Prime time: the sieve of Eratosthenes
Write the numbers from 1 to 100 in a grid, cross out the multiples of 2, 3, 5 and 7, and see the primes that are left. Count the primes up to a limit, and test whether numbers such as 91 and 97 are prime.
Core concept
In short: Cross out multiples on a number grid until only the prime numbers are left.
A prime number has exactly two factors, 1 and itself; crossing out the multiples of each prime in turn (the sieve of Eratosthenes) leaves only the primes, and a composite number has a smallest factor other than 1
Topic: Numbers: primes and factors
A prime number: A number with exactly two factors: 1 and itself, like 2, 3, 5 and 7. All key words has exactly two factor: A number that divides another exactly. 3 is a factor of 12. All key words: 1 and itself. 2, 3, 5 and 7 are primes. A composite number has more factors: 6 = 2 × 3. The number 1 has only one factor, so it is neither prime nor composite. More than two thousand years ago, Eratosthenes found a quick way to list primes. Write the numbers in a grid. Circle 2, then cross out every multiple: What you get when you multiply a number by 1, 2, 3 … 12 is a multiple of 3. All key words of 2. Circle the next number left, 3, and cross out its multiples. Do the same for 5 and 7. Up to 100, every number still standing is prime. To test one number, try dividing it by 2, 3, 5, 7 …: if one divides it exactly, that is its smallest factor and it is composite.
What you will learn
- Tell prime numbers from composite numbers.
- Use the sieve of Eratosthenes to list primes.
- Find the smallest factor of a composite number.
Before you start
- Know multiplication tables up to 10.
Materials
- A 10 × 10 number grid (1 to 100) and coloured pencils
Equipment
- None
Procedure
- With numbers up to 30, test 91 and record.
- Test 97 and record.
- Change the limit to 100 and record.
- Test 49 and record.
How this simulation is simplified
- The grid starts at 1, which is neither prime nor composite.