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A lot of people ask me about my favourite colour or my favourite dish, but I rarely get asked about my favourite things in math or about my favourite speech in history. How unfortunate, I tell you! Well, I have taken it upon myself to answer some of those unasked questions, let’s begin.
If someone asked what the most interesting thing in math was, I would say “Prime numbers” without any doubt.
To begin with, prime numbers are just as interesting to a mathematician as an atom is to a physicist. Prime numbers answer one of the most important questions of all time, “What are numbers made up of?”, well, the answer is obvious at this point, it’s prime numbers. Yes, those random natural numbers which are greater than 1 and have only two divisors namely 1 and the number itself. The fundamental theorem of arithmetic, states that every integer (larger than 1) can be written as a product of one or more primes. Hence making them infinitesimally small and big (and everything in between) building blocks of nature.
The second interesting thing is that they are the secret recipe for perfect numbers. A Perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of all its positive divisors excluding the number itself. To give you an example: consider 6, whose divisors are 1, 2 and 3, when you add them you get 6. To find these perfect numbers, you can try adding up all the divisors of every number or you can just use a simple key – yours truly “prime numbers”. Yes, if you take the equation- (2P-1) × (2p-1) where ‘P’ is a prime number and just keep changing the prime number, every prime will give you a perfect number. From what we know, there are infinite prime numbers, so that means an infinite number of perfect numbers. Here are examples of some more perfect numbers for your muse:
p = 2: 21(22 − 1) = 1+2+3 = 6
p = 3: 22(23 − 1) = 1+2+4+7+14 = 28
p = 5: 24(25 − 1) = 1+2+4+8+16+31+62+124+248 = 496
p = 7: 26(27 − 1) = 1+2+4+8+16+32+64+127+254+508+1016+2032+4064 = 8128
Mathematics is a fun world, where profits are added and losses are subtracted, where lines are parallel and angles are similar, where algebra is full of mystery and geometry is full of history, where decimals have a point and differentiating is good, where a pie is irrational and limits are pushed at the sine of trouble. Math is the foundation on which this world is built upon, like a layer of fabric which lies underneath every physical law, in turn it clothes this universe and binds it. It covers (Pun intended) everything from a black hole to the working of a stock market, it runs every engine and every computer. And this fabric is woven with threads of Prime numbers, the building blocks of mathematics!
-Rishyashringa J. S., Project Leader, BrainSTARS