CBSE Class 10 Maths: What we should really know about prime numbers!
Most kids learn about prime numbers when they are in grade 5. However, when kids and adults are quizzed about why we learn about them, it is generally followed by pin drop silence. So next time when you pick up your phone to order food through internet or do an online transaction be aware that you are using some properties of prime numbers!
Let’s go to the basics. A prime number is a number that is divisible by itself and 1. Some examples being 2, 3, 5, 7, 9, 11, 13.… The great mathematician Euler proved centuries ago that there are an infinite number of them. However, their real importance is given by what is known as the Fundamental Theorem of Arithmetic. It states that every number can be uniquely expressed as a product of prime numbers. Let’s take the example of 364 = 2 × 2 × 7 × 13. This is the only way that 364 can be obtained by prime numbers!
Prime Numbers in daily life
In modern times, prime numbers play a role in our lives every day, due to the following fact. Suppose you have two 200-digit prime numbers. Given a computer, it can multiply them together in a fraction of a second, and immediately give the resulting roughly 400-digit answer.
Suppose you now take this 400-digit answer and give it to another computer, and ask it to find the original two 200-digit prime numbers.
The best-known algorithms, working on all the world’s computers, would still take billions of years to find those two prime numbers!
Cryptography and Prime numbers
This property of prime numbers is used all the time in the field of Cryptography which deals with secure online transactions. So next time when you are using net banking or doing an online purchase or simply sending an email, the integrity and safety of your communication is maintained largely due to this property of prime numbers!
In fact, if someone somewhere discovers an algorithm of finding the original prime numbers from its product, internet security will largely collapse! This is the reason why the field of Number theory where we study prime numbers is the most funded research area in all of mathematics.
Prime Numbers and evolution
Prime numbers are the fundamental objects in the world of numbers, but it might come as surprise that prime numbers also arise in nature and evolution.
Cicadas an insect which lives underground emerge only once every N year, where N tends to be a prime number like 13 or 17. Why? If the Cicadas came out say every 8 year then all the predators who come out every two year or four year will have a chance of taking them to extinction. So, through evolution Cicadas have figured out that their best chance of survival is to come out in years 13 or 17 which are prime numbers!
In conclusion, when one learns about prime numbers or any other topic, it is important to ask the question why we are learning it and what are the applications? The search for that answer might just lead you in a glorious quest to the next big discovery!
(Pankaj Jha is the founder of makeageek.com. Having been educated in three continents- US, UK and India, he works closely with schools, teachers and students to help them achieve their very best.)