I have played with several numbers with the following rules:
Take a number. (Example 10)
Find the prime factors of the number (if it have) . ( Example 10 have prime factors 2 and 5)
Make a number using those prime factors in ascending order. (Example for 10 it will be 25 as prime factors are 2 and 5)
Now continue the process with the new number you have got. Continue this process until you get a prime number as it will not have any prime factors
Applying the whole process on 10 :
10 => 25 => 55 => 511 => 773
I have applied this procedure on many numbers. And I concluded a statement:
All numbers will eventually fall to a prime through the process
For 8 it was a quiet big task:
8 => 222 => 2337 => 31941 => 33371313 => 311123771 => 7149317941 => 22931219729 => 112084656339 => 3347911118189 => 11613496501723 => 97130517917327 => 531832651281459 => 3331113965338635107
Another incredible number was 20 and I am unable to obtain a prime yet. You can try it yourself.
You should also try out if you can find any number not falling to a prime, or if you can prove or disprove my statement.