After a bit of research I found that there is a proof [0][1] that BB(12) &gt; g_1. But that&#x27;s still a ways from g_2, let alone g_64.<p>[0]: &quot;A Lower Bound on Rado&#x27;s Sigma Function for Binary Turing Machines&quot; by Milton Green (1964)<p>[1]: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Busy_beaver#Known_values_for_.CE.A3_and_S" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Busy_beaver#Known_values_for_....</a>