Editing Collatz conjecture (section)

===Cycle length===
The length of a non-trivial cycle is known to be at least {{val|114208327604}} (or {{val|186265759595}} without shortcut). If it can be shown that for all positive integers less than <math>3 \times 2^{69}</math> the Collatz sequences reach 1, then this bound would raise to {{val|217976794617}} ({{val|355504839929}} without shortcut).<ref name="Hercher (2023)"/><ref name="Eliahou (1993)"/> In fact, Eliahou (1993) proved that the period {{mvar|p}} of any non-trivial cycle is of the form
<math display="block">p = 301994 a + 17087915 b + 85137581 c</math>
where {{mvar|a}}, {{mvar|b}} and {{mvar|c}} are non-negative integers, {{math|''b'' ≥ 1}} and {{math|1=''ac'' = 0}}. This result is based on the [[simple continued fraction]] expansion of {{math|{{sfrac|ln 3|ln 2}}}}.<ref name="Eliahou (1993)"/>