Mersenne: Factoring

[Alexey Guzeev]

  Ok, George's programs looks for only for factors of M(n) in form
1) 2kn+1
  that's clear why
2) 1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,or 119 modulo 120
  but this is not. Why factors 120k+13 are not considered? Or 120k+19? Why only those 
16 reminders of 
~30 primes below 120?