@article{Eliahou1993,
  author    = {{Shalom Eliahou}},
  title     = {{The $3x +  1$ problem: New Lower Bounds on Nontrivial Cycle Lengths}},
  journal   = {{Discrete Math.}},
  year      = {{1993}},
  volume    = {{118}},
  pages     = {{45--56}},
  doi       = {{10.1016/0012-365X(93)90052-U}},
  url       = {{https://www.sciencedirect.com/science/article/pii/0012365X9390052U}},
  abstract  = {{Let $T: \mathbb{N} \rightarrow \mathbb{N}$ be the function defined by $T(n) = \frac{n}{2}$ if n is even, $T(n) = \frac{3n+1}{2}$ if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17087915 elements.}},
  note      = {{MR 94h:11017}},
}