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