34 Mathematically

Thirty Four (34)

1. It is the 9th Fibonacci number. The Fibonacci series goes like--1, 1, 2, 3, 5, 8, 13, 21, 34—

2. All 4 x 4 magic square has a magic constant 34.

8 11 5 10
13 2 16 3
1 14 4 15
12 7 9 6

3. It is the smallest number with the property that it and its neighbours have the same number of divisors. 34 has 4 divisors so as its neighbours 33 and 35.

4. It is a heptagonal number. A heptagonal number is a figurative numbers that represents a heptagon. The nth heptagonal number is given by

5. It can be partioned into 12310 ways.

6. It is the smallest number which can be expressed as the sum of two primes in four distinct ways.

34 = 3 + 31 = 5 + 29 = 11 + 23 = 17 +17

7. The atomic number of Selenium is 34.

Dr Rajesh Thakur

33 Mathematically

Thirty Three (33)
1. It is the smallest odd repdigit that is not a prime number.

2. It is the sum of first four factorials.
33 = 1! + 2! + 3! + 4!

3. It can be partioned in 10143 ways.

4. It is the smallest member of triplets of successive semi primes. A semi prime is a number with only two
factors.

5. It is the largest positive integer that cannot be expressed as a sum of different triangular numbers.

6. It is a palindrome number on base 10 and also on base 2.
(33)10 = (100001)2

7. The atomic number of Arsenic is 33.

8. On Newtonian scale, it is the temperature on which water boils.

9. Any integer greater than 33 can be written as the sum of 5 non- zero squares.

10. It is a 3rd 12-gonal number

11. It is the number of Perfect graphs with 3 vertices.

12. The Sagrada Familia cathedral in Barcelona designed by Antoni Gaudí is a mathematician’s dream .The cathedral also contains a Magic Square — an arrangement of numbers that equal the same amount in every column, row, and diagonal. The magic number in Sagrada Familia’s case is 33, which alludes to multiple religious symbols. For example, Jesus performed 33 recorded miracles, and most Christians believe he was crucified at 33 years old in 33 A.D

Dr Rajesh Thakur

Importance of Number 32

Thirty two (32)

1. In chess there are 32 pieces on the board at the start of the game.

2. It is the third Leyland number. A Leyland number is written in the form of x^y + y^x.
32 = 2^4 + 4^2

3. It is the melting point of ice on the Fahrenheit scale.

4. A football has 32 panels with 12 regular pentagons and 20 regular hexagons. The football shape is called a Truncated Icosahedrons.

5. It can be partioned into 8349 ways.

Read more about any Number in my book
The Power of Numbers
by Prabhat Publication available on Flipkart, Amazon and other websites

Dr Rajesh Kumar Thakur

Mathematically 31

                                                     Thirty One (31)

1. It is a prime number.

2. It is the sum of five powers of 2.

2^0 + 2^1 + 2^2 + 2^3 + 2^4 = 31

3. It is the third Mersenne prime.
2^5 – 1 = 31

4. January, March, May, July, August, October, December have 31 days.

5. Sum of first 31 odd primes is a perfect square.
3 + 5 + 7 + 11 + …. + 83 + 87 + 89 = 31^2

6. It is a Centered Pentagonal number.

7. It is a repdigit in base 5 and base 2.
(111)5 = (11111)2 = 31

8. The numbers 31, 331, 3331, 33331, 333331, 3333331, and 33333331 are all prime but 333333331 is not a prime.

9. It can be partioned into 6842 ways.

10. It is amongst the two known number that can be written in 2 ways as the sum of successive powers starting with 1.
31 = 1 + 5 + 5^2                                               31= 1 + 2 + 2^2 + 2^3 +2^4

11. It is the sum of first two primes raised to themselves.

31 = 2^2 +3 ^3

12. The digit sum of 31st Fibonacci number (1346269) is 31
1 + 3 + 4 + 6 + 2 + 6 + 9 = 31

13. The number obtained by raising the first four prime to themselves comes out to be a prime.
22+33+55+77=826699


14 . It is a Happy Prime. A happy prime is a number that is both happy and prime.
The first happy primes are 7, 13, 19, 23, 31, 79 etc.
A happy number is defined in the following way:-- Start with any number, replace the number
by the sum of the squares of its digits. Repeat the process until you get 1.

