What is a Prime Number? Definition, Examples, List, How to Find it?

As a Mathematical student, you will have to deal with the prime numbers at every stage of your study, from class 1 to 12 in some other forms of mathematics. It is essential that they have a good understanding of the Prime numbers in order to achieve this. It is possible to strengthen this from the very beginning. The purpose of this guide is to provide the students with a complete guide on Prime numbers from 1 to 100 so that they can improve their knowledge of these numbers.

When it comes to prime numbers, they are almost always odd, other than 2. If they were even, they would’ve been divisible by 2, which is not considered a prime number characteristic. 

Proof of Euclid about Prime Number

There are infinitely many prime numbers in the universe, which is one of Euclid’s most famous proofs. Basically, the proof suggests that if we had only a finite number of primes and a list of them, we could multiply them together and add 1, thus, creating a new number incapable of being divided by any of the prime numbers on that list.

what prime number definition examples list how find
what prime number definition examples list how find

I can only think of two possibilities for that number: either it is a prime number that is not on our list, or it has a prime divisor that is not on our list. Either way, the idea is contradicted by the fact that there is no finite number of prime numbers, so the number of prime numbers must be infinite.

Define Prime Number

Prime numbers are natural numbers with only two factors, namely one and the number itself. In mathematics, a factor is a number that divides a given number completely. A prime number is one that cannot be divided into equal groups. Only when a number can be factorized as a product of two numbers can it be divided into groups with equal numbers of items.

For every prime number, there are exactly two factors that make up the number.It is called a prime number if it has factors 1 and itself. One of the simplest numbers is the prime number. Listed below are a few examples of prime numbers and a list of prime numbers from 1 to 100.

Example of Prime Numbers

Let’s take the number 11 as an example. There are two ways to write it: 11 × 1 and 1 × 11. The number 11 cannot be written in any other way. As a result, number 11 has two factors: 1 and 11. As a result, 11 is a prime number. Furthermore, the numbers 2, 3, 5, 7, 13, 17, and so on can only be written in two ways, so they are prime numbers.

There are only two divisible prime numbers: 1 and itself. Therefore, number 1 cannot be a prime number. Prime numbers should have only two factors, and they need to be greater than 1.

History of Prime Numbers

In the first century B.C., Eratosthenes (275-194 B.C.) discovered the prime number. Taking the example of a sieve, Eratosthenes used the example of a sieve in order to filter out the prime numbers from a list of natural numbers and drain out the composite numbers from the list.

There is a method of practicing this, in which students write the positive integers from 1 to 1000, circle the prime numbers, and cross all the composite numbers that they can remember later on.

What is the Best Way to Find Prime Numbers Up to 100?

An ancient mathematical technique known as the sieve of Eratosthenes can be used to find prime numbers. A prime number can be found up to a given limit using this ancient method. Eratosthenes’ method can be used to find all prime numbers up to 100. Since there are more than one prime numbers, the number 1 should be left out.

  • The first step is to create a list of integers between 2 and 100:  2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100.
  • Adding 2 or skip counting by 2s will clear out the 2nd number in the list after 2 as it is also a prime number. Two plus two equals four, four plus two equals six, and so on. The list will contain all the multiples of 2: 4, 6, 8, 10, 12, 14, & 16, and so on.
  • After number 3, cross out every third number in the list by adding 3 or skip counting by 3. Three plus three equals six, six plus three equals nine, etc. The list includes all multiples of 3, such as 6, 9, 12, 15, 18, 21, 24, etc.
  • In the following list, 5 is the next number after 3, so you should cross out the fifth number by adding 5 or skip counting by 5s. The sums of 5 + 5 are 10, 10 + 5 is 15, and so on up to 100 like these are all multiples of 5.
  • Adding 7 to the list after 5 or skipping by 7s is the next step after crossing out the 7th number in the list after 5. A 7 + 7 is a 14, a 14 + 7 is a 21, and so on. The list will contain all multiples of 7 such as 14, 21, 28, 35, 42, 49, 56, 63, and so on.

Numbers up to 100 on the Prime Number list

Below you will find a list of prime numbers up to 100. The total number of prime numbers is 25 up to 100. Accordingly, the prime numbers 1 to 100 can be written as follows: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Numbers up to 200 on the Prime Number List

The following is a list of prime numbers from 100 to 200: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

There are exactly two factors in a prime number, and it is a positive integer. The factors 1 and p alone are only necessary factors if p is a prime number. It is called a composite number if it does not obey this rule.

Properties of Prime Number

  • There is at least one prime number that can divide any number greater than 1.
  • There are two prime numbers for every even positive integer greater than 2.
  • A prime number that is odd, with the exception of number 2, is a prime number. Hence, the only even prime number is two.
  • A co-prime number is one that is co-prime to another prime number.

Uses of Prime Numbers

For students and professionals, prime numbers can be used in a number of ways, including:

  • As a matter of fact, in order for students to have a better understanding of how most modern computer cryptography works nowadays, it is emphasized that it is most commonly based on prime factors of large numbers.
  • It is of utmost importance to the number theorists that prime numbers are of utmost importance due to the fact that they form the base for all whole numbers.
  • There is no doubt that prime numbers are of immense importance to the world, due to their odd mathematical properties which make them perfect for present-day uses of people.
  • In this way, the students are able to make calculations using prime numbers even when they are doing regular math problems such as division, higher-level concept solving, and other important topics in the subject matter.

