No, 1 is not a prime number, because a prime has exactly two different factors and 1 has only one. Leaving 1 out keeps each number’s prime factors unique: 12 breaks into 2 × 2 × 3 and into no other set of primes. The smallest prime is 2, and it is the only even one, since 2 divides every other even number.

How do you check if a number is prime?

To answer “is it prime?”, divide the number by 2, 3, 5, 7, 11 and the next primes in turn. Stop once a prime times itself is bigger than the number. If no division comes out exact, the number is prime. For 113, you test only 2, 3, 5 and 7, because 11 × 11 = 121 is already too big. None of them fits, so 113 is prime.

How can you tell quickly that a number is not prime?

Two digit tests, one for 3 and one for 11, catch many non-primes in seconds. If the digits add up to a multiple of 3, then 3 divides the number: 2 + 3 + 7 = 12, so 237 = 3 × 79. For a three-digit number, add the outer digits and subtract the middle one. A result of 0 or 11 means 11 divides it, as in 209 = 11 × 19.

Why does my child think 51 is prime?

Your child probably expects odd numbers to be prime, because 3, 5 and 7 are. But 51 = 3 × 17, and its digits add up to 6, a sign that 3 divides it. Other lookalikes, such as 57 = 3 × 19 and 133 = 7 × 19, fool adults too. Ask your child to try 3, 7 and 11 before calling any number prime.

How can a teacher use this primes practice in a lesson, and what does it cost?

It costs nothing: any browser opens both levels, and no pupil registers or downloads anything. On the board, draw a ten-by-ten grid of 1 to 100. Pupils take turns crossing out 1 and the multiples of 2, 3, 5 and 7, but never those four primes. The 25 numbers left are every prime below 100. Afterwards, pupils hunt primes on their own tablets. The schools plan adds a teacher dashboard of who is improving, at a per-student price.

Math practice · reimagined

Prime Numbers Game

This prime number game shows numbers up to 1000, and its non-primes are all odd and never end in 5, so the last digit gives nothing away. Find the one number that does not fit before your rival, and your fighter hits first.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is a prime number?

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor divides a number exactly, with nothing left over. So 13 is prime, but 15 is not, because 3 × 5 = 15. A number above 1 that is not prime, like 15, is called composite.

Every level of Primes

Example: which is prime, 287, 87 or 89?

The instruction asks for the prime, so the other two numbers must each hide a factor.
The digits of 87 add up to 15, which 3 divides, and indeed 87 = 3 × 29.
Try 7 on 287: it divides exactly, because 7 × 41 = 287.
Only 89 is left, and none of 2, 3, 5 or 7 divides it, so you tap 89.

Learn it step by step

A prime number can only be built one way: 1 times the number itself. Nothing else divides into it evenly — it refuses to be split into equal groups.

Up here the numbers get bigger, so you test them. Try dividing by 2, then 3, then 5, 7, 11, 13… if any of them fits with nothing left over, the number is NOT prime. Watch out for sneaky ones like 91 — it looks prime, but 7 × 13 = 91, so it's hiding a factor.

Read whether the question wants the prime or the odd-one-out, then tap your pick.

Tips and common mistakes

Learn the primes below 20 in two groups of four: 2, 3, 5, 7 and 11, 13, 17, 19. Up to 400, you only need to divide by these.
A common mistake is stopping after 2, 3 and 5. 119 passes all three, yet 119 = 7 × 17, so keep testing 7, 11, 13 and beyond.
At home, arrange 12 coins into rectangles: 2 rows of 6, 3 rows of 4. Then try 13 coins. Only a single row works, because 13 is prime.

How to play

Each round shows three or four number buttons, such as 163, 141, 11 and 43, under one instruction: pick the prime, or pick the non-prime. The instruction switches at random, so read it before you tap. Tap the right number before your rival and Chilli strikes, harder the less time you took.

— Quick answers —

Primes: the short FAQ

Is 1 a prime number?: No, 1 is not a prime number, because a prime has exactly two different factors and 1 has only one. Leaving 1 out keeps each number’s prime factors unique: 12 breaks into 2 × 2 × 3 and into no other set of primes. The smallest prime is 2, and it is the only even one, since 2 divides every other even number.
How do you check if a number is prime?: To answer “is it prime?”, divide the number by 2, 3, 5, 7, 11 and the next primes in turn. Stop once a prime times itself is bigger than the number. If no division comes out exact, the number is prime. For 113, you test only 2, 3, 5 and 7, because 11 × 11 = 121 is already too big. None of them fits, so 113 is prime.
How can you tell quickly that a number is not prime?: Two digit tests, one for 3 and one for 11, catch many non-primes in seconds. If the digits add up to a multiple of 3, then 3 divides the number: 2 + 3 + 7 = 12, so 237 = 3 × 79. For a three-digit number, add the outer digits and subtract the middle one. A result of 0 or 11 means 11 divides it, as in 209 = 11 × 19.
Why does my child think 51 is prime?: Your child probably expects odd numbers to be prime, because 3, 5 and 7 are. But 51 = 3 × 17, and its digits add up to 6, a sign that 3 divides it. Other lookalikes, such as 57 = 3 × 19 and 133 = 7 × 19, fool adults too. Ask your child to try 3, 7 and 11 before calling any number prime.
How can a teacher use this primes practice in a lesson, and what does it cost?: It costs nothing: any browser opens both levels, and no pupil registers or downloads anything. On the board, draw a ten-by-ten grid of 1 to 100. Pupils take turns crossing out 1 and the multiples of 2, 3, 5 and 7, but never those four primes. The 25 numbers left are every prime below 100. Afterwards, pupils hunt primes on their own tablets. The schools plan adds a teacher dashboard of who is improving, at a per-student price.

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