15. It is the minimal move required to solve the Tower of Hanoi puzzle with 5 disks.


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Mathematically 30

Thirty (30)

1. It is the product of first three prime numbers.
30 = 2 x 3 x 5

2. It is the sum of first fours square number.
30 = 1^2 + 2^2 + 3^2 + 4^2

3. It is a Pyramidal number. A pyramidal number is a figurative number that represents a pyramid with a base and a given number of sides.

4. It is the largest number such that every smaller co prime to it is a prime.

5. Dodecahedron and Icosahedrons both have 30 edges.

Dodecahedron Icosahedron
6. A polygon with 30 sides is called a tricontagon.

7. It is a Harshad number because 30 is divisible by the sum of its digit 3 + 0 = 3.

8. The atomic number of zinc is 30.

9. It is the area of right angle triangle with side 5, 12 and 13. It also has the perimeter 30.

10. It is the 5th abundant number.

11. N^5 – N is divisible by 30.

12. It is a round number. A number (n) is said to be a round number if it has no prime factor greater than square root n.


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Dr Rajesh Kumar Thakur
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importance of 29

Twenty Nine (29)

1. It is the tenth prime number.

2. There are 29 days in the month of February in a leap year.

3. It is the smallest prime of the form 7n + 1, where n is any integer.
7 x 1 + 1 = 8 is not a prime
7 x 2 + 1 = 15 is not a prime
7 x 3 + 1 = 22 is not a prime
7 x 4 + 1 = 29 is a prime.

4. It is the sum of square of three consecutive numbers.
29 = 2^2 + 3^2 + 4^2

5. Probability of being born on 29th February is 1/ 1461

6. Seven straight cut through a pizza can divide it into as many as 29 pieces.

7. It is the seventh Lucas number. The series in Lucas number goes like- 1, 3, 4, 7, 11, 18, 29, 47, ---. Like Fibonacci series the next number in Lucas series also is the sum of previous two.

8. Twenty Nine is the only number written with as many strokes as the numerical value.

2 + 4 + 4 + 3 + 2 + 3 + 3 + 1 + 3 + 4

9. It is the third number following 1 and 5 for which 2n^2 – 1 is a square.
2 x 29^2 – 1 = 41^2

10. Saturn requires 29 years to orbit the Sun.

11. The atomic number of Copper is 29.

12. It is a Markov number. A Markov number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation x^2 + y^2 + z^2 = 3xyz. This equation was studied by Andrey Markov.
29 appears in the solution of the above equation in following manners.
{2, 5, 29 }, {2, 29, 169}, {5, 29, 433} etc.

13.The 29th day of the year; 2²⁹ = 536870912 a nine-digit number with no digit repeated. 

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Importance of Number 28

Twenty Eight (28)
1. It is a triangular number.

2. It is the 2nd perfect number. A number is said to be perfect if it is equal to the sum of its perfect divisors except itself.

28 has the factors 1, 2, 4, 7 and 14 that adds up to 28.
All known perfect numbers are even numbers as they end with 6 or 8.
The first five perfect numbers are- 6, 28, 496, 8128 and 33550336.

3. There are 28 days in the month of February except in a leap year when it has 29 days.

4. There are 28 dominoes in a standard double six set.

5. It is a hexagonal number. A hexagonal number is a figurative number.

The formula for the nth hexagonal number is given by --

6. It is the sum of first five consecutive primes.
28 = 2 + 3 + 5 + 7 + 11

7. A 28 side polygon is called Icosikaioctagon.

8. The Gregorian calendar repeats in 28 years. The calendar of 2013 will work in 2041.

9. It can be portioned into 3718 ways.

10. It is the third positive integer with a prime factorization in the form of 2^2q, where q is an odd prime.
28 = 2 x 2 x 7 = 2^2 x 7

11. It is used as an approximation to the number of days in the lunar month.

12. The atomic mass of Silicon is 28.

13. The atomic number of Nickel is 28.

14. The revolution time of the surface of the sun on itself is 28 days.


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