Googol : Large Number

                                                       Googol

Hey,

Googol is not similar to the Google Search engine. In fact, it is one of the largest number known so far.

Basically, this number is hardly used by anyone but it indicates the size of number. I doubt you will ever find yourself in a situation where you get a chance to write this number.

The name googol was proposed by Milton Sirotta , the nephew of US mathematician Edward Kasner and came into existence in 1940 through the book Mathematics and the Imagination.

I hope you want to know the size of this number.

Wait 

It is 1 followed by 100 zeros.

1 googol = 10,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000,​000.

Officially it is also known as ten- duotrigintillion or ten thousand sexdecillion.

It is such a large number that we can't even imagine. It is said that there are only 4 x 10^79 atoms in the universe which on calculation will yield a much lesser number than a googol.

It means a googol is larger than the drops of water in oceans, grains of sand. . . . 

Mathematically,

1 googol = 1. 0 x 10 ^100 

Happy reading

Dr Rajesh Kr Thakur

300 Mathematically

1. It is a triangular number.

2. It is the sum of first 24 numbers.
1 + 2 + 3 + ---- + 24 = 300

3. It is also the sum of two consecutive primes, called twin primes
300 = 149 + 151

4. It is the sum of 10 consecutive primes
13+ 17+ 19+ 23 + 29 + 31 + 37 + 41 + 43 + 47

5. It is a palindrome number in 3 consecutive  bases
606₇ = 454₈ = 363₉,

6. In Roman numeral system 
300 = CCC

7. It is the product of three primes 
300 = 2^2 x 3 x 5^2

Dr Rajesh Kumar Thakur

263 Mathematically

                                                           263

1. 263 is a Ramanujan prime.

Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.

( https://en.wikipedia.org/wiki/Ramanujan_prime )

2. 263^2=69169 is a strobogrammatic number that appears the same rotated by 180 degree.

3. 263 = 43 + 47 + 53 + 59 + 61

(Sum of 5 Prime numbers).

4.It is a happy number. Read about Happy number in the following link.

https://www.myqbook.com/MathConcept/667/Happy-numbers

5.It is a balanced prime.

263 = 257+ 269

2

https://en.wikipedia.org/wiki/Balanced_prime

6. It is a Chen Prime.

https://en.wikipedia.org/wiki/Chen_prime

Thanks for reading

Dr Rajesh Kumar Thakur

Mathematically 260

                                                                  260

1. It is a composite number.
2. It is the product of 3 three prime numbers-2, 3 and 13                                                                             260 = 2 x 2 x 5 x 13
3. It is the number of days in Mayan Calender
4. It is the magic sum of a 8 by 8 magic square. 
   
5. It is also the sum of Franklin magic square 
   

Dr. Rajesh Kumar Thakur

Source :- 

1. Wikipedia

2. Pats' Blog

3. The Power of Mathematical number

Mathematically 244

1. 244 is an anti-perfect. 

  Its proper divisors are 1, 2, 4, 61, and 122, & adding their reversal is 244.

                           1 + 2 + 4 + 16 + 221 = 244.

2. It is a palindromic in bases 3 (100001₃), 11 (202₁₁), 60 (44₆₀), 121 (22₁₂₁), 243 (11₂₄₃).

3. 244 is also the sum of three cubes,
                                   244=1^3+3^3+6^3 

4. It is the sum of two nonzero fifth powers
                                  244 = 1^5 + 3^5

5. It is a Harshad number on the base 3, 9, 11 ... . Harshad number was discovered by Indian mathematician Kaprekar.

Dr Rajesh Kumar Thakur

Mathematically 240

240

1. It is a semiperfect number.

2. It is a highly composite number since it has 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number.

3. It is a refactorable number or tau number, since it has 20 divisors and 20 divides 240.

4. It is a pronic number since it is the product of 2 consecutive number
240 = 15 × 16

5. 240 can be expressed as a sum of consecutive primes in two different ways: 240 = 53 + 59 + 61 + 67
 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

6. It is the product of 6 Fibonacci number.
240= 1 × 1 × 2 × 3× 5× 8

Number 211

Number 211

30th July in a normal year and 31st July in a leap year is the 211th day of the year
1. It is an odd number

2. It is the sum of three consecutive primes.
211 = 67 + 71 + 73

3. It is a Chen Prime. A prime number p is called a Chen prime if p + 2 is either a prime or product of two primes.

Rajesh Kumar Thakur