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# Let's celebrate World Maths Day with Prime Numbers

In celebration of World Maths Day, we are sharing a fascinating Prime Numbers lesson that you can take back to the classroom.
March 21, 2022

### Happy World Maths Day!

At Maths Pathway, we celebrate all things maths everyday, but especially today when we celebrate World Maths Day!

It's the perfect opportunity to come together with your students to take on an activity that will get everyone's problem solving skills working as you uncover which numbers are prime with a very useful algorithm.

# Prime Numbers Activity

Prime numbers are numbers that only have two factors — one and themselves.

People have been interested in finding large prime numbers since ancient times.  Euclid — a Greek mathematician from approximately 300 BC — proved that there are an infinite number of prime numbers. Large prime numbers have many applications, one of the big ones is their use in codes and ciphers (for more details see RSA code).

The first recorded largest prime number was 8191 found in the year 1456. More recently, using high powered computers, people have found much larger prime numbers. As of March 2022, the largest known prime has 24 862 048 digits!

There are still things that haven’t been proven about prime numbers. For example:

• Can every even number be written as the sum of two prime numbers? Goldbach noticed that every even number could be written as the sum of two prime numbers. However it has not been proven that this is true for all even numbers, so it’s called the Goldbach conjecture.
• How many pairs of twin prime numbers are there? A twin prime is a pair of primes with a difference of two. For example, 3 and 5 are twin primes, as are 17 and 19. It is still unknown if there are infinitely many pairs of twin primes.
• Is there a prime number between every two consecutive square numbers? In 1882 Adrien-Marie Legendre suggested that there will always be a prime number between every two square numbers. It has yet to be proven.

It can be slow to check if a number is prime, because we need to try dividing it by many numbers. The Sieve of Eratosthenes is an algorithm that was used to find prime numbers. It is a systematic approach that involves shading multiples, which can’t be prime numbers. It is called a sieve because we are sorting through all of the numbers, leaving behind the prime numbers.

Let’s try the Sieve of Eratosthenes for ourselves:

1. Put a cross through 1.
2. Circle 2, then shade in all of the multiples of 2.
3. Circle 3, then shade all of the multiples of 3 that haven’t been shaded yet.
4. Circle the next smallest remaining number, then shade all of its multiples which have not been shaded yet.
5. Repeat step 4 until all of the squares are crossed through, circled or shaded.

All of the circled numbers are primes and all of the shaded numbers are composites. 1 is crossed out because it is special — it is neither a prime number nor a composite number, because it's only factor is 1!