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The busy beaver function $bb(n)$ is not known for $n \geq 5$. Does Anyone know suitable lower bounds for $bb(7)$ and $bb(8)$?

Remark: $bb(6)$ as a trivial lower bound does not count as a suitable bound.

St Vincent
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Peter
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  • I don't know any upper bound that is not trivial from bb(6). But perhaps something was published recently ? – Xoff Sep 21 '13 at 21:45
  • Maybe the people on cstheory.stackexchange.com would be more likely to know about recent developments in this area. – MJD Sep 21 '13 at 22:15
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    Heiner Marxen keeps track of bounds and records at http://www.drb.insel.de/~heiner/BB/ Also of possible interest is http://cp4space.wordpress.com/2012/12/30/fast-growing-3/ – Gerry Myerson Sep 22 '13 at 00:14

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Recently on the Googology Wiki, user Wythagoras modified the Busy Beaver machine for six states to create a seven state machine that prints more than $10^{10^{10^{10^{18705353}}}}$ ones. The machine is listed here, and the computation is verified here. So $S(7) > \Sigma(7) > 10^{10^{10^{10^{18705353}}}}$.

I haven't heard of any good bounds for $\Sigma(8)$.

Deedlit
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