Mathematically 43

Forty Three (43)
1. It is a Prime number.

2. It forms a twin prime along 41. There are infinite twin primes.

The list of first ten twin primes are---
(3,5), (5,7), (11,13), (17.19), (29.31), (41,43) , (59,61), (71,73), (101,103), (107,109)

3. It is the smallest non palindromic prime which on subtracting its reverse gives a perfect square.
43 – 34 = 9 = 32

4. It is the smallest number which can be expressed as the sum of primes in different ways.
43 = 2 +41
= 3+17+ 23
=11 +13 +19
=2 + 5+ 7 +29
= 2 +11 +13 +17

5. It can be partitioned into 53174 ways.

6. It is the smallest prime that can grows 5 times by the right.
43 is prime
439 is prime
4391 is prime
43913 is prime
439133 is prime

7. It is the smallest prime which is not a Chen prime. A prime p is called Chen prime if p+2 is either a prime or a product of two primes. It is named after Chen Jingrun. The first few Chen Primes are- 2,3, 5,7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47—

8. It is the fourth term of Sylvester’s sequence.
43 = 2 x 3 x 7 + 1

9. The atomic number of Technetium is 43.

10. It is a centered Heptagonal number. A centered heptagonal number is a centered figurative number that represents a heptagon with a dot in the center and other dots surrounding the center dot in successive heptagonal layers. The formula for n centered heptagonal number is given by-

11. It is a centered 14 - gonal number.

12. It can be partioned in 53174 ways.


Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 42

Forty two (42)

1. It is the 8th abundant number

2. It lies between twin prime numbers 41 and 43.

3. It is the smallest perfect square that is the mean of two cubed primes.
422 = (113 + 133 ) / 2

4. It is the sum of first 6 even numbers.
42 = 2 + 4 + 6 + 8 + 10 + 12

5. n^2 – n is divisible by 42.

6. The 3 x 3 x 3 magic cube can be constructed with the help of numbers from 1to 27 such that the sum of every row, column and diagonal is 42.

7. It can be partitioned into 44583 ways.

8. It is a repdigit in base 4.
42 = (222)4

9. The atomic number of molybdenum is 42.

10. It is the product of first three terms of Sylvester’s sequence. Sylvester’s sequence is named after the mathematician James Joseph Sylvester. Sylvester’s sequence is an integer sequence in which each member of the sequence is the product of the previous members plus one. The first five members of Sylvester’s sequence is --- 2, 3, 7, 43 and 1807.

42 = 2 x 3 x 7

11. It is the reciprocal of sixth Bernoulli numbers (1/42) discovered by great Swiss mathematician Jakob Bernoulli. The first few Bernoulli numbers are--
B0 = 1, B1 = ±1⁄2, B2 = 1⁄6, B3 = 0, B4 = −1⁄30, B5 = 0, B6 = 1⁄42, B7 = 0, B8 = −1⁄30.

12. It is a Catalan number. The series for Catalan numbers are--- 1, 1, 2, 5, 14, 42, 132, 429---.Catalan numbers are probably the most frequently occurring combinatorial numbers, after the binomial coefficients. It is named after the Belgian mathematician Eugene Charles Catalan. The nth Catalan number is defined as --

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 41

Forty one (41)

1. It is the 5th centered square number.

2. It is a prime number

3. It is the sum of two consecutive squares.
41 = 4^2 + 5^2

4. It is the lowest number whose cube can be expressed as the sum of cubes of 3 numbers in two different ways.
41^3 = 2^3 + 17^3 + 40^3
= 6^3 + 32^3 + 33^3

5. It is the smallest non- palindromic prime which on subtracting its reverse gives a perfect cube.
41 – 14 = 3^3

6. It is the sum of first six prime numbers.
41 = 2 + 3 + 5 + 7 + 11 + 13

7. It is a centered square number. It is a centered figurative number that gives the number of dots in a square with a dot in the centre and all other dots surrounding the center dot in successive square layer. The first few centered square numbers are 1, 5, 13, 25, 41 etc.

8. It can be partitioned in 37338 ways.

9. x2 + x + 42 gives a prime number for all x from 0 to 39. It was discovered by Euler.

10. It is the largest known number n for which the decimal expansion of 11n does not contain any zero.

11. It is the smallest prime whose sum of the digits and difference of digits are twin primes. 4 + 1 = 5 and 4 – 1 = 3 are twin primes.

12. It is the smallest prime of the smallest set of three consecutive primes {41, 43, 47} whose sum of digits (5, 7, 11) is also a set of three distinct primes.

13. It is the sum of first 3 factorials plus the first three self powers.
1! + 2! +3! +1^1 + 2^2 + 3^3 = 41

14. It is the first number of a prime number sequence that is 41 numbers long. In other words, if you start from 41 and add 2 , 4, 6, 8, 10, --- etc you will have a string of 40 straight prime numbers.
41 + 2 = 43 43 + 4 = 47 47+6 = 53 etc.


