Prime Numbers Prime numbers consist of just two factors;1 and the number itself. Consider an example of number 7, which has only two factors 1 and 7. This means it is a prime number. Let us take another example of the number 8, which has more than two factors, i.e., 1, 2, 4, and 8. This means 8 is not a prime number. We know that the number 1 has just one element. Consequently, it cannot be a prime number since a prime number needs to have two components. This indicates that 1 is a unique number and neither a prime nor a composite number. Definition of Prime Numbers A prime number is a positive integer with exactly two factors, i.e. 1 and the number itself. If p is a prime, then its only factors are 1 and p itself. Any number that does not obey this rule is referred to as a composite number and can be factored into other positive integers. It can also be defined as a positive number that cannot be produced by multiplying the number by any other two positive integers except for 1, and by the number itself. Properties of Prime Numbers Some of the key properties of prime numbers are given below: A prime number is a positive integer number greater than 1. It consists of exactly two factors, one is 1 and the other is the number itself. 2 is the only even number that is a prime number. Any two prime numbers are always coprime to each other. Each number can be expressed as the product of prime numbers. Background of Prime Numbers The Greek scientist Eratosthenes (275–194 B.C.) discovered the prime number. He used the example of a sieve to drain out the composite numbers and separate the prime numbers from a list of natural numbers. He designed a smart way to determine all the prime numbers up to a given number. This method is called the Sieve of Eratosthenes. Prime numbers have created human interest since ancient times. Even today, mathematicians are trying to find prime numbers with mystical properties. Euclid proposed the theorem on prime numbers - there are infinitely many prime numbers. Is 1 a Prime Number? We are conferring on the definition of the prime number, which states that a number should have exactly two factors for it to be considered a prime number. Since a prime number is a natural number larger than 1 that is not the product of two smaller natural numbers, 1 is not regarded as the prime number. Easy Way to Calculate Prime Numbers Finding prime numbers can be done in a variety of methods. Let's examine one of these techniques. Method: All prime numbers (keep out 2 and 3) can be expressed as '6n + 1 or 6n - 1'. We will check it with positive integers. Let’s check- 6n-1, for the number 1, So, 6(1) - 1 = 5 6n+1, for the number 1, So, 6(1) + 1 = 7 6n-1, for the number 3, So, 6(3) - 1 = 17 6n+1, for the number 3, So, 6(3) + 1 = 19 Now, we know that the numbers 5, 7, 17, and 19 are prime. Applications of Prime Number Some of the most important applications of prime numbers are given below: One of the most important uses for prime numbers is in cyber security – making information shared over the internet safer. To encrypt (make secure) things like credit card details, medical records, and even some messaging services like WhatsApp, software engineers make algorithms using prime numbers. By multiplying two vast prime numbers together, we create an even larger number whose original factors are only known to us. We use this even larger number to encrypt our information. Conclusion In this article, we learned about prime numbers, their properties, methods to find prime numbers, different lists of prime numbers, and application of prime numbers.
