n\n\n\n\n\n\n\n\n\nCommon FAQs about prime numbers
\n\n\n\nA prime number is a number that can only be divided by itself and 1 without remainders.
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.
1 is not a prime number because it has only one factor, namely 1. Prime numbers need to have exactly two factors.
2 is a prime number because its only factors are 1 and itself.
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.
\n\t\t\t\t\t\t\t\tPrime Numbers Worksheets\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tTest your class\u2019 knowledge of prime numbers with 29 questions for grade 4 and 5 students, including explanatory questions and in-depth answers.\t\t\t\t\t\t\t
\n\t\t\t\t\t\tHow are prime numbers used in the real world?
\n\n\n\nOne of the most important uses for prime numbers is in cyber security \u2013 making information shared over the internet safer.
\n\n\n\nIn 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.
\n\n\n\nBy 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.
\n\n\n\nIf 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.
\n\n\n\nWondering how to explain other key math vocabulary to your children? Check out our Primary Maths Dictionary, or try these primary math terms:
\n\n\n\n- \n
- What Is A Cube Number: Explained For Primary Parents and Kids \n\n\n\n
- What Is The Lowest Common Multiple: Explained For Primary Parents And Kids \n\n\n\n
- What Is The Highest Common Factor: Explained For Primary Parents And Kids \n
Prime number questions
\n\n\n\n1) A square number and a prime number have a total of 22. What are the two numbers?
\n\n\n\nA: 9 and 13
\n\n\n\n2) 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.
\n\n\n\nA: 3 and 33; 5 and 31; 7 and 29; 13 and 23; 17 and 19
\n\n\n\n3) Circle the two prime numbers \u2013 29, 59, 39, 69, 29
\n\n\n\nA: 29 and 59
\n\n\n\n4) Write the three prime numbers which multiply to make 231.
\n\n\n\nA: 3 x 7 x 11
\n\n\n\nCHALLENGE 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.
\n\n\n\nA: 37, 41 or 43.
\n\n\n\nAll of our resources for primary schools can be found in the Third Space Maths Hub
Create your own free Maths Hub account\u00a0to access hundreds of free resources, guides and CPD videos. Premium Maths Hub access includes 36 weeks of Fluent in Five, Rapid Reasoning and Ready To Go Lesson Slides for years 1 to 6. It is available through a whole-school subscription or is included at no additional cost for schools using our online one to one maths tutoring.
Register free for the Third Space Maths Hub.
Enquire about Premium Maths Hub
Prime number worksheets
\n\n\n\n- \n
- Ready-to-go Lessons Year 5 Multiplication & Division (Autumn Block 4) Slides & Worksheets \n\n\n\n
- Ready-to-go Lessons Year 6 4 Operations (Autumn Block 2) Slides & Worksheets \n\n\n\n
- Year 5 Worked Examples Worksheet: Multiplication & Division 1 \n\n\n\n
- Year 6 Worked Examples Worksheet: Four Operations \n
Prime number videos
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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.
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