Yes. In fact, Allen Brady feared as early as 1988 that there would be a totally intractable machine with 5 states [0]: > Prediction 5. It will never be proved

Yes. In fact, Allen Brady feared as early as 1988 that there would be a totally intractable machine with 5 states [0]: > Prediction 5. It will never be proved that Σ(5) = 1,915 and S(5) = 2,358,064. (Or, if any larger lower bounds are ever found, the new values may be substituted into the prediction.) > Reason: Nature has probably embedded among the five-state holdout machines one or more problems as illusive as the Goldbach Conjecture. Or, in other terms, there will likely be nonstopping recursive patterns which are beyond our powers of recognition. Luckily, this prediction did not come to pass, but only by a margin of one extra state. [0] Allen Brady, "The Busy Beaver Game and the Meaning of Life", in Rolf Herken (ed.), The Universal Turing Machine: A Half-Century Survey, Oxford University Press, 1988, pp. 259–277. This chapter can also be found in the 2nd ed., Springer, 1995, pp. 237–254.