2D Prime numbers

Learning intentions for this section:

• To know what prime numbers and composite numbers are

• To be able to determine whether a number is prime, by considering its factors

• To be able to find the prime factors of a given number

Past, present and future learning:

• This section consolidates and extends Stage 3 concepts which are used in Stage 4

• These concepts are assumed knowledge for future learning beyond Stage 4

A prime number is defined as a positive whole number that has exacty two distinct factors: itself and 1. It is believed that prime numbers (i.e. positive whole numbers with only two factors) were first studied by the ancient Greeks. More recently, the introduction of computers has allowed for huge developments in this field. Computers have allowed mathematicians to determine which large numbers are primes. Programs have also been written to automatically generate huge prime numbers that could not be calculated previously by hand.

There are some interesting prime numbers that have patterns in their digits; for example, 12345678901234567891. This is known as an ascending prime.

You can also get palindromic primes, such as 111191111 and 123494321

Below is a palindromic prime number that reads the same upside down or when viewed in a mirror.

| 88808 | 80888 |

Lesson starter: How many primes?

How many numbers from 1 to 100 are prime?

You and a classmate have 4 minutes to come up with your answer.

Key Ideas

■ A prime number is a positive integer that has only two factors: 1 and itself.

■ The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

■ A number that has more than two factors is called a composite number.