Prime Numbers

Numbers are very intriguing and there are so many ways to decipher them. Let us start with examples to understand the concept of prime numbers.

Let us take the numbers 5 and 7. Assuming you have 5 marbles, in how many ways can you arrange them in equal groups?

There are only 2 ways

What if you had 7 marbles. In how many ways can you arrange them in equal groups?

Now we have 6 marbles and we have to arrange them in equal groups. How many do we get?

Looking at the above examples, we find there are some numbers which are not divisible by any other number other than one and itself without leaving a remainder. These numbers are called Prime Numbers

What is a prime number?

By definition, prime numbers are those numbers that have only two factors, one and itself.

A prime number is a whole number that is greater than one. All prime numbers are odd numbers, apart from the number two.

Why are they called Prime Numbers?

Prime means first. That is, prime numbers come first. Simply put, they are the first numbers from which other numbers emerge through multiplication.

History of Prime Numbers

Greek mathematician Euclid first mentioned prime numbers in his work ‘Elements’. He mentioned ‘Protos’ which translates into a word that means prime numbers. It was another Greek mathematician Eratosthenes who invented the “Sieve of Eratosthenes” which helps in filtering out prime numbers from natural and composite numbers. It’s an algorithm that calculates prime numbers.

However, it was not until the 17th century that mathematicians like Fermat, Euler, and Gauss began to examine the structure within prime numbers.

Sieve of Eratosthenes method

Let us use the method given by Greek Mathematician, Eratosthenes, to identify prime numbers between 1 and 100.

 

• First, we list all the numbers from 1 to 100. The numbers are arranged in a 10 x 10 square

 

 

• Let us shade out the number 1. Why are we excluding the number 1?
• Now go to the next number, which is 2 and circle it. Start by identifying all multiples of 2 and cross them out. For example, 4,6, 8,10 up to 100.

 

 

• Now we go to the next available number, which is 3. Circle it out and start identifying the multiples of 3 and cross them. For example, 9,15, 21, up to 100.

 

 

• We now move on to the next number, which is 5 and circle it. We identify all multiples of 5 and cross them.

 

 

• The next number is 7. Like before, we circle it and cross all the multiples of 7

 

 

• The next number is 11. Like before, we circle it and cross all the multiples of 11.

 

Now, what happens when you go the next numbers? All the numbers now do not have any other multiple. So, we can just circle each of them as we go forward on the number grid.

Look at the square now. We have no more numbers to cross and circle.

All the numbers that are circled (2, 3, 5, 7, 11, 13 etc..) are prime numbers. So, we have sieved or filtered the prime numbers from the number grid. This method is called the “Sieve of Eratosthenes”

Prime numbers chart 1 to 100

A prime number chart systematically represents all prime numbers from 1 to 100. All prime numbers are odd numbers, with two being the only even prime number. So, the chart of prime numbers can start from number three onwards and include all odd numbers. Here are some examples of prime numbers 3, 5, 7, 11……….31, 37 so on and so forth. Two is the smallest prime number and also the only even prime number. Since numbers are infinite, the largest prime number cannot be identified.

Co-Prime Numbers and Prime numbers

Two numbers have only one common factor between them, namely, the number one is said to be a co-prime number. However, it is not necessary that these numbers need to be prime numbers. For example, 9 and 10 can be considered co-prime numbers, since the common factor between them is one.

Prime numbers on the other hand have two common factors, 1 and itself.

List of Prime numbers from 1 to 100

Number Range	Prime Numbers List
Between 1 and 10	2, 3, 5, 7
Between 11 and 20	11, 13, 17, 19
Between 21 and 30	23, 29
Between 31 and 40	31, 37
Between 41 and 50	41, 43, 47
Between 51 and 100	53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Interesting facts about Prime numbers

• Carl Sagan, in his 1985 book “Contact”, claimed that extra-terrestrial beings try to communicate with us humans using prime numbers as signals.

• Encryption methods used to protect critical information from cyber-crimes use prime numbers as a coding system.

• Zero and one are not considered to be prime numbers, as they are divisible only by themselves.

• Prime numbers 7 and 13 have been associated with superstitious beliefs. The number 7 is considered lucky, while the number 13 is considered to be unlucky in many cultures across the world.

• Prime numbers are infinite. This was discovered by the Greek mathematician Eratosthenes. He established the fact that as they go on infinitely and their occurrence, gets less than the digits increase.

• Interestingly, prime numbers can be seen in nature as well. The arrangement of a bee hive, the scales present in pineapples, or even how the petals of a rose are arranged, indicate the existence of prime numbers.

• Researchers have shown the Cicada insects use gaps of 7, 13, or 17 years to come out of their burrows and lay eggs.

From the beginning of human history, these numbers have aroused curiosity. On the surface, it may seem that they occur randomly; however, there is a pattern to them that has not yet clearly been deciphered. From its presence in nature to its use in modern encryption technology, prime numbers play a key role. By learning about them, we can learn about various technological advancements and intriguing scientific theories.

Is 1 a prime number and Why?

The number 1 isn’t a prime number since its only divisible factor is 1 itself. However, a prime a number should have two positive factors.

Which is the smallest prime number?

The number 2 is the smallest prime number. As mention ed earlier 1 cannot be considered the prime number since it has only 1 divisible factor. The next number is 2, and it is also a prime number since it has two factor the number 1 and 2 itself. Therefore 2 is the smallest prime number.

How many prime numbers exist between 1 and 100?

As shown in the list of prime numbers above, there are 25 prime numbers between 1 and 100. They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Know more about other concepts of Number Systems on Decimal Numbers, Fractions, Natural Numbers, Unit Conversions and Whole Numbers.