Prime Number

Prime Number

Sep 06, 2022, 16:45 IST

All natural numbers that have one and itself only as their factors are called prime numbers i.e. prime numbers are exactly divisible by 1 and themselves. For More Mathematics Doubts visit main page of Physcis Wallah.

e.g. 2,3,5,7,11,13,17,19,23....etc.

If P is the set of prime number then P = {2,3,5,7....}.

List of Prime numbers

The list of all prime numbers from 1 to 100 is given below:

Properties of Prime Numbers

• Every number greater than 1 is divisible by at least 1 prime number.
• Every even positive integer which is greater than 2 can be expressed as the sum of two prime numbers.
• Except for 2, all other prime numbers are odd. As, we can say that 2 is the only even prime number.
• Two prime numbers are always coprime.
• Every composite number can be divided into prime factors; individually, they are all unique.

Methods to find Prime Numbers

Method-1

We all know that 2 is the only even prime number. And the only two consecutive natural numbers that are prime are 2 and 3. Apart from them, every prime number can be written as 6n + 1 or 6n – 1 (except for multiples of primes, i.e., 2, 3, 5, 7, 11), where n is a natural number.

For example: 6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13

6(3) – 1 = 17

6(3) + 1 = 19

Method-2

The formula below can be used to know the prime numbers greater than 40.

n ² + n + 41, where n = 0, 1, 2, ….., 39

For example:

(0) ² + 0 + 0 = 41

(1) ² + 1 + 41 = 43

(2) ² + 2 + 41 = 47

List of Odd Prime Numbers

A prime number chart is a chart that displays a list of prime numbers in standard order. It is important to know that all prime numbers are odd numbers except for the number 2, which is the only even number. Therefore, 2 is the only even prime number. This means that the list of odd numbers can start from 3 and continue since the remaining prime numbers are odd. For eg, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and so on are odd prime numbers.

History of Prime Numbers

A Prime number was discovered by Eratosthenes (275-194 BC, Greece). He took the example of a sieve to separate the prime numbers from the list of natural numbers and exhaust the composite numbers. Students can practice this method by writing down the positive integers from 1 to 100, circling the primes, and crossing the composites. This kind of all activity refers to the Sieve of Eratosthenes.

Solved Examples

Q1. Is 23 a prime number?

Ans. Yes, it is a prime number. The factor of 23 are 1 and 23

Lets, write the given number in the form of 6n-1

6 (4) - 1 = 23.

Q2. Is 19 a Prime number?

Ans. Yes, it is a prime number. The factor of 19 are 1 and 19

Lets, write the given number in the form of 6n + 1

6 (3) + 1 = 19.

Q3. Why 20 is not a prime number?

Ans. 1, 2, 4, 5, 10, and 20 are the factor of 20. Therefore, 20 has more than two factors. Since the factors of 20 is more than two numbers, it is NOT a prime number (20 is a composite number).

Frequently Asked Question (FAQs)

Q1. Is 0 a prime number?

Ans. No, zero is not a prime number.

Q2. What is the next prime number after 7?

Ans. The next prime number after 7 is 11,13,17,19,23,29 and so on.

Q3. Can negative numbers be prime?

Ans. No, Negative integers cannot be prime by the standard definition of prime for integers. By this definition, primes are integers greater than one with no positive divisors besides one and itself. Negative numbers are excluded.

Q4. How do you know if a number is prime or not?

Ans. To know whether a number is a prime number, try dividing it by two and then see if you can get a whole number. It can't be a prime number if you get a whole number. If you don't get a whole number, try dividing it by prime numbers, i.e., 3, 5, 7, 11, and soon.