testing 123456789
  split into groups: 789, 456, 123
  add/subtract alternately: 789 - 456 + 123 = 456
  factorise what's left: 456 = 2^3 * 3 * 19
  so 123456789 is not divisible by 7 or 11 or 13

##</code><code>##

  456 = 400 + 56 (so it isn't divisible by 7)
  456 = 390 + 66 (so it isn't divisible by 11 or 13)