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===Cycle length===
As of 2025, the best known bound on cycle length is {{val|217976794617}} ({{val|355504839929}} without shortcut).<ref name=Barina/> In 1993
<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)"/>
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