# Ramanujan Number

When you love mathematics you can see magic in numbers. Your face gets lit up when you observe something new about a number. Something similar and very interesting happened with great Indian mathematician

You can see the title of this post is Ramanujan Number. You might have already guessed that he might have a stumbled up on some very interesting number with some peculiar characteristics. If you have guessed that, you are right.  Ramanujan number is 1729.

1729 is also known as the Hardy – Ramanujan number . This number is also called the Taxicab number.

Ramanujan number is so named after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan.

In Hardy’s own words:

“I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number…1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two positive cubes in two different ways.”

The numbers is such that,

1729 = 1^3 + 12^3 = 9^3 + 10^3

Some observations related to Ramanujan Number

1. If negative cubes are allowed, 91 is the smallest possible number with similar quality 91 = 6^3 + (?5)^3 = 4^3 + 3^3
2. Interestingly 91 is also a factor of 1729. (91×19=1729)
3. If taking “positive cubes” would not have been a condition, Ramanujan number could have been ?91, ?189, ?1729, and further negative numbers
4. 1729 is also the third Carmichael number and the first absolute Euler pseudoprime.  (If you want to know more about this numbers I can discuss it in some other post)
5. Masahiko Fujiwara showed that 1729 is one of four positive integers (with the others being 81, 1458, and the trivial case 1) which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:     1 + 7 + 2 + 9 = 19;                       19 x 91 = 1729
6. Till date only 10 Taxicab numbers are known.  Subsequent Taxicab numbers are found using computers.

## 39 thoughts to “Ramanujan Number”

1. devendra says:

nice post, pl give me maths posts because i ma fan of maths

2. devendra says:

very very nice post

3. Sejal says:

Amazing mathematician Srinivas Ramanujan.. .. Hats off to him

4. arun says:

exalaint indin

5. Ramanujam sir magic No's so interesting , I was studied with in one hour I was created my. own magic square. says:

Ramanujan sir magic No’s were so interesting & I want to further research the same.

6. rajeev ranjan shrivastava says:

I knom about taxicab no. But I don’t know about so much properties of this no this is very wonderful to think that a simple no.has so much property.but it can do only by great mathematician Srinivasan Ramanujam.please tell me some other wonderful no.of ramanujam at my I’d(rajeevranjanshrivastava3@gmail.com)

7. Sruthi says:

1+7+2+9+=19
19*91=1729

8. shravan kumar says:

Good morning sir it is really an excellent collection of an indian mathematician when i am reading the article i felt very proud being an indian sir please keep sending the updations related to our incredible indians

9. sooooo good
U can also add his characteristics.

10. anoosha shetty says:

very nice.but i want some interesting topics plz send to my e-mail……..thank u

HELLO! FREINDS
I WANT TO KNOW THE MAXIMUM RAMANUJAN NUMBERS
SENT IT ON MY ID!

13. Amrutha says:

You can add a small history of ramanujam in the beginning.
But anyway it’s good

14. i want to know relation between ramanujam and pythagorean number

15. goms says:

i need various explanation of ramanujam number.. please kindly send to my mail id

1. rh says:

email..

16. ABHI says:

CAN YOU GIVE SOME DETAILED INFORMATION ABOUT IT I HAVE TO WRITE AN ARTICLE ON THIS TOPIC (ramanujan’s number)

1. rh says:

email..

17. joju says:

i need 10 hardy ramanujan numbers and their significants

18. saanchi says:

lovely

19. futhaima says:

20. what are the new findings about ramanujan number

21. vimal says:

i want to know about all taxicab number. and please tell me the reason why ramanujan number famouse? (in detail)

22. My cousin recommended this blog and she was totally right keep up the fantastic work!

23. I know many more numbers which can be expressed as a sum of two cubes in two different ways.

24. forex robot says:

My cousin recommended this blog and she was totally right keep up the fantastic work!

25. suyash says:

very good
do any combination, u will find the same nos. again & again