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Learn the Prime Numbers

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Learn the Prime Numbers

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Prime numbers are like the superheroes of the number world: they are only divisible by themselves and one. In this article, we will discover what they are, how to find them, and some interesting facts about their super powers.

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Learn Prime Numbers with Smartick

What Are Prime Numbers?

Finding Primes in a Set

Properties

Solved Examples

Some Facts about Prime Numbers

What are Prime Numbers?

Prime numbers are natural numbers that can only be divided by 1 and themselves. They are like the building blocks of all other numbers. 

For example, the number 7 is prime because it can only be divided by 1 and 7. However, the number 8 is not prime because it can be divided by 1, 2, 4, and 8.

Below is a table of the first ten prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Finding Primes in a Set 

One of the easiest ways to find prime numbers in a set is to use the Sieve of Eratosthenes. This method involves creating a list of all numbers between two limits. When searching for primes, cross out all numbers that are their multiples starting with the smallest prime in the number set. Cross off all multiples of this number, and then do the same for the multiples of the next lowest prime, and so on.

Properties

Prime numbers have several unique properties. For example, every prime greater than 3 can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.

There are an infinite number of primes, which means that you can always find a new one if you keep looking!

Prime and Composite Numbers

Prime numbers are often contrasted with composite numbers. Composite numbers are natural numbers that have more than two factors. For example, the number 12 is a composite number because it can be divided by 1, 2, 3, 4, 6, and 12.

Co-prime Numbers

Co-prime numbers are numbers that share no common factors other than 1. When two numbers are co-prime, it means that they are not divisible by any common prime number. For example, the numbers 7 and 15 are co-prime because the only common factor they have is 1. However, the numbers 12 and 15 are not co-prime because they have a common factor of 3.

Some other examples of co-prime numbers include 3 and 4, 5 and 7, and 9 and 16.

The Tiniest Prime 

The smallest prime number is 2. It is the only even prime number AND the building block of all other prime numbers. This is because all even numbers are divisible by 2, and the only way for a number to be prime is if it is only divisible by 1 and itself.

Prime Numbers in the Real World 

Prime numbers might seem like dead-end digits, but in reality, they’re super useful!

Software engineers use them numbers all the time for cyber security. In the world of cyber security, it’s important to keep information locked up and safe. Software engineers encrypt things like credit card details and online messaging platforms to make sure that hackers can’t get at your private information—or your personal messages!

To do this, cyber security companies choose two REALLY big prime numbers (some have over a hundred digits!) and multiply them together. With the new even BIGGER number, cyber security engineers can lock our personal information up safely. 

If any hackers try to get to our personal information, they have to figure out what the two original factors were. With such long prime numbers in the game, it could take hackers years—or even decades—to crack the prime number puzzle! All thanks to prime numbers, our personal information online stays locked up safe!

History of Prime Numbers

Prime numbers have fascinated mathematicians for centuries. The ancient Greeks were particularly interested in primes and made significant contributions to the study of these numbers. Euclid, a Greek mathematician, proved that there are an infinite number of prime numbers.

The Largest Prime Known to Men 

The largest prime number currently known is 2^82,589,933-1. It was discovered in 2018 and has 24,862,048 digits! 

Let’s Review

  • A number is prime if it is only divisible by 1 and itself.
  • The only even prime number is 2.
  • The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Prime numbers are essential to many areas of mathematics, and their properties continue to be explored and discovered to this day. Whether you’re a mathematician, a cyber security expert, or just a kid in math class, knowing how primes work is key to understanding the world of numbers—and their super powers! 

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