Mathematically 61

Sixty One (61)

1. It is the smallest prime whose reverse 16 is a square.

2. It is the smaller prime such that its square can be expressed as the sum of 1, 2,3 and 4 distinct squares.

61^2 = 60^2 + 11^2
= 52^2 + 24^2 + 21^2
= 56^2 + 22^2 + 10^2 + 1^2

3. The 61st Fibonacci number (2, 504, 730, 781, 961) is the least Fibonacci number that contains all the digits from 0 to 9.

4. It is a hex number. If you have 61 coins you can arrange it into a hexagonal pattern with one coin in the middle.

5. The reciprocal of 61 = 1/61, has the decimal period of 60 which includes 6 occurrence of each of the digits 0 to 9.
1/61 = 0.0169442622950819672111---- It is the smallest reciprocal whose period has this property.

6. It is the 5th hexagonal number.

7. It is the 9th Mersenne prime exponent.
261 − 1 = 2,305,843,009,213,693,951

8. It can be expressed as the sum of squares of two consecutive numbers.
61 = 5^2 + 6^2
9. It is the 8th Keith number which moves like the Fibonacci sequence where the next term is obtained by adding the previous two terms.
6, 1, 7, 8, 15, 23, 38, 61---
10. The atomic number of Promethium is 61

Mathematically 60

Sixty (60)

1. The Babylonian used the sexagesimal number system (base 60) to write numbers.

2. It can be divided by all numbers from 1 to 6 and also by 10, 12, 15, 20, 30 and 60. The Sumerians used this property to divide the sky into 6 parts each divided into units of 600.

3. It is the smallest number to have 12 factors—1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

4. The internal angle of equilateral triangle is 60degree.

5. The product of first Pythagorean triplet is 60.
3 x 4 x 5 = 60

6. It is the sum of twin prime 29 and 31.
60 = 29 + 31

7. It is a Harshad number because it is divisible by the sum of its digit.

8. The icosahdron has 60 equivalent edges.

9. It is a Heptagonal Pyramidal number.

10. The atomic number of Neodymium is 60.

11. In one hour there are 60 minutes and in 1 minute there is 60seconds.

12. Archimedian solids – truncated icosahedrons, rhombicosidodecahedron and snub dodecahedron have 60 vertices
13. It is a 21- gonal number.

14. It is an abundant number.

15. It is the sum of four consecutive primes.
60 = 11 + 13 + 17 + 19

16. It is the smallest number that can be expressed as the sum of two odd primes in 6 ways.
60 = 7 + 53
= 13 + 47
=19 + 41
= 17 + 43
= 29 + 31
= 23 + 37

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 59

Fifty Nine (59)

1. It is the smallest number which on division by 2, 3, 4, 5 and 6 leaves remainder 1, 2, 3, 4 and 5 respectively.

2. For every 59 rotations of Earth , Mercury rotates once.

3. It is one of the solution of the number which says –a^4 + b^4 = c^4 + d^4 where a< b < c < d. This was solved by Euler in 1772. 59^4 = 133^4 + 134^4 – 158^4 4. Only 59% of the moon’s surface can be observed from the earth. 5. It is the 17th smallest prime number. 6. Icosahedron has 59 Stellations. Stellation is a process of constructing new polygons in 2 dimensions and new polyhedral in 3 dimensions.

7. It lies in the middle of 3 x 3 prime magic square with magical constant as

17 89 71
113 59 5
47 29 101

8. It is one of the factors that divide the smallest composite Euclid number. Euclid numbers are integers of the form En = pn# + 1 where pn# is the product of first n primes. 13# + 1 = 30031 = 59 x 509 is the first composite Euclid number.


Dr Rajesh Kumar Thakur

Mathematically 58

Fifty Eight (58)

1. It is the sum of first seven prime numbers.
2 + 3 + 5 + 7 + 11 + 13 + 17 = 58

2. It is the sum of four consecutive numbers.
13 + 14 + 15 + 16 = 58

3. It is a Smith number. Smith number is a composite number, the sum of whose digits is the sum of digits of its distinct prime factors.
58 has two factors 2 and 29 58 = 2 + (2+9)

4. It is an 11- gonal number.

5. It is a centered 19- gonal number.

6. The atomic number of Cerium is 58.

7. It is the minimum wind speed mile/h needed to issue a severe thunderstorm warning.


Read More about Numbers in my book THE POWER OF NUMBERS available on flipkart, amazon and other online book selling companies

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 57

Fifty seven (57)

1. It is a 20 gonal number.

2. It can be expressed as the sum of -- x^y + y^x where x and y are integers.
2^5 + 5^2 = 57

3. It is the sum of digits from 7 up to 12.
7 + 8 + 9 + 10 + 11 + 12 = 57

4. It is the product of two primes.
57 = 3 x 19

5. On base 7 it is a repeated digit.
57 = (111)7


Dr Rajesh Kumar Thakur

Mathematically 56

Fifty Six (56)

1. It is a tetrahedral number. It is the sum of first six triangular numbers.
1 + 3 + 6 + 10 + 15 + 21 = 56

2. It is an abundant number.

3. It is a tetranacci number. Like Fibonacci sequence, in the tetranacci numbers the next number is the sum of previous four terms. The first few tetranacci numbers are---
0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773—

4. It is the maximum number of regions into which 10 lines can divide a plane.

5. Here is an interesting puzzle involving 56.
111 + 1 / 1 + 1 = 56 222 + 2 / 2 + 2 = 56
333 + 3 / 3 + 3 = 56 444 + 4 / 4 + 4 = 56

6. The atomic number of Barium is 56.

7. The number of reduced 5 x 5 Latin square is 56. Here is an example---
1 2 3 4 5 2 3 5 1 4 3 5 4 2 1 4 1 2 5 3 5 4 1 3 2


Dr Rajesh Kumar Thakur

Mathematically 55

Fifty Five (55)

1. It is the sum of first 10 natural numbers.
1 + 2 + --+10 = 55

2. It is a triangular number. It is the first triangular number composed of repeated digits.
The other are 66 and 666.

3. It is the largest triangular number in Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

4. The sum of squares of first five natural numbers is 55. The sum of squares of n natural number is given by --- 1^2 + 2^2 + 3^2 +---- + n^2 = n (n+1) (2n+1) /6
1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55

5. It is a Palindromic number.

6. Every integer greater than 55 is the sum of distinct primes of the form 4n + 3.

7. The square of 55 shows an interesting pattern.
55^2 = 3025 and 30 + 25 = 55

8. It is the product of 3rd and 5th prime numbers.
55 = 5 x 11

9. Sum of 8 factors of 36 is 55.
1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55

10. It is a square pyramidal number.

11. It is a centered nonagonal number.

12. It is a centered 18 - gonal number.

13. It is the 4th Kaprekar number.

14. It is a cubic recurring digital invariant. Add the cubes of its digits together and repeat the operation twice and you will get 55 back.
55 : 5^3 + 5^3 = 250
250: 2^3 + 5^3 + 0^3 = 133
133: 1^3 + 3^3 + 3^3 = 55

15. It is a heptagonal number. A polygonal number of the form of n(5n – 3 ) / 2 is called heptagonal number.

16. If you multiply any odd numbers from 91 to 109 by 55, you will get a palindrome number each time.
91 x 55 = 5005 93 x 55 = 5115

17. We all know
                           3^2 + 4 ^2 = 5^2
but                      33^2 + 44^2 = 55^2

Dr Rajesh Kumar Thakur