Mathematics K–6 · Years 5–6
Sieve of Eratosthenes: an algorithm that finds the primes to 100
Number and algebra
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The idea
Crossing out the multiples of each prime in turn removes every composite number, and once the multiples of 2, 3, 5 and 7 are gone every number left up to 100 is prime, because 11 × 11 is already more than 100.
What you need
- a 1 to 100 chart in 10 columns per learner
- a 1 to 100 chart printed in 6 columns
- 4 coloured pencils
How to do it
- Cross out 1, which is neither prime nor composite. Circle 2 and colour every later multiple of 2.
- Circle 3, the next number not coloured, and colour every later multiple of 3 not already coloured in a second colour. Count the new colourings.
- Repeat with 5 and then 7, using the third and fourth colours, and count each time.
- Find the next uncoloured number after 7 and explain why its multiples up to 100 are already coloured.
- Circle every number left and count the primes.
- Repeat the sieve on the 6-column chart and describe the columns in which the primes above 3 appear.
What you should see
The multiples of 2 colour 49 numbers (4 to 100), the new multiples of 3 add 16 (9, 15, 21 and so on to 99), those of 5 add 6 (25, 35, 55, 65, 85, 95) and those of 7 add 3 (49, 77, 91). The next number, 11, has its first uncoloured multiple at 121, beyond the chart, so the 25 numbers left are the primes to 100, from 2 to 97. On the 6-column chart every prime above 3 lies in column 1 or column 5, one more or one less than a multiple of 6.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Every odd number is prime.
- 1 is a prime number.
Safety card
Hazards
- none beyond an ordinary classroom
Controls
- none needed
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
- vocabulary.curriculum.edu.au/MRAC/2024/04/LA/MAT/db8ccd2e-3f45-4121-b3df-f195d91d7589
- www.mathematicshub.edu.au/planning-tool/5/number/follow-and-create-algorithms
- www.mathematicshub.edu.au/planning-tool/5/number/factors-multiples-primes
- nrich.maths.org/problems/sieve-eratosthenes