23 Sept 2017 Collatz: Search finished
After less than one and a half months (14 August to 23 September), we were able to successfully complete our search project:
  • We have found all the smaller path records as well as all starting numbers <260, whose maximum > 2 * 1016 * starting number (only such numbers are given as candidates) which were found by other persons (mainly Tomas Olivera e Silva and Eric Roosendaal); and thus validate our approach in the opposite direction.
  • We have found 4 new path records and have been able to prove that all starting numbers <87 * 260 (in particular also all <1020) land at 1 and pass into the trivial cycle.
  • Thus, we have also shown that a non-trivial cycle must consist of more than 17 billion sequence members