the natural number that is greater than one and cannot be expressed as a product of two smaller natural numbers is called a prime number. Any natural number that is greater than 1 but not a prime number is called a composite number. Prime numbers are the most crucial component of number theory because of the fundamental theorem of arithmetic. It states that every natural number that is greater than 1 is either a prime number or can be expressed as a product of prime factors in a unique order.
History of Prime Numbers
In 1550 BC, the Rhind Mathematical Papyrus gave expansions of different forms for prime and composite numbers. However, when we come to the explicit study of prime numbers, the earliest surviving records come from ancient Greek mathematics. Euclid’s elements have detailed proof of the infinity of prime numbers and the fundamental theorem of arithmetic. The Sieve of Eratosthenes is used to construct primes to date. Ibn al-Haytham and Fibonacci also made several breakthrough discoveries where prime numbers are concerned. In 1640 Pierre de Fermat stated Fermat’s theorem without proof. As technology progressed, great minds further researched this topic. As of today, prime numbers are the most vital topic that is used in several industries.
Properties of Prime Numbers
- All prime numbers are greater than 1.
- Prime numbers can be divided by at least one prime number.
- 2 is the only even prime number. All the other prime numbers are odd numbers.
- Any two prime numbers are always coprime to each other.
- Every even positive integer that is greater than 2 can be expressed in the form of prime numbers.
What is the difference between Prime and Composite Numbers?
- A prime number has two factors only, whereas composite numbers have more than two factors.
- A prime number can only be divided by one or the number itself, while composite numbers are divisible by all its factors. For example, 3 is a prime number and can be divided by only 1 and 3. 8 is a composite number that can be divided by 1, 2, 8.
Use of Prime Numbers
1. Mathematical Uses
Prime numbers are used in several Mathematical topics, such as to find the LCM and GCF of numbers. By expressing numbers in the form of their prime factors, also known as prime factorization, we can easily determine the LCM and GCF of numbers
2. Cyber Security
Encryption and other concepts related to computer security make use of prime numbers to ensure that the information being transferred is completely secure. For example, if you are making an online payment, you will be required to entire your credit card details. If these details are not transmitted in a safe and secure manner, your card will get hacked. This will lead to you losing all your money in the bank. Thus, the RSA encryption system or the RSA algorithm makes use of prime numbers to encrypt data for the purpose of cybersecurity.
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