Prime numbers are natural or whole numbers, divisible only by one and the number itself. They are greater than one. Hence they are positive integers. 

They have only two factors. 

Examples of Prime Numbers are Mentioned Below

2, 3, 5, 7, 17, 19, 23, 31, 59, 11, 67, 71, 73 etc. 

1 neither falls in the prime number category nor the composite number category. 

Characteristics of Prime Numbers

The characteristics of prime numbers are mentioned below:

• They are divided by one and the number themselves
• They are positive numbers
• They are greater than one
• They are whole or natural numbers
• All prime numbers are odd, except 2, the smallest even prime number
• Co-prime numbers are two numbers that might be prime but have no common factor. For example, 11 and 13
• The number of prime numbers becomes less and less as we move up the number line. For example, there are eight prime numbers between 1 and 20, whereas there are only three between 980 and 1000
• Only prime numbers are left after every possible factoring
• If a and b are prime to one another, then b and a are also prime to each other 

Importance of Prime Numbers

The importance of prime numbers is listed below: 

• The whole number line consists of prime numbers
• You can produce a whole number line just by prime numbers. For example, you can write 12 as 2 * 2 * 3, and all these numbers are prime
• A mathematical proof has shown that any group of prime numbers can be multiplied to produce any number
• Modern computer cryptography works on the prime factors of large numbers
• Primes are crucial as they act as the building blocks of whole numbers 
• Primes’ odd mathematical characteristics make them very useful 
• New mathematical strategies or quantum computers lead to faster prime factorisation of large numbers to break modern encryption effectively

Applications of Prime Numbers

The applications of prime numbers in real life are: 

• We constantly use and rely on prime numbers for cyber-age security
• Primes’ odd mathematical property is used in encryption and decryption
• They are used in generating error-correcting codes used in telecommunications. They ensure that message is sent and received with automatic correction
• Primes act as the base for creating the public-key cryptography algorithms
• They are used for hash tables
• They are also used for generating pseudorandom numbers
• Primes are also used in rotor machine designing. A number is either prime or co-prime to the number on another rotor in one rotor. This helps in generating the full cycle before repeating any possible rotor positions
• Primes are used in computing in the RSA encryption system

Conclusion

We learned how prime numbers can be applied in real-life situations in this article. Prime numbers are natural or whole numbers, divisible only by one and the number itself. 

We also discussed the importance of prime numbers and the applications of prime numbers. We also studied the characteristics of prime numbers.