# Is 4104 a Ramanujan number?

1. Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed as sum of two cubes in two different ways.

## What is special about number 4104?

It is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729, is called the "Ramanujan–Hardy number". 4104 is the sum of 4096 + 8 (that is, 163 + 23), and also the sum of 3375 + 729 (that is, 153 + 93).

## What are some Ramanujan numbers?

{2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737, ...}

## How do you know if a number is a Ramanujan number?

Step 2: Sum up the individual digits. Step 3: Find the reverse of the sum. Step 4: Calculate the product of the original number and reversed number. If the product is the same as the original number (that we have entered), the number is a Ramanujan number, else not.

## What are the 3 Hardy-Ramanujan numbers?

{1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, ...}

## What are the 5 Hardy-Ramanujan Number?

"1729: Taxi Cab Number or Hardy-Ramanujan Number".

## What is Ramanujan prime number?

-Ramanujan primes are 11, 29, 59, 67, 101, 149, 157, 163, 191, 227, 269, 271, 307, 379, 383, 419, 431, 433, 443, 457, 563, 593, 601, 641, 643, 673, 701, 709, 733, 827, 829, 907, 937, 947, 971, 1019.

## What is the hardest Ramanujan number?

Ramanujan said that it was not. 1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

## Is 1729 the only Ramanujan number?

It's the smallest number expressible as the sum of two cubes in two different ways." Because of this incident, 1729 is now known as the Ramanujan-Hardy number. To date, only six taxi-cab numbers have been discovered that share the properties of 1729.

## What is the smallest Hardy Ramanujan number?

So, as per the definition of Hardy Ramanujan's number, we get that number. 1729 is the smallest integer which can be represented in the form of two cubes in two ways.

## What is 1 2 3 n Ramanujan?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

## What is Ramanujan formula?

In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent.

## What is the rarest number?

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).

## Which is the most mysterious number?

Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.

## Why is the number 2147483647 special?

The number 2,147,483,647 remained the largest known prime until 1867. In computing, this number is the largest value that a signed 32-bit integer field can hold.

## What is Ramanujan IQ?

Srinivasa Ramanujan: IQ 185

Born in India in 1887, Srinivasa Ramanujan is one of the most influential mathematicians in the world. He made significant contributions to the analytical theory of numbers, as well as elliptic functions, continued fractions, and infinite series. He had an estimated IQ of 185.

## What is Ramanujan's magic square?

Ramanujan magic square is a special kind of magic square that was invented by the Indian mathematician Srinivasa Ramanujan. It is a 3×3 grid in which each of the nine cells contains a number from 1 to 9, and each row, column, and diagonal have the same sum.

## What did Ramanujan invent?

Circle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring's conjecture and other additional questions.

## Was Ramanujan better than Euler?

But Ramanujan had a weak constitution that eventually killed him at the age of 32, while Euler had enough energy to reinvent several disciplines, have 13 children, and still perform huge mental calculations when he was blind and nearly dead. So they both sissy-slap each other under Ramanujan passes out.

## Is 1729 a perfect cube?

Is 1729 a Perfect Cube? The number 1729 on prime factorization gives 7 × 13 × 19. Here, the prime factor 7 is not in the power of 3. Therefore the cube root of 1729 is irrational, hence 1729 is not a perfect cube.

## How many theorems Ramanujan have?

In 1913 he wrote to Hardy at Cambridge. Hardy would've ignored the letter, but he took a moment to glance at 120 theorems Ramanujan had included. It was the oddest pastiche. Here were familiar results, reinvented.

## What is the last theory of Ramanujan?

In mathematics, the Hardy–Ramanujan theorem, proved by G. H. Hardy and Srinivasa Ramanujan (1917), states that the normal order of the number ω(n) of distinct prime factors of a number n is log(log(n)). Roughly speaking, this means that most numbers have about this number of distinct prime factors.

## Why is Ramanujan number special?

THE MYSTERY OF RAMANUJAN NUMBER

Ramanujan explained that 1729 is the only number that is the sum of cubes of two different pairs of numbers: 123 + 13, and 103 + 93.

## Which prime number is infinite?

The number of primes is infinite. The first ones are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 and so on. The first proof of this important theorem was provided by the ancient Greek mathematician Euclid. His proof is known as Euclid's theorem.
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