Co-primes are any two numbers whose common factor is 1. For example, (2, 3), (9, 10)

No, 0 is not a prime number nor a composite number.

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Table of Contents

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Last updated on April 11th, 2025

Prime Numbers

Q: Why is 2 a prime number?

The number 2 is a prime number as it is only divisible by 1 and 2.

Q: Are all prime numbers odd?

No, not all prime numbers are odd. Because 2 is a prime number but an even number too.

Q: How do you calculate the prime numbers?

To find prime numbers we can use methods such as the prime factorization method, counting divisors, divisibility test, etc.

Q: What is the smallest prime number?

Two is the smallest prime number. Because we consider prime numbers as the natural numbers greater than 1 and whose factors are 1 and the number itself.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The natural numbers greater than one are the prime numbers. These numbers are only divisible by one and the number itself. We use prime numbers in cryptography, internet security, digital signatures, and so on.

Importance of Prime Numbers in Mathematics

Based on their properties numbers are classified into many. The numbers are classified into prime and composite numbers based on the divisibility. In mathematics, prime numbers are used to build positive integers. That is, all positive composite numbers can be expressed as products of prime numbers.

Prime and Composite Numbers

Prime number	Composite number
Natural numbers are greater than one and have only two factors that are one and the number itself	Natural numbers greater than one and have more than two factors
Prime numbers cannot be written as the product of two smaller integers. For example: 5 = 5 × 1	The numbers that can be expressed as the product of prime numbers are composite numbers For example: 12 = 2 × 2 × 3 = 2² × 3
The numbers which are only divisible by 1 and the number itself are the prime numbers Example: 11 is only divisible by 1 and 11	Composite numbers have more than two factors Example: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24
Examples: 2, 3, 5, 7, 11, etc.	Examples: 4, 6, 8, 10, 12, etc.

Twin Primes

The pair of prime numbers where the difference between the prime numbers is 2 are the twin primes. In between a pair of twin primes, there is a composite number.

For example, (3, 5), (5, 7), (11, 13), (17, 19), etc.

Co-prime Numbers

Co-primes are a pair of numbers where the common factor of the two numbers is 1. In co-primes, one number can be prime, and the other can be a composite number. Here, the only condition is that the common factors should be 1.

For example, (2, 3), (5, 9), (9, 10), etc.

Prime Factorization

Any composite number can be expressed as the product of its prime factors. This process is known as prime factorization.

For example, the prime factorization of 34 is 2 × 17, here 2 and 17 are the prime factors of 34.

Common Mistakes and How to Avoid Them in Prime Numbers

Tips and Tricks to Master Prime Numbers

Confused about how to learn and master prime numbers? When learning prime numbers try to follow these tips and tricks to master it. These tricks can help you learn prime numbers quickly.

All the even numbers except 2 are non-prime numbers because it has more than 2 factors.

For example, 256 is not a prime number as it has more than two factors. The common factor between any two prime numbers is 1. So all prime numbers are co-primes.

The two prime numbers whose difference is 2 are twin primes.

All composite numbers can be expressed as a product of prime numbers.

No prime numbers end in 5 except 5 as it is divisible by 5.

The numbers ending in 0 are not prime numbers as it is divisible by 2 and 10.

All the even numbers except 2 can be expressed as the sum of two odd number. For example; 10 = 5 + 5; 8 = 5 + 3; 16 = 11 + 5.

Real-world Applications of Prime Numbers

In our daily life, we use prime numbers in different fields such as cryptography and data security, analyzing number patterns, and so on. Let’s learn a few real-world applications of prime numbers.

Cryptography and Data Security: Prime numbers are used to encrypt algorithms through public-key cryptography like RSA. Cryptography is used to decrypt or encrypt data. For data security, prime numbers can be used as passwords.

Simplification of fraction: Prime numbers can be used to find the GCF of more than two numbers. GCF is used to simplify the fractions.

Analyzing number pattern: As prime numbers are considered the building blocks of all integers, it helps to understand the relationship between numbers. So we use prime numbers in hash tables to spread the data key evenly.

Solved Examples of Prime Numbers

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

What is the sum of the first five prime numbers?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

How many primes are there between 2 and 20

Explanation

Problem 3

If x is a prime number how many factors does x2 have?

Explanation

Problem 4

Which of the following is not a prime number 83, 101, 105, 89, 11.

Explanation

Problem 5

Which is the greatest prime number between 11 and 30?

Explanation

Problem 6

Is 97 a prime number?

Explanation

FAQs on Prime Numbers

1.Why is 2 a prime number?

2.Are all prime numbers odd?

3.How do you calculate the prime numbers?

4.What is a co-prime?

5.Is 0 a prime number?

6.What is the smallest prime number?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.