prime boxes of (82) Torsten Sillke >>>>>>>>>>> 3D complete <<<<<<<<<< Initial version: March 1993 Update: 2x12x25,30,35; 3x9x30; 3x12x15; H Postl [1] Update: 3x10x18-23,25,26,28,29; 3x20x13,14 H Postl [1] Update: 4x9x10; 4x15x6,7,9; 5x6x9; H Postl [1] Update: 6x6x1x,15; no 3x11xN H Postl [1] Update: 3x9x25 1998-08-03 Update: 3x9x35 1998-08-11 Update: 3x15x13, 14, 15 2008 Johan van de Konijnenberg Update: 3x20x16, 17 2008 Johan van de Konijnenberg Update: 3x25x13, 14 2008 Johan van de Konijnenberg Update: 5x7x7, 8, 9 2008 Johan van de Konijnenberg Update: 3x15x16, 17, 18, 19, 21 2009 Johan van de Konijnenberg 2 1 1 1 2x5x 5p, 8p, 10, 11p, 13, 14p, 15, 16, 17p, ... {13..17}+5n 4x5x 5, 8, 10, 11, 12p, 13, 14, ... {10..14}+5n 5x5x 2p, 4, 6, 8, 10, 11p, ... {10..11}+2n 6x5x 5, 7p, 8, 9p, ... {5..9}+5n 7x5x 6p, 7p, 8p, 9p, 10, 11, ... {6..11}+6n 2x10x 5, 8, 10, 11, 13, 14, 15, 16, 17, ... {13..17}+5n 3x10x 12p, 15p, 18p..23p, 24, 25p, 26p, 27, 28p, 29p, ... {18..29}+12n 4x10x 5, 6p, 7p, 8, 9p, ... {5..9}+5n 5x10x 2, 4, 5, ... {4,5}+2n 6x10x 4p, 5, 6p, 7, ... {4..7}+4n 2x15x 5, 8, 10, 11, 13, 14, 15, 16, 17, ... {13..17}+5n 3x15x 10p, 12p, 13p, 14p, 15p, 16p, 17p, 18p, 19p, 20, 21p ... {12..21}+10n 4x15x 5, 6p, 7p, 8, 9p, ... {5..9}+5n 6x15x 4p, 5, 6p, 7, ... {4..7}+4n 7x15x 4p, 5, 6, 7, ... {4..7}+4n 2x20x 5, 8, 10, 11, 12p, 13, 14, ... {10..14}+5n 3x20x 9p, 10p, 12, 13p, 14p, 15, 16p, 17p, 18, 19, 20, ... {12..20}+9n 2x25x 5, 8, 10, 11, 12p, 13, 14, ... {10..14}+5n 3x25x 9p, 10, 12, 13p, 14p, 15, 2x30x 5, 8, 10, 11, 12p, 13, 14, ... {10..14}+5n 3x30x 9p, 10, 12, 13, 14, 15 2x35x 5, 8, 10, 11, 12p, 13, 14, ... {10..14}+5n 3x35x 9p, 10, 12, 13, 14, 15 Impossible: 2xNx{3,4,6,7,9} 3xNx{3,4,5,6,7,8,11} 4xNx4 2x12x{5,10,15} 3x9x{10,15} 3x10x{10,13,14,16,17} 4x5x{6,7,9} 5x5x{5,7,9} 5x6x6 Annotations: cross symmetry 2 b b 2 2 2 = a a a b b b 2 a a the 2x5x(5+3n) boxes: 1 1 1 8 7 1 1 1 . . 1 1 1 . . 5 5 5 4 3 2 2 x 8 7 2 2 x . . 2 1 x . . 6 5 x 4 3 3 x x x 7 3 x x x . . x x x . . x x x 3 3 4 x 6 6 3 4 x 5 6 . . x 3 4 . . x 2 2 3 4 5 5 5 3 4 5 5 5 . . 3 3 3 . . 1 1 1 2 1 8 8 8 2 1 . . 2 2 2 . . 6 6 6 4 4 4 2 1 x 7 7 2 1 x . . 2 1 x . . 6 5 x 3 3 2 x x x 6 2 x x x . . x x x . . x x x 2 3 3 x 5 6 3 3 x 5 6 . . x 3 4 . . x 1 2 4 4 4 5 6 4 4 4 6 6 6 . . 4 4 4 . . 