Skelet 1

Unsolved problem:

What is the exact cycle preperiod of Skelet 1?

A skeleton warrior holding a sword. The runic inscription on its blade is a string that is particularly often encountered on a tape during Skelet 1 simulation.

1RB1RD_1LC0RC_1RA1LD_0RE0LB_---1RC (bbch), called Skelet #1, was one of Skelet's 43 holdouts and one of the last holdouts in BB(5). It was eventually proven to be a Translated Cycler by Pavel Kropitz and Shawn Ligocki. It is one of the few TMs to have required an individual proof of non-halting in Coq-BB5.

It has a period 8,468,569,863 and start step about $5.42\times 10^{51}$. Both of these values are gigantic in comparison to the runtime of the 5-state busy beaver winner which runs for a "mere" 47 million steps.

Preperiod

The exact preperiod (minimum cycle start start step) for Skelet 1 is not known, but @hipparcos computed it to be approximately 5418883027667422764169643414989497193809945789706483. This is an upper bound (by this point the TM is cycling). This value is probably accurate to within about one period.

See Also

• Skelet #1: What I Know. 25 Feb 2023. Shawn Ligocki
• Skelet #1: A Halting Counter Config. 27 Feb 2023. Shawn Ligocki
• Skelet #1 is infinite ... we think. 13 Mar 2023. Shawn Ligocki
• Simulation code by Pavel & Shawn: https://github.com/univerz/bbc/tree/no1