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
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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 22q, where q is an odd prime.
28 = 2 x 2 x 7 = 22 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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Importance of Number 27

Twenty seven (27)
1. It is the smallest two digit number in which the sum of digits is equal to the sum of prime factors.

27 = 3 x 3 x 3 and 2 + 7 = 3 + 3 + 3

2. It is the largest number which is equal to the sum of the digits of its cube.
27^3 = 19683 and 1 + 9 + 6 + 8 + 3 = 27

3. It is the magic constant of the multiple of 1/7.

1/7 = 0. 142857… 2/7 = 0.285714-- 3/7 = 0.428571-- 4/7 = 0.571428-- 5/6 = 0.714285-- 6/7 = 0.857142--

Digit 1 4 2 8 5 7 Digit Sum
1 1 4 2 8 5 7 27
2 2 8 5 7 1 4 27
3 4 2 8 5 7 1 27
4 5 7 1 4 2 8 27
5 7 1 4 2 8 5 27
6 8 5 7 1 4 2 27
Column sum 27 27 27 27 27 27

4. It is the third decagonal number. A decagonal number represents a decagon. The nth decagonal number is given by the formula--

5. It is a cubic number.
27 = 3 x 3 x 3

6. It is the only positive integer that is 3 times the sum of its digits.
27 = 3 x (2 + 7)

7. In Hindu astrology there are 27 nakshatra (stars) each controls a section of the zodiac signs.

The first few are – Ashwini, Bharani, Kritika –

8. If you add up all the digits from 2 to 7 it will give you 27. It is the second two digit number besides 15 with this property.
2 + 3 + 4 + 5 + 6 + 7 = 27

9. The atomic number of Cobalt is 27.

10. The atomic weight of Aluminum is 27.

11. It is the first odd perfect cube apart from 1.

12. It is the smallest number that can be expressed as the sum of 3 squares in 2 ways.
27 = 3^2 + 3^2 + 3^2 27 = 5^2 + 1^2 + 1^2

13. There are 27 cubes in a Rubik’s


14. It can be portioned in 3010 ways.

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Importance of Number 26

Twenty Six (26)

1. There are 26 letters in English which can make 40,329 x 1022 different combination.

2. It is the only number between a square number and a cube number.
25 = 5^2 < 26 < 27 = 3^3 

 3. It is the smallest number which is not a palindrome number but its square is a palindrome. A palindrome number read from left to right and vice versa gives the same result. 26^2 = 676 this is a palindrome number. 

 4. It is the sum of three consecutive Fibonacci number. 26 = 5 + 8 + 13 

 5. It is the difference of the 2nd pair of amicable numbers. Two numbers are said to be amicable if the sum of factors of one number excluding itself gives the other number and vice versa. The first pair of amicable number is 220 and 284. The second pair of amicable number is 1184 and 1210. 1210 – 1184 = 26 

 6. A rhombicuboctahedron has 26 sides. It is an Archimedean solid with 8 triangular and 18 square faces.

7. In ternary system it has repeated digit. 26 written on base three is equal to 2223.

8. The atomic number of Iron is 26.

9. It is the third heptagonal pyramidal number. The heptagonal number for n can be calculated by adding up the heptagonal numbers for 1 to n, or

by using the formula ----n(n + 1)(5n - 2)/6.

The first 5 heptagonal pyramidal numbers are – 1, 8, 26, 60 and 115.

10. It is the sum of its cubes.
26^3 = 17576 and 1 + 7 + 5 + 7 + 6 = 26

11. Here is a Heptagonal puzzle which is quite difficult to solve. This puzzle is due to Henry Dudeney (1847 -1930). The puzzle goes like this—using the number 1 to 14 place a different number in each circle so that the three numbers along every side add up to 26. Henry himself has given this solution.

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Importance of 25

Twenty Five (25)
1. It is a centered octagonal number.

2. It is a square number.


3. It is the smallest square number that can be written as a sum of 2 consecutive squares.
25 = 3^2 + 4^2

4. It is the sum of first 5 odd numbers. 1 + 3 + 5 + 7 + 9 = 25

5. It is the sum of two triangular numbers.

+ =
6. If you place 6 with 25 in two different ways you get two square numbers.
625 = 25^2 and 256 = 16^2

7. A number ending with 25, 50, 75 or 00 will be divisible by 25.
Example:- 450, 625, 875, 1900 are divisible by 25.

8. It is the difference of squares of two consecutive numbers.
25 = 132 – 122

9. It is the sum of squares of two consecutive numbers.
25 = 32 + 42

10. It can be portioned in 1958 ways.

11. All powers of 25 ends with 25

25^2 = 625
25^3 = 15625

12. It is the only solution of (n – 1 )! + 1 = n^k
25 = 5^2 = (5 – 1 )! + 1


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Number 24

Twenty Four (24)

1. It is the smallest number to have 8 different factors. These factors are – 1, 2, 3, 4, 6, 8, 12 and 24.

2. A day has 24 hours.

3. It is a Harshad number. A number is known as Harshad number if it is divisible by the sum of its digits. 24 is exactly divisible by 2 + 4 = 6. This number was discovered by the Indian mathematician D R Kaprekar.