1 2 the 2x12x20 box (unique solution upto x-symmetry, symmetric) 01 98 92 92 92 76 76 76 65 59 51 51 51 41 33 33 33 98 98 98 01 98 95 92 83 77 77 77 65 59 52 52 48 41 34 33 26 22 01 01 01 95 95 95 82 82 77 70 66 59 53 48 48 42 34 29 29 29 19 02 02 02 94 89 84 78 70 70 62 62 53 50 48 43 34 35 29 19 19 02 03 96 96 96 85 78 78 70 63 63 53 50 45 36 35 35 35 23 19 02 03 99 93 85 85 78 71 71 71 64 57 50 45 37 37 37 27 23 17 17 03 99 93 93 85 80 74 69 64 64 64 49 49 49 37 30 24 20 20 20 04 00 93 86 87 79 74 69 67 60 54 54 54 38 38 30 30 21 21 21 04 00 XX 87 87 79 74 72 67 60 55 55 46 39 39 30 28 XX 04 04 04 XX XX XX 87 79 72 72 72 60 56 56 56 40 40 40 XX XX XX 05 05 05 XX 91 88 81 75 73 68 61 58 56 47 44 40 32 31 XX 06 05 06 06 06 88 88 88 73 73 73 58 58 58 44 44 44 31 31 31 06 05 98 98 98 83 83 83 76 65 65 65 52 51 41 41 41 26 26 26 98 01 01 01 95 92 83 82 76 66 59 59 52 51 42 42 42 33 26 22 98 01 02 94 89 89 89 82 77 66 66 62 52 48 43 42 34 34 22 22 22 01 02 94 94 89 84 82 70 66 63 62 53 53 43 43 36 35 29 19 02 02 02 94 96 84 84 84 78 71 63 62 50 50 43 36 36 27 23 23 23 17 03 03 96 85 80 80 80 71 63 64 57 45 45 45 36 27 27 24 20 17 99 99 99 93 86 80 69 69 69 57 57 57 49 38 37 27 24 24 20 17 00 00 00 86 86 74 74 67 67 67 55 54 49 38 39 28 30 24 21 04 04 04 XX 87 86 79 79 72 60 60 55 54 46 38 39 28 28 XX 21 04 05 XX XX XX 81 81 81 68 68 68 55 46 46 46 39 28 XX XX XX 04 05 06 XX 91 88 81 75 73 68 61 58 56 47 44 40 32 31 XX 05 05 05 06 91 91 91 75 75 75 61 61 61 47 47 47 32 32 32 06 06 06 the 3x10x12 box is unique 77 78 64 64 64 46 46 46 27 27 27 12 78 78 78 64 55 47 46 33 33 33 21 13 79 79 79 65 56 47 47 40 33 21 21 13 80 79 65 65 56 47 40 40 40 22 21 13 80 80 70 65 56 48 41 41 28 22 22 17 80 70 70 63 52 52 45 34 29 22 17 17 81 71 70 58 58 58 49 34 29 29 23 17 81 71 71 66 58 49 49 34 29 23 23 23 81 71 66 66 66 53 49 39 35 24 24 24 82 72 72 72 53 53 53 35 35 35 24 16 77 78 67 55 55 55 37 37 37 27 18 12 77 77 67 64 55 50 46 37 30 27 12 12 74 74 68 59 54 44 47 40 33 21 13 13 75 79 65 56 56 48 48 41 31 19 14 14 75 80 63 60 52 48 38 41 28 28 22 11 75 70 63 63 52 51 45 41 26 28 17 11 76 76 69 61 52 45 45 34 34 29 23 11 81 81 71 66 58 49 42 36 32 20 15 15 82 82 72 62 57 53 43 39 35 25 16 16 82 73 72 57 57 57 39 39 39 25 24 16 77 67 67 67 50 50 50 30 30 30 18 12 74 68 59 59 59 50 44 37 30 18 18 18 74 68 68 59 54 44 44 31 31 31 19 14 74 68 60 54 54 54 44 38 31 19 19 14 75 75 60 60 51 48 38 38 28 26 19 14 76 69 60 63 51 51 45 38 26 26 11 11 76 69 69 61 51 42 36 36 36 26 20 15 76 69 61 61 61 42 42 36 32 20 20 15 73 73 73 62 57 42 43 32 32 32 20 15 82 73 62 62 62 43 43 43 25 