# Sieve of Eratosthenes

Your first task is to click on number 1. One is not a prime number as it does not have two factors.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Number one has been removed.

The multiples of two greater than two have been removed.

The multiples of three greater than three have been removed.

Multiples of five have been removed.

Multiples of seven have been zapped.

Multiples of eleven are no more.

Goodbye multiples of thirteeen.

Asta lavista multiples of seventeen.

No more multiples of nineteen.

Do you miss the multiples of twenty nine?

Good riddance multiples of thirty one.

Bye bye multiple of thirty seven.

Chao multiple of forty one.

The multiple of forty three has been exterminated!

The one multiple of forty seven has been removed.

Well done!

There is no simple formula for generating the sequence of prime numbers but this is a method devised many years ago by the mathematician Eratosthenes of Cyrene (he also invented Geography!). It involves methodically eliminating the numbers that are know not to be prime until only the prime numbers remain. Begin by crossing out one as it is not a prime number (it does not have two factors, it is a square number). Two is a prime number but all of its multiples a not (they are composite numbers) so cross out all of the multiples of two but leave two as the first prime number. Next cross out all of the multiples of three except three itself. The number four and all of its multiples have already been crossed out as they are also multiples of two. Next cross out all the multiples of five except five itself. Continue this process until you have discovered as many prime numbers as you need.

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## Extension Activities

1. Which number was clicked on the greatest number of times while doing this activity? Why?
2. Make a plan for extending this task to find all prime numbers up to 200. Minimise the work you will need to do!
3. Try doing this task with number grids of different dimensions. You can do it online by visiting the Number Grid page.

"If you have completed and enjoyed this activity and are looking for another, similar challenge you won't be disappointed with Pascal's Triangle. Levels two to five involve colouring the cells of a large Pascal's Triangle following a number rule to produce an interesting pattern. You can find this activity here: Pascal's Triangle"

Transum,
Friday, October 12, 2018

"Make a note of the prime numbers that you found.
Now go to the Transum Number Grid activity:
Transum.org/go/?Num=727
Go to the Settings Tab and choose 6 Columns and 17 Rows.
Please don't get this the wrong way around or it won't work !!
You have now created the Tab "17 rows and 6 columns"
Go to this tab and colour those squares which contain your prime numbers.
When you have finished, look at the pattern. If you ignore the first row, what do you see ?
Are you surprised ? Look at the columns without any prime numbers. Can you see why they don't have any coloured squares ?"

Ann Roberts, London
Tuesday, September 29, 2020

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## Other activities involving prime numbers

#### Factor Trees

Create factor trees to find the prime factors of the given numbers. This is a useful skill to develop.

www.transum.org/go/?to=factortrees

#### Prime Labyrinth

Find the path to the centre of the labyrinth by moving along the prime numbers.

www.transum.org/go/?to=labyrinth

#### Prime Square

Drag the numbers into the red cells so that the sum of the three numbers in each row and column is prime.

www.transum.org/go/?to=psquare

#### Scallywags and Scoundrels

Arrange the numbers on the chairs so that the sum of any two sitting next to each other is prime.

www.transum.org/go/?to=scallywags

#### HCF and LCM

Practise finding the highest common factor (H.C.F) and the lowest common multiple (L.C.M) of two numbers.

www.transum.org/go/?to=hcf

#### Satisfaction

This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.