Friday, August 28, 2020

prime numbers

 

Generating Prime numbers

Few methods have been suggested  to generate prime numbers. Here is yet another way.

Take any odd  (o) and even (e) numbers. The difference between its product and its sum [eo – e – o] or sum of its product and its sum  [eo + e + o] in most cases give prime numbers. When the numbers end with 3 and 4 respectively , the resultant invariably ends with 5 , a non-prime. If both the numbers are even, the resultant will be even which cannot be prime.

 e.g -1       

                          allowed                                                     forbidden  

5    2       10- 7 = 3         10 + 7 = 17                11     2     22 -13 =9   22 + 13 = 35

7    2       14 -9 = 5         14 + 9 = 23                17     2     34 – 19 = 15

9    2       18 – 11 = 7     18 + 11 = 29  

13   2      26 – 15 = 11   26 + 15 = 41

15   2      30 – 17 = 13   30 + 17 = 47

17   2                              34 + 19 = 53

19   2      38 – 21 = 17   38  + 21 = 59

 

e.g.-2

                         allowed                                                       forbidden

3     4       12 – 7  =  5       12 + 7 = 19       3    6      18 – 9 = 9     18 + 9 =  27

3     8       24 – 11 = 13     24 + 13 = 37     3    12    36 -  15 = 21  36 + 15 = 51

3    10      30 – 13 = 17     30 + 13 = 43     3    14    42 – 17  = 25

3    14                               42 + 17 = 59 

3    16      48 -  19 = 29    48  + 19 = 67