15. It is the smallest number that is not in the form of 2^x – 3^y

16. It is the smallest prime such that the sum of factorials of its distinct digits is a square number.

4! + 1! =5^2

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 40

Forty (40)
1. It is the only number whose letters are in the alphabetical order.
FORTY

2. It can be partitioned into 31185 ways.

3. It is a pentagonal pyramid number being the sum of first four pentagonal numbers. The first few pentagonal pyramid numbers are – 1, 6, 18, 40, and 75. The formula for the nth pentagonal pyramid number is given by--

4. It is the 7th abundant number.

5. The Celsius and Fahrenheit temperature come together at minus 40.
- 40degree C = - 40degreeF

6. One Furlong is equal to 40 rods.

7. It is an octagonal number. An octagonal number is a number that creates a octagon. The first few octagonal numbers are 1, 8, 21 and 40.

8. It is the fourth star number. This pattern is made up of a square and four equilateral triangles.

Dr Rajesh Kr Thakur
rkthakur1974@gmail.com

Mathematically 39

Thirty Nine (39)

1. It is the sum of five consecutive prime numbers.
39 = 3 + 5 + 7 + 11 + 13

2. It is the product of two odd primes.

39 = 3 x 13

3. It can be partioned in 26015 ways.

4. It is the sum of 10th odd and 10th even number.
39 = 19 + 20

5. It is the sum of first three powers of 3.
39 = 3^1+ 3^2 + 3^3

6. It is the sum of numbers 4 through 9.
39 = 4 + 5 + 6 + 7 + 8 + 9

7. It is the sum of 6th, 7th and 8th odd numbers.
11 + 13 + 15 = 39

8.It (39) is the smallest number with multiplicative persistence 3. [Multiplicative persistence is the number of times the digits must be multiplied until they produce a one digit number; 3(9)= 27; 2(7) = 14; 1(4)=4. ] - 

9. The F26A graph is a symmetric graph with 39 edges. In graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges.

10. It is equal to the number of plus (+) signs needed to write the partitions of 7.

11. It is the smallest natural numbers which has 3 partitions into three parts (25, 8, 6), (24, 10, 5) and (20, 15, 4)-which all give the same product when multiplied.

12. It is a 14- gonal number or Tetradecagonal number. The formula to obtain a 14 gonal number is ½ (12n^2 – 10n).

13. The largest Armstrong number in decimal numbers has 39 digits. (115,132,219,018,763,992,565,095,597,973,522,401 is the largest)

A number is called Armstrong number if it can be expressed as the sum of the its own digits , each raised to the power  of the number of digits of the number. It is also called Narcissistic number.

There are just four numbers, after unity, which are the sums of the cubes of their digits: , , , and 407 = 4^ 3 + 0^3 + 7^3

Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com

Mathematically 38

Thirty Eight (38)

1. The only possible magic hexagon has the magical constant as 38. The following magic hexagon has the digits from 1 to 19.

2. It is the largest known even number which can be represented as the sum of two distinct primes in one and only one way.

38 = 31 + 7

3. It is the sum of squares of first three primes.

38 = 2^2 + 3^2 + 5^2

4. 38th digit of pi (excluding decimal) is a Prime number
 31415926535897932384626433832795028841 

5. It is the largest even number which cannot be written as the sum of two odd composite numbers.

6.

5. The atomic number of Strontium is 38.

6. It is the product of two prime factors.
38 = 2 x 19

Dr Rajesh Kumar Thakur

Mathematically 37

Thirty Seven


1. It is the fourth Hexagonal number, because it can be arranged in a pattern of nested hexagon.

2. It is a prime number.

3. Normal body temperature of a healthy man is 37 degree C

4. If you multiply 37 with the multiple of 3 you will get an astonishing result.
37 x 3 = 111
37 x 6 = 222
37 x 9 = 333
37 x 12 = 444 etc.

5. Take any 6 digit number in which the first three digits are consecutively increasing and last three digits are consecutively decreasing, the number will be divisible by 37.
123987 is divisible by 37

6. It is the only two digit number which, when multiplied by 2 and subtracted by 1 gives the number in reverse order.
2 x 37 – 1 = 73 is reverse of 37

7. The atomic number of Rubidium is 37

8. 37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.

9. The reciprocal of 37 has three periods.
1/37 = 0.027 027 027 …
It is the only prime that has three digit periods after decimal expansion.

10. It is a centered 12- gonal number.

11. It is a maximal number of regions into which 8 lines divide a plane.

12. It can be partioned in 21687 ways.

Dr Rajesh Kumar Thakur