4. The sum of squares of first 24 natural numbers is a square number. It is the only integer except 1 with this property.
1^2 + 2^2 + --- + 24^2 = 4900 = 70^2

5. It is one of the kissing numbers in fourth dimensional space. A kissing number is defined as the number of non overlapping unit spheres that can be arranged such that each touch another given unit sphere. Kissing numbers are also known as Newton number.

6. Unlike English alphabets, Greek alphabets have 24 letters.

7. It is the product of first four consecutive numbers.
24 = 1 x 2 x 3 x 4

8. It is the first number which can be expressed in the form of 2^3q, where q is an odd prime.
24 = 2^3 x 3

9. Puzzle: - Take any four consecutive numbers. Multiply them and the answer will be divisible by 24. Example: - Let us take the four consecutive numbers 34, 35, 36 and 37.

Its product is 34 x 35 x 36 x 37 = 1585080 which when divided by 24 gives 66045 as quotient.

10. It is the product of second triangular number and second cube numbers.
24 = 3 x 8

11. It can be partioned in 1575 ways.

12. It is the sum of 4 consecutive odd numbers.

24 = 3 + 5 + 7 + 9

13. It is the fourth abundant number.

14. It is the third nonagonal number. A nonagonal number is a polynomial number that represents a nonagon. The nth nonagonal number is given by – n (7n – 5 ) / 2.

15. It is the sum of twin prime 11 and 13.
24 = 11 + 13

16. It is the largest integer that is divisible by all natural numbers less than its square root. The square root of 24 is 4.89 approximately therefore it is divisible by 1, 2, 3 and 4.

17. For any prime number greater than 3, p^2 – 1 is divisible by 24. If we take p = 7 then 7^2 – 1 = 48 is divisible by 24.

18. The atomic number of Chromium is 24.

19. The purest form of gold is 24 carat.

20. The 24th dimension is the highest dimension for which the exact "kissing number", the number of spheres that can be placed around a central sphere so that they all are touching it, is known. For the 24th dimension, the "kissing number is 196,560. Beyond the fourth dimension, only the eighth and twenty-fourth are known exactly.  (From the blog of Pat Ballew) 


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Number 23

                            Twenty Three (23)

1. It is a prime number and more interestingly it’s both digits are also prime so is its sum. 2 and 3 are prime and 2+ 3 = 5 is also a prime.

It is a Cousin prime with 19 (differ by 4) and a sexy prime with 17 (differ by 6).

2. Biorhythm theory proposed by Wilhelm Fleiss states that men’s physical and emotional characteristics follow a 23 day cycle.

3. It is the smallest prime number with two consecutive digits.

4. In a group of 23 people, the probability of at least 2 persons having same birthday is more than 50%.

5. It is the smallest odd prime which is not a twin prime.

6. 1 repeated 23 times gives a prime number.
11, 111, 111, 111, 111, 111, 111, 111 is a prime number.

7. 23 balls can be arranged in two different ways.

8. The factorial of 23 has exactly 23 digits.

23! = 25,852,016,738,884,976,640,000

9. It is the sum of three consecutive primes 5, 7 and 11. It is the first prime number with this characteristic. 23 = 5 + 7 + 11

10. The sum of first 23 prime numbers is divisible by 23. The sum of first twenty three primes is 874

11. David Hilbert had presented 23 problems to the International Congress of Mathematicians in 1900. These problems were unsolved by that time and it was first published by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society in 1902.

12. It is the atomic number of Vanadium.

13. It is the fifth Sophie Germain prime. A prime number p is a Sophie Germain prime if 2p + 1 is also prime.

This is named after French mathematician Marie Spphie Germain. The first few Sophie Germain Primes are

–2, 3, 5, 11, 23, 29, 41, 53, 83, --

23 is a prime and 2 x 23 + 1 = 47 is also a prime.

14. It can be partioned into 1575 ways.

15. The 23rd number of English Alphabet is W and in a normal computer board W lies between 2 and 3.

16. In English alphabet 23rd letter W has two downwards and 3 upward move.

17. Trivia :- 

•Aryabhata wrote his first book ARYABHATIYA at the age of 23.

•Johann Bernoulli wrote the manuscript of De Calculo differentatium at the age of 23.

•Ramanujan got his first article published in the journal of Indian mathematical society at the age of 23 and the problem was a nested radical roots

18. It is a Happy Number. A number is called Happy Number if sum of squares of its digit after repeated operation comes out to 1.

Be happy, 23 is a Happy Number

19, 23! (Factorial of 23) has only 23 digits and it is the only number following this properties. The factorial expansion has all digits from 0 to 9.

                  23!=25,852,016,738,884,976,640,000

20. Enjoy this beautiful expression

2 ! + 3 ! = 2^3

1! + 2 x 2! +3 x 3! = 23

You can watch the movie Number 23 on the given link

https://www.youtube.com/watch?v=uTIXSKBxf-0

Happy reading 

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Dr. Rajesh Kumar Thakur