# Integers, Prime Numbers

13/07/2020

### Integers

Integers are like whole numbers, but they also include negative numbers … but still no fractions allowed!

So, integers can be negative {−1, −2,−3, −4, … }, positive {1, 2, 3, 4, … }, or zero {0}

We can put that all together like this:

Integers = { …, −4, −3, −2, −1, 0, 1, 2, 3, 4, … }

Examples: −16, −3, 0, 1 and 198 are all integers.

(But numbers like ½, 1.1 and 3.5 are not integers)

#### Prime Numbers

Number s which have only two factors namely 1 and the number itself are called prime numbers.

For example:

2, 3, 5, 7, 11, 19, 37 etc are prime numbers.

Composite Numbers

Numbers having more than two factors are called as composite numbers.

For example:

4, 6, 8, 10 etc are composite numbers.

Notes:

(a) 1 is neither prime nor composite.

(b) 2 is the lowest and the only even prime number.

(c) 9 is the lowest odd composite number.

#### Co-prime Numbers

Two numbers are said to be co-prime if they do not have a common factor other than 1 or two numbers whose HCF is 1 called co-prime numbers.

Co-prime numbers needs not be prime numbers.

For example:

• 7 and 10 are co-prime.
• 15 and 17 are co-prime.

Twin Prime Numbers

Twin prime numbers are the two prime numbers whose difference is 2.

For example:

• 3 and 5
• 17 and 19
• 41 and 43
• 29 and 31
• 71 and 73.