“The end is the same no matter which way you take
There can be only one answer, no mistake!
That’s the beauty of a mathematical equation!
In every way all you can see is perfection!”
By now you must have understood at least from my blogs and sketches that no one is perfect! All are mortals are imperfect and imperfection is the key!
But (perfect prediction that a but was coming!); there are some number which are called perfect numbers!
But (this but was unexpected!); there exist a problem in mathematics among many other problems which has not been solved for the past 2000 years or so!
read on!
When we were young (er!); and we used to study in the night for examinations, the one trick I used to do when I used to feel sleepy was to start working on some mathematical problems!
I used to love mathematics (still do!) and solving them used to really make me awake and active!
Mathematics was also one of the few subjects where there was only one right answer and many ways to get it! It was like religion! So many ways to get the same destination!
Another cool thing was if you have done the mathematics examination well then that was one of the very few subjects where you can score full marks which in KV was a cool thing to do!
Many times even if you do not get the final solution, even if you write the steps properly you can still score marks!
So late night when you feel sleepy and then solve a couple of mathematical problems even if you know them already; the sight of the final correct answer used to give me a amazing pleasure and sense of achievement!
It was one of the few work or job in the world which we could confidently and actually complete! A feeling of closure given by an amazing subject!
Though I have changed multiple schools, in all of them my favourite subjects and teachers have most of the times been my mathematics teacher and I was lucky to have been their favourite student once in a while!
The only issue was when you solve a problem and know that you have solved it wrong almost immediately! The feeling that is real! There is only one right answer to any mathematics problem!
Sometimes you would have done the problems properly in the rough and not noted it same to same in the final draft! Every symbol and every number has a perfect place and there is only one way to represent the answer!
Mathematics was perfect in every sense!
Now did you know that there are some numbers in Mathematics which are called perfect numbers!?
A number is perfect if it is a positive integer, n, whose divisors add up to exactly twice the number itself, 2n. Or if you do not count the number itself then all its divisors except the number itself add up to the number!
The first and simplest example is 6, since its divisors — 1, 2, 3 and 6 — add up to 12, or 2 times 6. Or if you only include the divisor and not the number; 1, 2 and 3 when added give 6!
You would think that these numbers are very common! Well they are not! In fact in the first ten thousand numbers there are only 4 perfect numbers! Two of them are less than 100!
Then comes 28, whose divisors of 1, 2, 4, 7, 14 and 28 add up to 56. Or if you use only the divisors then 1, 2, 4, 7, 14 add up to 28!
If you are free you can try to find out more! But let me tell you that the next
examples are 496 and 8,128!
There are apparently several formulas to find the perfect number and Euclid devised a formula for generating even perfect numbers long back!
Before that you must know about Mersenne prime!
Mersenne prime is a prime number that is one less than a power of two.
That is, it is a prime number of the form Mn = 2n − 1 for some integer n.
They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.
Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31! You can see that these are not the perfect numbers! But there is a theorem which relates them!
The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form 2p−1(2p − 1), where 2p − 1 is a prime number.
So if p and 2p − 1 are prime numbers (whose only divisors are 1 and themselves), then 2p−1(2p − 1) is a perfect number.
Do not get confused (like me!) now see this example;
The text here does not allow p to be on the upper part of 2!
Please read the formula as 2 (raised to the power of p-1) multiplied by (2 raised to the power of p and the product is subtracted by 1!)
If p is 2, the formula gives you 21 × (22 − 1) or 6, and if p is 3, you get 22 × (23 − 1) or 28 — the first two perfect numbers.
Euler proved 2,000 years later that this formula actually generates every even perfect number, though it is still unknown whether the set of even perfect numbers is finite or infinite!
A Japanese publishing house Nanairosha’s offered a strange book that had become surprisingly popular!
In just four days, some 1,500 copies of the book were sold !
The book, “The Biggest Prime Number in 2017”, contains just one thing — a newly discovered prime number that has broken the record for the largest ever found, coming in at a whopping 23,249,425 digits that covers the 791 pages in the book! In fine print by the way!
As far as the largest known prime number is concerned; as of now the largest known prime number is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search!
The Great Internet Mersenne Prime Search has also helped in finding more and more prime and perfect numbers!
But! (The final but for now!); the issue or the problem which is not solved for ages now is the question whether there is a number which is perfect which is an odd number! So are there any odd perfect numbers?
It is unknown whether any odd perfect numbers exist!
Let us hope that the 2000 year old problem can be solved soon!
The world of mathematics is divided into two camps; one who believe it exists or can be solved and can be found while the other does not!
Now that does some odd! It’s not Odd though but perfect fact that the birthday celebrity Darshan Jariwala is a great actor! Just his expressions make me laugh!
Now be a perfect person and try to sleep on time!
Shubh ratri!
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