What makes a number Prime?
We can arrange objects in rectangular shapes.
- 12 figs: Can be arranged as , , .
- 7 figs: Can ONLY be arranged as .
Numbers like 7, which have only two factors (1 and the number itself), are called Prime Numbers. Numbers like 12, which have more than two factors, are called Composite Numbers.
| Type | Definition | Examples |
|---|---|---|
| Prime | Exactly 2 factors (1 and itself). | 2, 3, 5, 7, 11, 13, 17, 19 |
| Composite | More than 2 factors. | 4, 6, 8, 9, 10, 12, 14, 15 |
| Neither | The number 1 has only 1 factor. | 1 |
Warning
Important: 1 is neither prime nor composite.
Finding Primes: Sieve of Eratosthenes
Eratosthenes, a Greek mathematician, developed a method to find primes between 1 and 100.
Steps:
- Cross out 1.
- Circle 2 (Prime), then cross out all multiples of 2 ().
- Circle 3 (Prime), then cross out all multiples of 3 ().
- Circle 5 (next uncrossed number), cross out its multiples.
- Continue this process. The circled numbers are Primes.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
(Partial grid shown for illustration)
Twin Primes
Pairs of prime numbers that have a difference of exactly 2 are called Twin Primes.
- (3, 5)
- (5, 7)
- (11, 13)
- (17, 19)
- (41, 43)
Tip
Fun Fact: Mathematicians are still trying to find the largest prime number. The largest known prime is millions of digits long!