Determine the distinct prime factors of 6153^3 - 6000^3 - 153^3

Finding the distinct prime factors of number between 15 billion and 20 billion without knowing its Hindu-Arabic Expanded form. This is a larger constant version of problem presented by Math Icon Michael Penn. Devotee and mathematics lover bathy_thesub has expressed his appreciation multiple times for Doctor Penn's lucid efforts. The binomial cubed expansion gave rise to a favorable factored form where 293 was identified as the largest of the six distinct prime factors of the exponential expression 6153^3 - 6000^3 - 153^3. Also divisibility by 7 test was used to show 2051 is a multiple of 7.
To wit, 205 - 2x1 = 203 = 29x7. Subtracting double the last digit from number formed by remaining digits is the key aspect of this tiny algorithm. Smartick, fancying quotes from author Diane Ackerman, carefully explains the mechanics of various divisibility tests.