Prime Packings of the Pseudo-Pentomino glider Torsten Sillke, BI initial version 1993 Update: 15xk (k>=26) H. Postl Update: 20x19, H. Postl Update: 25x{16,17,19,21,23} Postl Update: 30x{13,14,15,17} Postl Update: 5x5x{6,7,9} Postl Update: 3x3x{20,25,30,35} Postl completed 2+3 dim, 1998-07-09, Postl 1 glider 1 . 1 1 1 2-dim: ------ 10x 6p, 10p, 12, 16, 18, 20, ... {16, 18, 20}+6n 15x 18p, 22p, 24p, 25p...35p, 36, 37p, 38p, 39p, 40, 41p, ... {24..41}+18n 20x 6, 10, 11p, 12, 16, 17, 18, 19p, 20, 21, ... {16..21}+6n 25x 12p, 13p, 15p, 16p, 17p, 18, 19p, 20, 21p, 22, 23p, 24, 25, 26, ... {15..26}+12n 30x 6, 10, 12, 13p, 14p, 15p, 16, 17p, ... {12..17}+6n 35x 11p, 12, 13p, 14p, 15p, 16, 17p, 18, 19p, 20, 21p, ... {11..21}+11n 40x 6, 10, 11, 12, 13p, 14p, 15, ... {10..15}+6n 45x 12, 13p, 14p, 15, 16, 17, 18, 19, 20, 21, 22, 23, ... {12..23}+12n 50x 6, 10, 11p, 12, 13, 14p, 15, ... {10..15}+6n 55x 11, 12, 13, 14p, 15, 16, 17, 18, 19, 20, 21, ... {11..21}+11n 60x 6, 10, 11, 12, 13, 14, 15, ... {10..15}+6n 65x 11p, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, ... {11..21}+11n Nx 6, 10, 11, 12, 13, 14, 15, ... {10..15}+6n 3-dim: ------ 3x5x 4p, 6p, 7p, 8, 9p, ... {6..9}+4n 4x5x 3p, 4p, 5p, ... {3..5}+3n 5x5x 4p, 6p, 7p, 8, 9p, ... {6..9}+4n 6x5x 3p, 4, 5p ... {3..5}+3n further prime boxes: 3x3x{20,25,30,35} Complete list of prime rectangles (# = 46): 6x10, 10x10, 11x{20,35,50,65}, 12x25, 13x{25,30,35,40,45}, 14x{30,35,40,45,50,55}, 15x{18,22,24-35,37,38,39,41}, 16x25, 17x{25,30,35}, 19x{20,25,35}, 21x{25,35}, 23x25. Complete list of prime boxes (# = 13): 3x3x{20,25,30,35}, 3x4x5, 3x5x{6,7,9}, 4x4x5, 4x5x5, 5x5x{6,7,9}. Impossible: Nx{3,4,5,7,8,9} 6x5u with u odd. 10xu with u odd. 10x14 11x{15,25,30,45} 12x15 13x{15,20} 14x{15,20,25} 15x{15,16,17,19,20,21,23} 3x3x{5,10,15} 5x5x{3,5} Annotations: two gliders give the following decominoes 1 1 2 1 2 1 2 1 1 2 1 2 1 2 2 2 1 1 2 2 rectangle 6x10: unique 1 1 1 2 2 2 3 3 3 3 1 1 1 2 4 4 4 3 3 3 1 1 1 1 2 4 4 3 3 3 5 5 5 5 6 4 4 7 7 7 5 5 5 6 4 4 4 7 7 7 5 5 5 6 6 6 7 7 7 7 rectangle 10x10: unique 1 1 1 1 b b b b b b 1 1 1 1 b b b b b b 1 2 2 1 3 b b b b b 4 2 3 2 3 b b b b b 4 2 4 3 3 b b b c c 4 4 d d d c c c c c d d d d d c c c c c d d d d d c c c c c d d d d d d c c c c d d d d d d c c c c rectangle 13x25: unique solution (odd) 69 69 67 60 60 60 58 58 50 50 50 40 40 40 38 32 32 28 28 21 21 21 10 10 10 69 67 69 60 61 58 54 58 50 46 46 46 38 40 38 32 28 32 28 21 18 18 18 11 10 69 67 67 67 60 61 54 58 54 50 47 46 40 38 38 32 29 29 28 25 21 19 18 10 11 70 70 70 61 61 61 54 54 55 47 46 41 41 41 39 33 29 25 29 25 19 18 11 11 11 70 71 71 62 62 62 55 56 55 47 47 47 39 41 39 33 29 33 25 25 19 19 19 12 12 71 70 71 62 63 63 56 55 55 48 48 48 41 39 39 33 33 26 26 26 20 20 12 15 12 72 72 71 63 62 63 56 56 56 48 49 42 42 42 34 34 34 27 27 26 20 15 20 15 12 72 68 72 66 66 63 57 51 51 51 48 49 43 42 35 35 34 27 26 27 20 16 15 15 13 72 68 66 68 66 64 57 51 57 49 49 49 42 43 35 34 35 27 23 23 23 16 13 16 13 73 68 68 64 66 64 57 57 51 52 44 43 43 43 35 36 30 30 30 24 23 16 16 13 13 73 74 73 65 64 64 59 52 53 52 44 45 