Prime Numbers  – Definition with Examples

In mathematics, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is a prime number because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83 and 89. The next prime is 97.

What are prime numbers?

A prime number is any natural number greater than 1 that cannot be divided evenly by any other number except for itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Prime numbers have many uses in mathematics and elsewhere. They are used to create and solve problems in a wide variety of fields, including cryptography and physics. In fact, the distribution of prime numbers in the universe is a deep mystery that has yet to be fully understood by mathematicians.

Understanding prime numbers through illustrations

In arithmetic and number theory, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The Fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering of the factors.

There are infinitely many prime numbers. As of December 2020, the largest known prime number has 24,862,048 decimal digits. Prime numbers have been studied throughout history. Greek mathematicians first studied them around 600 BC; Euclid proved there are infinitely many in 300 BC. Many questions regarding prime numbers remain open, such as Goldbach’s conjecture: that every even integer greater than 2 can be expressed as the sum of two primes. Ancient cultures did not generally consider 1 to be a natural number at all because many things multiplied by one remain unchanged (thus having no inherent value), but modern mathematicians since Gauss have recognized 1 as naturally belonging to the set of positive integers due to its role as the identity element in multiplication.

Prime Numbers List

Prime numbers are whole numbers that have only two factors – 1 and themselves. This means that they can’t be divided by any other number except for 1 and themselves. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

There are an infinite number of prime numbers. You can keep going forever! Some mathematicians think that the next prime number after 2 will be discovered in the year 2038.

The study of prime numbers is called number theory. Number theorists look for patterns in prime numbers and try to find new ones. They also try to prove whether certain conjectures (unproven ideas) about primes are true or not.

Properties of Prime Numbers

Prime numbers are whole numbers that cannot be made by multiplying other whole numbers. That is, they cannot be evenly divided by any number except for 1 and themselves. The first prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

There are several interesting properties of prime numbers that make them unique among all the other numbers. For example:

-The sum of any two primes is also a prime.
-There are an infinite number of primes.
-No two primes are consecutive (i.e., there is always a gap of at least 2 between any two primes).
-The product of any two primes is also a prime.
-Every composite number has at least one prime factor (i.e., can be evenly divided by a prime number).

How to find prime numbers

Prime numbers are those numbers which are divisible by 1 and itself only. In other words, prime numbers cannot be divided by any other number than 1 or itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

Now let us see how to find prime numbers between 1 and 100. The easiest way is to use a Sieve of Eratosthenes. This is an ancient method which was actually used by the Greek mathematician Eratosthenes to find prime numbers.

First we make a list of all the numbers from 1 to 100. Then we start with the number 2 and strike off all the multiples of 2 from the list (i.e. 4, 6, 8, 10, 12, 14, 16,…). The next number in the list is 3 and we strike off all the multiples of 3 (i.e. 6, 9, 12, 15,…). We continue in this way until we reach the number 100. The remaining numbers in the list are all the prime numbers between 1 and 100.

Another way of finding prime numbers is using a Prime Factorization method. This method is based on the fact that every composite number can be written as a product of prime factors. For example:

24 can be written as 24 = 2 x 2 x 2 x 3
30 can be written as 30 = 2 x 3 x 5
42 can

Types of Prime Numbers

There are two types of prime numbers: natural prime numbers and twin prime numbers. Natural prime numbers are any whole number that is greater than 1 and cannot be divided evenly by any other number except for itself and 1. The first 10 natural prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Twin prime numbers are a pair of prime numbers that differ by 2. For example, 3 and 5 are twin primes because they differ by 2 (they are both odd), but 2 and 4 are not because they do not differ by 2. The first 10 twin prime numbers are (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139).

Facts about Prime Numbers

Prime numbers are those positive integers which have only two factors – 1 and the number itself. In other words, a prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. For example, 2, 3, 5, 7 and 11 are prime numbers.

The first prime number is 2. The smallest prime number is 2. There are an infinite number of prime numbers.

The last digit of a prime number can be: 1, 3, 7 or 9 but never 5 or 0. This is because if the last digit were 5 or 0, the number would be divisible by 5 (or 10).

Examples of Prime Numbers

As we know, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Now, let’s look at some examples of prime numbers:

2 is the smallest prime number.

3 is the next smallest prime number.

5 is also a prime number.

7 is another prime number.

11 is yet another example of a prime number.

Frequently Asked Questions?

1. What is a prime number?

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Prime numbers also cannot be created by multiplying other whole numbers together. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

2. How many prime numbers are there?

Mathematicians have not been able to find a definitive answer to this question yet, but it is believed that there are an infinite number of prime numbers.