Prime Numbers 03:50 minutes

Video Transcript

Transcript Prime Numbers

Meet Roscoe. He’s the world’s foremost diamond hunter and a big fan of prime numbers. No wonder his last find was a 113 karat diamond! For as long as anyone can remember, other diamond prospectors have been using hammers to look for prime diamonds. However, Roscoe invented a quicker method of identifying which rocks contain diamonds. He built a machine that tests for prime numbers. The only catch is his machine only works up until the number 120. Roscoe puts all the rocks he gathered for the day into his machine. His machine then perfoms a series of tests on each rock to see if they are prime. Roscoe knows that prime numbers are very special. A prime number is only divisible by one and itself. It cannot have any other factors! Numbers that are not prime are composite numbers, which means they're composed of more factors than one and itself. For example, 11 is a prime number because its factors are one and 11. While 10 is a composite number. Its factors are 1, 2, 5, and 10.
So, Roscoe’s machine first checks if the numbers on the rocks are divisible by 2. Two is the first prime number. It’s also the only even prime. Because every even number must also be divisible by 2, Roscoe’s machine removes all the rocks that are even numbers greater than 2. It does not remove the two because the factors of two are just one and itself, and therefore it's prime. The next number Roscoe’s machine checks for is the number 3. Just like before, if a number is also a multiple of 3, it means the number is not prime because at the very least it has a factor of 1, 3, and itself. Three is a prime number, so it remains, while all other multiples of three are removed. After removing all numbers greater than 3 that are divisible by 3, Roscoe’s machine moves on to the number 5. The machine removes all numbers greater than 5 that are also multiples of 5 before moving on to the last step. Again, the 5 stays because its factors are only 1 and itself. The last step for Roscoe’s machine is to remove all numbers greater than 7 that are multiples of 7. It makes quick work of these numbers as well. Let’s take a look at what Roscoe has left over: All of these numbers are prime except for one special number, which seems to have gotten stuck in the seive. With one last shake, Roscoe's machine removes the number one, which is by definition NOT a prime number nor a composite. Now, if we look for factors of each of these numbers that are still remaining, we'll find that all the numbers are only divisble by 1 and themselves. Roscoe checks each one of the rocks and sure enough, there're diamonds in dem dar rocks! Roscoe plans to treat himself and spend some of his newfound riches. If only he were a little closer to civilization…

1 comment
  1. Default

    Are the factors of a composite number prime numbers? That’s what is says in the bonus problem...confusing. The factors of 27 are 1, 3, 9, and 27. 9 is not a prime number.

    Posted by Spolcen, 9 months ago