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A while ago I attempted to write down all the unique five move algorithms for the Rubik's cube, but was eventually overcome with the sheer number of them. This time however, I plan to go much farther; how much farther remains to the level of my patience in finding these by hand.

Middle slice turns and cube rotations have been excluded, note to that double-turns count as only one move, and the algorithms recorded are in the following form: <algorithm><cycle length>. Not all combinations of moves are recorded, because certain sequences of moves like RU and D'B' are isomorphic to one another and therefore have the same cycle length and properties. My list also excludes mirror images of algorithms. In general I have favored right-handed algorithms.

Zero Move Algorithms

There is exactly 1 0-move algorithm; it is shown below.

<><0>

One Move Algorithms

There are exactly 18 1-move algorithms; the two unique ones are shown below.

<R><4>

<R2><2>

Two Move Algorithms

There are exactly 324 2-move algorithms; the 8 unique ones are shown below.

<RU><105>

<RU'><63>

<RU2><30>

<RL><4>

<RL'><4>

<RL2><4>

<R2U><30>

<R2U2><6>

Three Move Algorithms

There are 5,832 3-move algorithms; [to be filled in later] of which are shown below.

<RUD><90>

<RUD'><180>

<RUD2><168>

<RUF><80>

<RUF'><60>

<RUF2><36>

<RUB><84>

<RUB'><360>

<RUB2><9>

<RUL><90>

<RUL'><360>

<RUL2><168>

<RUR><30>

<RUR'><4>

<RUR2><63>

<RU'D><180>

<RU'D'><90>

<RU'F><60>

<RU'F2><63>

[To be finished.]