As promised in >>44 third-order S-groups have been added to >>36. The code still needs a bit of cleanup because, while the runtime order of growth is now O(n^(1/8)), the constant factor given by the more complex S-group folding step is much higher than for second-order S-groups. As a preview here is R(10^31):
k 31 index 10000000000000000000000000000000
levels: 5
10000000000000000000000000000000 -> 50000000000000029814239195666197369782628797813806672178028303 0x1F1D75A5709C1FEA650A7046A3AAD99F2BC662D8153503D79F0F 205