Importance of Number 17

Seventeen (17)

1.      Seventeen can be poartioned in 297 ways.

2.      Studies have shown that if you ask the people to pick a number from 0 to 20, 17 will come most of time. That’s why it is also known as psychologically random number.

3.      It is the 7^th Prime number and only prime of the form – p^q + q^p, where p and q are primes.                   
                   17 = 2³ + 3²

4.      It is the only prime which is the sum of four consecutive prime.                                            
                  17 = 2 + 3 + 5 + 7

5.      It is the lowest number which can be written as A³ + B² in two distinct ways.                     
       17 = 2³+ 3²                                                                                                                      
                          = 1³ + 4²

6.      It is the third Fermat Prime. 

.                                   17 = 2⁴ + 1

7.      C F Gauss (1777- 1855) has discovered a way of accurately drawing a regular heptagon (17 side polygon) by using compass and ruler.

8.      There are exactly 17, two dimensional space groups known as wallpaper groups because they represent the 17 possible symmetry types that can be used for wallpaper.

9.      It is also known as Feller number after the name of famous mathematician William Feller. It is said that while discussing unsolved mathematical problem with his students he would say to try this problem for an arbitrary value of n = 17          

10.  The atomic number of Chlorine is 17.

11. It is the sum of two distinct fourth powers.     

                                                                                   17 = 1⁴ + 2⁴

12.  It is the only prime with the property that it is equal to the sum of digits of its cube.                 17³ = 4913 and its digit sum = 4 + 9 + 1 + 3

13.  It lays exactly half way between 16 which is a square and the number 18 which is divisible by a square number 9. These two numbers 16 and 18 have the distinction that the areas and perimeter are equal. The area of square and perimeter is 16 while the area and perimeter of the rectangle is 18.

14. There are 17 Prime partition of Number 17.

15. If you write out the numbers from 1 to 5000 in English (e.g., THREE THOUSAND EIGHT HUNDRED SEVENTY-THREE), it turns out that 17 is the only one that has a unique number of characters (nine). (Spaces and hyphens count as characters) .

15. The sum of square of all primes up to 17 is a beast number.

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Rajesh Kumar Thakur

rkthakur1974@gmail.com