44 36 37 36 30 31 24 23 22 17 17 17 14 73 73 74 65 59 65 59 53 52 52 44 44 45 37 36 36 31 30 24 24 24 22 14 17 14 74 74 74 65 65 59 59 53 53 53 45 45 45 37 37 37 31 31 31 22 22 22 17 14 14 rectangle 11x35: (odd) 82 82 82 75 75 75 69 69 66 66 61 61 58 58 53 53 53 45 45 45 39 39 39 31 31 31 25 25 25 19 19 19 10 10 10 82 83 78 78 78 75 69 66 69 66 61 58 61 58 53 48 48 48 46 45 40 40 39 31 32 32 26 26 25 19 20 20 10 11 11 83 82 78 79 75 72 69 70 70 66 61 59 59 58 55 53 49 48 45 46 40 39 40 32 31 32 26 25 26 20 19 20 11 10 11 83 83 83 78 79 72 70 72 70 67 62 59 55 59 55 49 48 46 46 46 40 36 35 35 35 32 26 22 22 22 16 20 15 15 11 84 84 79 79 79 72 72 67 70 67 62 59 62 55 55 49 49 49 42 42 42 36 35 36 29 29 29 23 23 22 16 15 16 15 12 84 81 84 80 80 73 73 73 67 67 62 62 56 56 56 50 50 50 42 43 43 36 36 35 29 30 30 23 22 23 16 16 12 15 12 84 81 80 81 80 73 74 74 65 65 64 64 57 57 56 50 51 51 43 42 43 37 37 37 30 29 30 23 24 24 17 17 17 12 12 85 81 81 76 80 74 73 74 65 64 65 64 57 56 57 51 50 51 44 44 43 37 38 33 33 33 30 24 27 24 17 18 13 13 13 85 86 85 76 77 76 71 74 65 68 63 64 57 60 54 54 52 51 44 47 44 41 37 38 34 33 27 28 27 24 21 17 18 14 13 85 85 86 76 76 77 71 68 71 68 63 60 63 60 54 52 54 47 44 47 41 38 38 38 33 34 28 27 27 21 18 18 18 13 14 86 86 86 77 77 77 71 71 68 68 63 63 60 60 54 52 52 52 47 47 41 41 41 34 34 34 28 28 28 21 21 21 14 14 14 rectangle 17x30: 53 53 50 50 41 41 41 29 29 29 20 20 20 10 10 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 53 50 53 50 41 37 37 37 30 29 20 21 12 12 12 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 53 51 51 50 48 41 38 37 29 30 21 20 12 13 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 54 51 48 51 48 38 37 30 30 30 21 21 21 12 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 54 51 54 48 48 38 38 38 33 24 24 22 13 13 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 54 54 55 44 44 44 33 34 33 24 22 24 14 14 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 55 56 55 44 45 45 34 33 33 24 22 22 22 15 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 56 55 55 45 44 45 34 34 34 25 25 25 15 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 56 56 56 46 46 45 39 35 35 26 26 25 15 15 15 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 57 57 57 46 49 46 35 39 35 26 25 26 16 11 11 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 57 58 49 46 49 39 39 39 35 26 27 27 16 11 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 58 57 52 49 49 40 40 36 36 27 23 27 16 16 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 58 58 58 52 42 40 36 40 36 31 23 27 23 17 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 59 52 52 52 42 40 42 31 36 31 23 23 17 18 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 59 60 59 47 42 42 43 32 31 31 28 18 19 18 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 59 59 60 47 43 47 43 32 28 32 28 19 18 18 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 60 60 60 47 47 43 43 32 32 28 28 19 19 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 References: [1] H. Postl many new prime packings. letter from 9. July 1998