Mathematical Problems on Prime Numbers

What makes 28 a non-prime number?

28 is the given number where the factors of 28 are 1, 2, 4, 7, 14 & 28. There are more than two factors in 28. The number 28 does not qualify as a prime number since it has more than two factors.

Choose four prime numbers from the following list: 34, 47, 67, 71, & 73?

There are 47, 67, 71 & 73 four prime numbers & 34 composite numbers, among the given numbers.

23 or 25 is the prime number or not among the two given numbers?

23 and 25 are the given numbers, where 1, 5,  25 are the factors of 25. There are more than two factors involved in number 25. 23 have only two factors: 1 and 23. There are exactly two factors in number 23. Thus, 23 is a prime number since it has only two factors, whereas 25 is not a prime number since it has more than two factors.

Composite Number

A composite number is a number that has at least one factor other than the number itself and 1 which makes it different from a pure number. The following examples will give you a better understanding of composite numbers.  It is possible to divide composite numbers by 1 as well as some other numbers. There are 4 factors, 1, 2, and 4; there are 20 factors, 1, 2, 5, and 20, and so on.

  • We will take the number 4, for instance. The factors of 4 can be written as 4 x 1, 1 x 4, and 2 x 2. Due to its multiple factors, 4 can be considered a composite number.
  • Consider the number 6, which can be written as 6 × 1, 1 × 6, 2 × 3, and 3 × 2. As a result, number 6 has factors 1, 2, 3, and 6. We can therefore say that the number 6 is composite.
  • Take the number 8, for example. There are four ways to write the numbers 8, 8 x 1, 1 x 8, 2 x 4, and 2 x 4. Eight has the factors 1, 2, 4, as well as 8. It is, therefore, possible to say that 8 is a composite number.

It is possible for composite numbers to be odd or even depending on their components. If it contains at least one even number, it will be an even integer. Integers with odd components will be odd if they do not contain any even numbers.

Difference Between Prime Number & Composite Number

The main difference between prime and composite numbers is that prime numbers have one variable and the number itself, whereas composite numbers have many more variables: 1, the number itself, and additional numbers. The prime number, which excludes 2, is an odd number, while the composite number is even. 

Prime numbers are natural numbers higher than one that is not the sum of two lower natural numbers. It can be divided by one and by itself. As a result, it only has two factors. The smallest prime number is 2, and there are more primes than composites. 

In mathematics, a composite number has at least one divisor other than 1 and itself, which implies it, has more than two elements. There are two or even more prime numbers that make up every composite number. The number four is the lowest composite, with many more than primes.

  • Prime numbers are defined as integers that are divisible by 1 as well as themselves, while composite numbers are defined as integers that are divisible by 1 as well as themselves & other numbers.
  • There are only two factors in a prime number, while there are more than two factors in a composite number. 
  • It is 2 which is the smallest prime number, while 4 is the lowest composite number. 
  • Prime numbers are fewer than composite numbers, and composite numbers are more common. 
  • Except for two, all prime numbers are odd, while all composite numbers are even. 

Tips & Tricks of Prime Number

  1. Due to the fact that they can be divided by 2, the remaining even numbers are not prime numbers.
  2. Numbers greater than 5 and ending in 5 cannot be prime numbers since they can be divided by 5.
  3. The prime numbers 0 and 1 do not have exactly two factors so they are not primes.
  4. There are only two factors in prime numbers, one and the number itself.
  5. Numbers that are non-zero whole numbers can be prime numbers. 
  6. Finding prime numbers is done through prime factorization.

Wrapping it Up

Mathematics can be difficult for some people, but grasping the fundamental concepts might help. These fundamental ideas include prime numbers and composite numbers. 

The study of prime numbers is one of the most common and basic topics for students for the study of mathematics in the branch of science known as number theory. In addition, the primary goal of studying numbers is to gain a deeper understanding of the properties of the prime numbers. Mathematicians have, over the years, discovered a few facts about prime numbers that they have been interested in for a long time.

When one component is 1 and the other is the integer alone, there are prime numbers in the natural numbers ranging from 1 to infinity. A prime number is one that cannot be divided by 1 and is itself. Therefore, they have only two divisors as a result of this.

FAQs on Prime Numbers

Are 7 a Prime number or not?

It is a prime number since it does not have any factors that make it a prime number. The only factors of 7 are 1 and itself, which means that it has no other factors. In order to be certain that we are on the right track, let’s verify that none of the numbers greater than 1 and less than 7 divide 7. Two, three, four, five, and six are the numbers that are greater than 1 and less than 7.

Why 1 is neither prime nor composite number?

The number 1 is not a prime number because a prime number should have two divisors: 1 and itself. 
In this case, 1 has only one divisor, which is 1. In this case, 1 has only one divisor, 1 which is not 1. A composite number has a divisor other than 1 and itself, so it is not a composite number.

Why 2 are called even Prime Number?

There are only two whole number factors for the number 2, 1, and itself. Basically, the other even numbers up from two are all divisible by that number in some way. Due to the fact that it is the only even prime, it is also referred to as the oddest prime.

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