Study on Prime Numbers

A number is a mathematical or arithmetical value used for measuring, calculating and counting. There are two numbers- positive and negative numbers.

The different types of numbers are natural numbers, whole numbers, integers, real numbers, rational numbers, irrational and rational numbers, etc. 

In this article, we will study prime numbers. 

Definition of Prime Numbers

Prime numbers are natural or whole numbers, divisible only by 1 and the number itself. 

They are greater than 1; hence they are positive integers. 

They have only two factors. 

Numbers having more than two factors are composite numbers.

The prime number property is known as primality.  

The number of prime numbers between 1 & 100 is 25. 

Examples of Prime Numbers

Examples of prime numbers are mentioned below:

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

1  is neither a prime nor a composite number.  

The smallest and the only even prime number is 2.

Every other prime number other than 2 is odd and is called an odd prime. 

History of Prime Numbers 

Euclid, a great Greek mathematician, first discovered prime numbers. 

In 200 B.C., he created an algorithm to calculate prime numbers. This algorithm was called the Sieve Of Eratosthenes. 

After this, there was a long gap in the history of prime numbers, known as the Dark Ages. Fermat made the subsequent discovery at the beginning of the 17th century. 

Prime numbers were studied for about 1000 years. 

Euclid published a book about the prime numbers named ‘Elements’. In this, he stated that there are infinite prime numbers. Euclid also proved the fundamental theorem of arithmetic. According to the theory, every integer may be uniquely expressed as a product of prime numbers.

Properties of Prime Numbers

The properties of prime numbers are mentioned below:

• They are divisible by 1 and the number themselves
• They are positive numbers
• They are greater than 1
• 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, 22 & 35
• The number of prime numbers becomes less as we move up the number line. For example, there are 8 prime numbers between 1 & 20, whereas there are only 3 prime numbers between 980 & 1000 
• Suppose a and b are two prime numbers, then there are two positive numbers x & y so that ax – by = +1 or -1

For example, x = 5, y = 2, ax – by = 1. 

• If a and b are two primes and each divides another number, c, then c is also divisible by the product of a and b. Let a=3 and b=7 and c=42, then 42 is also divisible by the product of 3 * 7 = 21 
• If a and b are prime to one another, then a & b are also prime to each other

Let a = 4 and b = 9 and c = 2, then 42 & 92 are also prime to each other.

Conclusion

This article explores prime numbers. Prime numbers are natural or whole numbers, divisible only by 1 and the number itself. They are positive integers. We also mentioned some examples of prime numbers. Examples of prime numbers are 11, 13, 15, 7, 11, 13 etc. We also discussed the properties of prime numbers and the history of prime numbers. This is a very crucial topic for maths students and students appearing in board exams. This topic is also helpful for students or aspirants appearing in SSC exams.