The magic of Primes

We all know what a prime number is. It is a number that is divisible only by 1 and itself. But do you know how fascinating these numbers are?
You could call them the building block of all numbers.

Why do I say that?
We all know numbers that are not prime numbers are called composite numbers.  But you may not know that all composite numbers can be built from prime numbers in a unique way by multiplication. In fact, this fact is called the “Fundamental Theorem of Mathematics” – that any number can be written as a factor of two or more primes in a unique way (by unique I mean there is only one way to write it as a factor of primes).

For example, take 96. If you factor it in primes, you will get 96  = 2 * 48 = 2 * 2 * 24 = 2 * 2 * 2 * 12 = 2 * 2 * 2 * 2 * 6 = 2 * 2 * 2 *2 * 2 * 3

So 96 can be represented as 2 * 2 * 2 * 2 * 2 * 3. There is no other way to factorize it using primes.
And this is true for all prime numbers. Isn’t it fascinating?

There are many fascinating things about prime numbers and their role as the building block for all numbers.
But let me tell you about one strange fact – there is no largest prime number. It is just not possible to have something called the “largest prime number”. A Greek Mathematician called Euclid proved it more than 2000 years ago.

There is an active search going on for finding larger and larger prime numbers. The largest one found so far is 243,112,609 - 1. What is that? It is 2 multiplied by itself 43 million, one lakh, twelve thousand, six hundred and nine times, and one subtracted from that number. That number is 12 million digits long.
How big is that? Let me tell you – If you could write 80 numbers in a line, and your notebook page had 40 lines, and your notebook had 50 pages,  it would take you 80 notebooks to write down this number. Of course, the search for still larger prime numbers continues.

1. Posted by Rohit Gautam| 2010-11-17 07:56:25

thanks for the gr8 and fascinating information abt the prime nos.
I HOpe we never get the largest prime no. as there is no largest no.. it is believed to have infinite nos.

2. Posted by Surbhit| 2011-01-26 14:54:32

I studied prime numbers in my class, but never realized the beauty and complexity of these numbers before reading this article.

Great work.

3. Posted by Malinda| 2011-04-19 07:17:49

THX that's a great aneswr!

4. Posted by Spike| 2011-04-19 07:28:57

Kudos to you! I hadn't thoguht of that!

5. Posted by SJS Inamdar| 2011-09-18 00:10:54

Mind blowing...!!!

6. Posted by SJS Inamdar| 2011-09-18 00:11:26

Marvellous...!

7. Posted by Alfarhan Zahedi| 2012-04-12 16:04:44

Really a good article.
thanks for the information.

8. Posted by Deependra| 2012-08-15 10:04:08

THIS IS GOOD ARTICLE.

9. Posted by Ayush| 2013-05-26 16:01:04

Thanks for the edugain for help in my educatin. it is a good article.

10. Posted by aditya| 2014-05-27 18:23:49

thanks. today i got a very interesting fact.
i like it .

11. Posted by CHANDRIMA| 2014-06-05 15:16:11

i like it very much

12. Posted by CHANDRIMA| 2014-06-05 15:21:44

Very fascinating wonderful story.I enjoyed reading it very much.

13. Posted by Ebasco| 2014-06-27 02:37:45

Properly, it is the Fundamental Theorem of ARITHMETIC (not mathematics) and it was proven by Gauss. I'm not sure any school textbook has tackled the concept properly since Dolciani, et al in Modern Introductory Analysis (1967). The extensions of the complexities of prime numbers include the Goldbach Conjecture and the Riemann Conjecture.

14. Posted by Tharkesh| 2014-07-08 21:11:23

WOW !! PRIME NO. FACTS ARE AMAZING.

15. Posted by ankush bhunia| 2014-12-17 09:34:38

that's cool

16. Posted by Bea Binu| 2016-03-06 21:53:30

Thanks! This was a lot of help!! Keep on writing!! : )

17. Posted by Shivaahnee| 2016-12-26 01:11:16

Cool info! Never thought that way

18. Posted by Sejal | 2017-12-19 10:55:34

That's great

19. Posted by Archita Pal| 2018-01-16 14:06:38

There is new largest prime number announced recently, please check bbc news

20. Posted by Khushi | 2018-07-11 10:59:56

Great trivia about the largest prime number :)

21. Posted by Mohit kandra| 2018-07-23 09:24:55

thank you

22. Posted by Mohit kandra| 2018-07-23 09:25:00

thank you

23. Posted by Ani Huang| 2020-04-21 03:37:47

Wow this is such an interesting article. I was scrolling through safari to find some cool maths facts but this is truly amazing. If anyone thinks about this the largest number of prime must have taken