Primes of the dekomino

27 × 160, 27 × 180, 27 × 190, 27 × 200, 27 × 210, 27 × 220, 27 × 230, 27 × 240, 27 × 250, 27 × 260, 27 × 270, 27 × 280, 27 × 290, 27 × 300, 27 × 310, 27 × 330
30 × 46, 30 × 66, 30 × 72, 30 × 76, 30 × 82, 30 × 83, 30 × 86, 30 × 90, 30 × 93, 30 × 94, 30 × 96, 30 × 98, 30 × 99, 30 × 100, 30 × 101, 30 × 102, 30 × 104, 30 × 105, 30 × 106, 30 × 108, 30 × 109, 30 × 110, 30 × 111, 30 × 113, 30 × 114, 30 × 115, 30 × 116, 30 × 117, 30 × 119, 30 × 120, 30 × 121, 30 × 123, 30 × 124, 30 × 125, 30 × 126, 30 × 127, 30 × 130, 30 × 131, 30 × 133, 30 × 134, 30 × 135, 30 × 137, 30 × 141, 30 × 143, 30 × 153
31 × 80, 31 × 90, 31 × 100, 31 × 110, 31 × 120, 31 × 130, 31 × 140, 31 × 150
33 × 90, 33 × 100, 33 × 110, 33 × 120, 33 × 130, 33 × 140, 33 × 150, 33 × 160, 33 × 170
34 × 50, 34 × 65, 34 × 70, 34 × 80, 34 × 85, 34 × 90, 34 × 95, 34 × 105, 34 × 110, 34 × 125
35 × 76, 35 × 80, 35 × 84, 35 × 86, 35 × 88, 35 × 90, 35 × 92, 35 × 94, 35 × 96, 35 × 98, 35 × 100, 35 × 102, 35 × 104, 35 × 106, 35 × 108, 35 × 110, 35 × 112, 35 × 114, 35 × 116, 35 × 118, 35 × 120, 35 × 122, 35 × 124, 35 × 126, 35 × 128, 35 × 130, 35 × 132, 35 × 134, 35 × 136, 35 × 138, 35 × 140, 35 × 142, 35 × 144, 35 × 146, 35 × 148, 35 × 150, 35 × 154, 35 × 158
36 × 65, 36 × 85, 36 × 90, 36 × 95, 36 × 100, 36 × 105, 36 × 110, 36 × 115, 36 × 120, 36 × 125, 36 × 135, 36 × 140, 36 × 145
37 × 70, 37 × 80, 37 × 90, 37 × 100, 37 × 110, 37 × 120, 37 × 130
38 × 50, 38 × 60, 38 × 65, 38 × 70, 38 × 75, 38 × 80, 38 × 85, 38 × 90, 38 × 95, 38 × 105
39 × 60, 39 × 80, 39 × 90, 39 × 100, 39 × 110, 39 × 130
40 × 60, 40 × 65, 40 × 68, 40 × 70, 40 × 74, 40 × 75, 40 × 76, 40 × 77, 40 × 78, 40 × 79, 40 × 80, 40 × 81, 40 × 82, 40 × 83, 40 × 84, 40 × 85, 40 × 86, 40 × 87, 40 × 88, 40 × 89, 40 × 90, 40 × 91, 40 × 92, 40 × 93, 40 × 94, 40 × 95, 40 × 96, 40 × 97, 40 × 98, 40 × 99, 40 × 100, 40 × 101, 40 × 102, 40 × 103, 40 × 104, 40 × 105, 40 × 106, 40 × 107, 40 × 108, 40 × 109, 40 × 110, 40 × 111, 40 × 112, 40 × 113, 40 × 114, 40 × 115, 40 × 116, 40 × 117, 40 × 118, 40 × 119, 40 × 121, 40 × 122, 40 × 123, 40 × 124, 40 × 126, 40 × 127, 40 × 129, 40 × 131, 40 × 132
41 × 60, 41 × 70, 41 × 80, 41 × 90, 41 × 100, 41 × 110
42 × 50, 42 × 60, 42 × 65, 42 × 70, 42 × 75, 42 × 80, 42 × 85, 42 × 90, 42 × 95, 42 × 105
43 × 60, 43 × 70, 43 × 80, 43 × 90, 43 × 100, 43 × 110
44 × 60, 44 × 65, 44 × 70, 44 × 75, 44 × 80, 44 × 85, 44 × 90, 44 × 95, 44 × 100, 44 × 105, 44 × 110, 44 × 115
45 × 48, 45 × 50, 45 × 52, 45 × 54, 45 × 56, 45 × 58, 45 × 60, 45 × 62, 45 × 64, 45 × 66, 45 × 68, 45 × 70, 45 × 72, 45 × 74, 45 × 76, 45 × 78, 45 × 80, 45 × 82, 45 × 84, 45 × 86, 45 × 88, 45 × 90, 45 × 92, 45 × 94
46 × 50, 46 × 65, 46 × 70, 46 × 75, 46 × 85
47 × 60, 47 × 70, 47 × 80, 47 × 90, 47 × 100, 47 × 110
48 × 50, 48 × 55, 48 × 60, 48 × 65, 48 × 70, 48 × 75, 48 × 80, 48 × 85
49 × 50, 49 × 60, 49 × 70, 49 × 80, 49 × 90
50 × 50, 50 × 52, 50 × 54, 50 × 56, 50 × 58, 50 × 60, 50 × 62, 50 × 64, 50 × 65, 50 × 66, 50 × 69, 50 × 70, 50 × 74, 50 × 77, 50 × 78, 50 × 81, ...
51 × 60, 51 × 80, ...
52 × 55, 52 × 60, ...
53 × 60, ...
57 × 60, ...
60 × 60, 60 × 61, 60 × 65, 60 × 69, 60 × 73, ...
...

smallest rectangle: 30 × 46




smallest odd rectangle: 34 × 65

The smallest rectangle was found by Marshall [1, Figure 2]. It has a unique tiling. See also [1, Figure 3] and [2, Figure 7] for a way to generalize this to get an infinite family of rectifiable polyominoes.
The smallest odd rectangle was given in [2, Figure 11].

References

[1] William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192.
[2] Michael Reid, Tiling Rectangles and Half Strips with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 80 (1997), no. 1, pp. 106-123.

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Updated May 17, 2012.