Definition:
A prime number is a number that can be divided only by 1 and itself. This means that the number has exactly two factors.
For example, 13 is a prime number because 13 can only be divided evenly by 1 and 13.
If the number has more than two factors, we say that the number is composite.
For instance, 12 is a composite number because 12 can be divided by numbers other than 1 and 12, such as 2, 3, and 4.
1 is neither prime nor composite because it has only one factor. According to the definition, a number must have at least 2 factors before it can be prime or composite.
Notice also that 2 is the only number that is even and prime at the same time.
How many numbers less than 100 are prime?
You can use the definition to test every single number. It is somewhat time-consuming.
As a shortcut, you can use a method or algorithm called Sieve of Eratosthenes, named after a famous Greek mathematician.
Sieve's Algorithm:
Make a list of all numbers from 1 to 100
Start by crossing out 1 because it is not prime. Then, circle the next number after 1 that is prime, which is 2
Cross out all the multiples of 2 until you get to 100, such as 2, 6, 8, 10, 12...
Look for the next number after 2 that is prime. That number is 3. Circle 3 and cross out all multiples of 3, such as 6, 9, 12, ...
Repeat the process with 5 and 7. After you are done, you should find 25 prime numbers.
We show you the process for all numbers from 1 to 50
Take the quiz below to see how well you understand this lesson.
Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.
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Feb 17, 19 12:04 PM
There is no rational number whose square is 2. An easy to follow proof by contraction.