Primes of the octomino

26 × 96, 26 × 104, 26 × 112, 26 × 120, 26 × 128, 26 × 136, 26 × 144, 26 × 152, 26 × 160, 26 × 168, 26 × 176, 26 × 184
28 × 128, 28 × 132, 28 × 136, 28 × 140, 28 × 144, 28 × 148, 28 × 152, 28 × 156, 28 × 160, 28 × 164, 28 × 168, 28 × 172, 28 × 176, 28 × 180, 28 × 184, 28 × 188, 28 × 192, 28 × 196, 28 × 200, 28 × 204, 28 × 208, 28 × 212, 28 × 216, 28 × 220, 28 × 224, 28 × 228, 28 × 232, 28 × 236, 28 × 240, 28 × 244, 28 × 248, 28 × 252
29 × 208, 29 × 224, 29 × 240, 29 × 256, 29 × 272, 29 × 288, 29 × 304, 29 × 320, 29 × 336, 29 × 352, 29 × 368, 29 × 384, 29 × 400
30 × 80, 30 × 88, 30 × 96, 30 × 104, 30 × 112, 30 × 120, 30 × 128, 30 × 136, 30 × 144, 30 × 152
31 × 128, 31 × 144, 31 × 160, 31 × 176, 31 × 192, 31 × 208, 31 × 224, 31 × 240
32 × 74, 32 × 78, 32 × 82, 32 × 83, 32 × 84, 32 × 86, 32 × 88, 32 × 90, 32 × 92, 32 × 93, 32 × 94, 32 × 96, 32 × 97, 32 × 98, 32 × 99, 32 × 100, 32 × 101, 32 × 102, 32 × 103, 32 × 104, 32 × 105, 32 × 106, 32 × 107, 32 × 108, 32 × 109, 32 × 110, 32 × 111, 32 × 112, 32 × 113, 32 × 114, 32 × 115, 32 × 116, 32 × 117, 32 × 118, 32 × 119, 32 × 120, 32 × 121, 32 × 122, 32 × 123, 32 × 124, 32 × 125, 32 × 126, 32 × 127, 32 × 128, 32 × 129, 32 × 130, 32 × 131, 32 × 132, 32 × 133, 32 × 134, 32 × 135, 32 × 136, 32 × 137, 32 × 138, 32 × 139, 32 × 140, 32 × 141, 32 × 142, 32 × 143, 32 × 144, 32 × 145, 32 × 146, 32 × 147, 32 × 149, 32 × 150, 32 × 151, 32 × 153, 32 × 154, 32 × 155, 32 × 159, 32 × 163
33 × 112, 33 × 128, 33 × 144, 33 × 160, 33 × 176, 33 × 192, 33 × 208
34 × 64, 34 × 72, 34 × 80, 34 × 88, 34 × 96, 34 × 104, 34 × 112, 34 × 120
35 × 112, 35 × 128, 35 × 144, 35 × 160, 35 × 176, 35 × 192, 35 × 208
36 × 72, 36 × 76, 36 × 80, 36 × 84, 36 × 88, 36 × 92, 36 × 96, 36 × 100, 36 × 104, 36 × 108, 36 × 112, 36 × 116, 36 × 120, 36 × 124, 36 × 128, 36 × 132, 36 × 136, 36 × 140
37 × 64, 37 × 80, 37 × 96, 37 × 112
38 × 64, 38 × 72, 38 × 80, 38 × 88, 38 × 96, 38 × 104, 38 × 112, 38 × 120
39 × 80, 39 × 96, 39 × 112, 39 × 128, 39 × 144
40 × 56, 40 × 60, 40 × 64, 40 × 68, 40 × 72, 40 × 76, 40 × 80, 40 × 82, 40 × 84, 40 × 86, 40 × 88, 40 × 90, 40 × 92, 40 × 94, 40 × 96, 40 × 98, 40 × 100, 40 × 102, 40 × 104, 40 × 106, 40 × 108, 40 × 110, ...
41 × 48, 41 × 64, 41 × 80
42 × 64, ...
45 × 48, 45 × 64, ...
46 × 64, ...
48 × 48, 48 × 49, 48 × 53, 48 × 57, 48 × 61, 48 × 65, 48 × 69, 48 × 73, 48 × 77, 48 × 81, ...
49 × 64, ...
50 × 64, ...
53 × 64, ...
54 × 64, ...
56 × 56, 56 × 60, 56 × 64, 56 × 68, 56 × 72, 56 × 76, ...
57 × 64, ...
58 × 64, ...
61 × 64, ...
62 × 64, ...
64 × 64, 64 × 65, 64 × 66, 64 × 69, 64 × 70, 64 × 73, ...
...

smallest rectangle: 41 × 48

The first rectangle for this octomino, 26 × 96 , was found independently by Karl Dahlke [1, Figure 1] (see also [2, Figure 154]) and Wrede [3, Figure 5.3.8]. This is the second known polyomino, after the P 11-omino, whose rectangular order, 246, is congruent to 6 mod 8.

References

[1] Karl A. Dahlke, Solomon W. Golomb and Herbert Taylor, An Octomino of High Order, Journal of Combinatorial Theory, Series A 70 (1995) pp. 157-158.
[2] Solomon W. Golomb, Polyominoes, Second edition, Princeton University Press, 1994.
[3] Ingo Wrede, Rechteckzerlegungen mit kleinen Polyominos, 1990 Diplomarbeit, Technische Universität Braunschweig, (unpublished).

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Updated May 19, 2012.