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You may also see list of all polyomino sets for which data is available here.

Prime rectangles: ≥ 1.

Smallest known rectangle and smallest known square (36x36):

Blue number (*P*) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (*W*) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (*C*) - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h | 1-22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | N>0 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1-22 | 0 | |||||||||||||||

23 | 0 | 00 | ||||||||||||||

24 | 0 | 00 | 00 | |||||||||||||

25 | 0 | 00 | 00 | 00 | ||||||||||||

26 | 0 | 00 | 00 | 00 | 00 | |||||||||||

27 | 0 | 00 | 00 | 00 | 00 | 00 | ||||||||||

28 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | |||||||||

29 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | ?? | ||||||||

30 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | |||||||

31 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ||||||

32 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | |||||

33 | 0 | 00 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ||||

34 | 0 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | |||

35 | 0 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ||

36 | 0 | 00 | 00 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ≥1≥1P | |

37 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

38 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

39 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

40 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

41 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

42 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

43 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

44 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

45 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

46 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

47 | 0 | 00 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

48 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

49 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

50 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

51 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

52 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

53 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

54 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

55 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

56 | 0 | 00 | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ?? | ? |

N>0 | x | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? |

- Smallest rectangle taken from here http://www2.stetson.edu/~efriedma/mathmagic/0810.html