25 25 16 the 5x5x11 box (odd) 03 03 03 89 79 79 79 66 66 66 56 04 04 89 89 85 79 71 71 60 60 60 05 97 90 89 80 80 80 67 68 60 57 05 97 97 91 86 80 76 68 68 57 57 05 97 91 91 91 76 76 76 68 58 57 04 03 96 85 85 85 71 65 66 56 56 04 03 89 90 85 79 71 69 66 56 54 04 00 90 90 83 78 71 67 67 60 55 05 05 97 91 86 80 76 68 67 57 58 02 02 02 86 86 86 70 70 70 58 58 99 95 96 82 82 82 69 65 65 54 56 00 96 96 96 77 77 69 69 65 54 54 00 00 90 83 83 78 69 67 63 54 55 00 02 94 83 78 78 78 70 63 55 55 01 02 94 84 84 84 75 70 64 58 53 99 95 95 87 82 77 72 65 59 59 59 99 99 95 87 82 77 72 62 62 52 52 98 98 92 81 83 77 73 63 63 63 55 01 01 93 88 84 75 74 64 61 53 51 01 94 94 94 84 75 75 64 64 53 53 99 95 87 87 87 72 72 72 62 59 52 98 92 92 92 81 73 73 73 62 59 52 98 93 92 81 81 74 73 61 62 51 52 98 93 93 88 81 74 74 61 61 51 51 01 93 88 88 88 74 75 61 64 51 53 the 3x9x20 box: 13 14 98 98 98 88 75 75 75 61 61 61 51 42 42 42 23 23 23 11 14 14 99 99 99 88 76 76 76 69 61 57 51 45 42 33 24 24 24 12 15 14 00 99 89 89 89 76 69 69 59 57 45 45 35 35 35 24 19 12 15 15 00 00 90 89 77 77 77 69 59 57 46 45 41 35 25 19 19 12 15 12 00 01 91 85 78 78 78 68 59 54 46 46 36 37 25 25 19 17 16 07 01 01 01 85 85 78 70 70 70 54 46 47 37 37 25 26 17 17 16 07 07 02 94 85 79 79 79 70 62 54 47 47 47 37 26 26 26 17 16 07 02 02 02 92 80 80 80 62 62 62 53 48 38 38 38 20 20 20 17 08 08 08 92 92 92 80 71 63 63 63 48 48 48 31 31 31 20 16 13 13 03 98 88 88 88 75 66 66 66 51 51 51 33 33 33 23 11 11 14 13 03 98 93 86 74 75 67 67 61 55 49 40 42 33 27 23 11 10 11 11 04 99 90 90 81 76 69 64 57 57 45 41 34 34 22 24 12 12 12 15 05 00 90 89 82 77 68 68 59 59 50 41 41 35 28 19 13 14 12 12 97 01 91 91 82 77 72 68 58 58 43 46 36 36 29 25 14 14 12 09 06 94 94 91 85 78 73 60 60 54 54 47 37 36 29 26 17 14 16 16 07 02 94 87 83 79 73 70 62 52 44 44 44 32 30 18 15 15 17 17 08 96 95 92 84 79 71 71 63 56 53 48 39 38 31 21 16 16 17 10 08 95 95 95 84 80 71 65 63 53 53 53 39 38 31 21 20 16 13 03 03 03 86 86 86 74 67 66 55 49 49 49 40 27 27 27 10 11 11 04 04 04 93 86 74 74 67 66 55 55 49 40 40 34 27 22 10 10 11 05 04 93 93 93 81 74 67 64 55 50 50 50 40 34 22 22 10 13 11 05 05 97 90 81 81 81 64 64 64 58 50 43 41 34 28 22 13 13 09 05 97 97 91 82 82 82 72 68 60 58 43 43 36 28 28 28 14 13 09 09 06 97 87 87 87 72 72 72 60 58 52 43 32 29 29 29 18 15 09 06 06 06 94 87 83 73 73 73 60 52 52 44 32 32 30 18 18 15 10 10 10 96 95 83 83 83 65 65 65 56 52 44 32 30 30 30 18 15 17 10 96 96 