The students of Maths have to deal with the Prime numbers in every stage of their study from class 1 to 12 in some of the other forms. For this, they need to have strong knowledge of the Prime numbers. This can be strengthened from the very beginning. Here, Vedantu has provided the students with a complete guide on Prime numbers from 1 to 1000 to help them improve their knowledge.
For the students, Prime numbers are one of the most common and base-level topics for the study of mathematics in the branch known as number theory. Moreover, the study of numbers is basically to study the properties of the prime numbers. Most Mathematicians have, over the decades, found out some facts about prime numbers. One of Euclid’s most famous proofs shows us that there are infinitely many prime numbers.
The basic idea behind the proof is that if we had only finitely many primes, and we had a list of all of those prime numbers, then we could multiply them all together and add 1, thus, creating a new number that is not divisible by any of the prime numbers on the list. That number would either be a prime number not on the list or would have a prime divisor, but not on our list. Either way, the idea is contradicted that there could be a finite list of primes, and so there have to be infinitely many primes.
What are Prime Numbers?
Every prime number has exactly 2 factors. The numbers that have factors 1 and number itself are known as prime numbers. The prime number is known to be the simplest of a number. Let us see a few examples of prime numbers and the list of prime numbers from 1 to 1000.
For example, let us take the number 11. It can be written as 11 × 1 and 1 × 11. There is no other way of writing the number 11. So the factors of number 11 are 1 and 11. So, we can say that 11 is a prime number. Similarly, we can say for the numbers 2, 3, 5, 7, 13, 17, … etc can only be written in two forms with a single factor as 1, hence are the prime numbers.
Each prime number is only divisible by the number 1 and itself. This means that number 1 can never be a prime number. So any prime number should have only two factors and the number should be greater than 1.
History of Prime Numbers
The prime number was discovered by Eratosthenes (275-194 B.C.). Eratosthenes took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers.
Students can practice this method, by writing the positive integers from the numbers 1 to 1000 and circling the prime numbers, and putting a cross mark on all the composite numbers.
Applications of Prime Numbers
Prime numbers are useful in a number of ways and some of the following are the applications of Prime Numbers in real life for students and professionals:
For the knowledge of the students, it is highlighted that most of the modern computer cryptography works nowadays by using the prime factors of large numbers.
The Prime numbers are of utmost importance to the number theorists as they are the building blocks for the whole numbers.
Prime numbers are important to the world as their odd mathematical properties make them perfect for people’s current uses.
The prime numbers are useful for the students while making calculations in regular maths problems like divisions, higher-level concept solving, and other important topics covered in the subject.
Properties of Prime Numbers
Some of the properties of prime numbers are:
Every number that is greater than 1 can be divided by at least one prime number.
Every even positive integer greater than the number 2 can be expressed as the sum of two primes.
Except for number 2, all other prime numbers are odd. In other words, we can say that two is the only even prime number.
Two prime numbers are coprime to each other.
Difference Between Prime Numbers and Composite Numbers
Here’s the list of prime numbers from 1 to 1000. There are a total of 168 prime numbers in the list of prime numbers from 1 to 1000.
List of Prime Numbers Prime Numbers From 1 to 1000
Composite numbers are numbers that have at least one factor other than the number itself and 1. Let’s look at a few examples.
Let us take a number say 4. It can be written as 4 × 1, 1 × 4, and 2 × 2 So the factors of 4 are 1, 2, and 4. Therefore, we can say that 4 is a composite number as it has more than 2 factors.
Now, let us take a number, say 6, that can be written as 6 × 1, 1 × 6, 2 × 3, and 3 × 2. So, the factors of number 6 are 1, 2, 3, and 6. Therefore, we can say that number 6 is composite.
Let us take a number say 8. The number 8 can be written as 8 × 1, 1 × 8, 2 × 4, and 4 × 2. So the factors of 8 are 1, 2, 4, as well as 8. Therefore, we can say that the number 8 is a composite number.