96 84 84 84 71 65 56 56 56 39 39 39 21 21 21 16 the 3x9x25 box: 159157144144144129129129112112112 97 96 86 78 78 78 67 57 57 57 41 41 41 31 157157157139139139129121111111111 96 96 86 86 78 67 67 67 57 51 40 40 40 30 156148148148131131131116110111101 94 96 86 84 74 74 62 62 51 51 51 40 35 30 156156148141132132126119110110101 94 94 84 84 73 66 66 66 49 49 38 35 35 30 156147141141130126126119110107101 94 92 83 84 72 72 72 55 55 55 38 38 35 27 153147147141130130126114107107107 92 92 89 81 71 72 64 53 53 53 38 37 27 27 153147146136130123124114114103103103 92 88 81 71 64 64 64 53 44 37 37 37 27 153146146146134123124114106106106 98 88 88 81 71 63 63 63 48 48 48 33 33 33 151145145145134123118118118106 98 98 98 88 75 75 75 59 59 59 42 42 42 33 25 159157150144139133121121121112105 97 97 90 79 79 79 67 58 58 58 47 41 31 31 159159150144139133129121117112104 96 97 90 86 78 74 69 62 57 51 47 41 31 32 158158149143132131128116115111104 95 95 85 85 77 74 68 62 56 49 46 40 30 30 155156148138132131127116116110101101 94 84 83 73 74 66 62 50 49 39 35 29 28 155155141142132126119119119107100100 93 83 83 73 73 66 61 55 49 45 38 28 28 155154147136136130125120108108108 92 89 89 82 76 72 64 54 55 44 44 37 27 28 153153146136137124124124114109103 91 89 81 81 71 71 65 60 53 44 43 34 26 26 152151145140135123123118113102103 98 88 87 80 75 70 63 59 52 48 42 36 25 25 151151145134134134122118113106 99 99 99 87 80 75 70 63 59 52 48 42 36 33 25 159150150150133133133117117117105 97 90 90 90 79 69 69 69 58 47 47 47 32 31 158149143143143128128128117105105105 95 85 77 79 68 69 56 58 46 46 46 32 32 158149149143138127128116115104104104 95 85 77 77 68 68 56 56 50 46 39 32 29 158149142138138127127115115115100 93 95 85 77 73 68 61 56 50 50 39 39 29 29 154155142142138127120120120108100 93 93 83 76 76 76 61 61 54 50 45 39 28 29 154154142137137137125120109108100 93 91 89 82 76 65 61 54 54 45 45 45 34 26 154152140136137125125125109109102 91 91 82 82 82 65 65 60 54 44 43 34 34 26 152152140140135122122122109102102 99 91 80 80 80 65 60 60 60 43 43 43 34 26 151152140135135135122113113113102 99 87 87 87 70 70 70 52 52 52 36 36 36 25 the 3x9x30 box = A & A: 90 88 75 75 75 59 59 59 49 37 32 32 32 21 . . . part A 88 88 88 68 68 68 59 49 49 37 37 32 21 21 21 . . 87 79 79 79 63 57 57 57 49 37 30 25 25 25 13 . . 87 87 79 71 63 62 57 46 46 46 30 30 25 13 13 . . 87 78 71 71 63 62 55 45 46 35 30 28 19 18 13 . . 84 78 78 71 67 55 55 45 45 39 28 28 18 18 18 . . 84 78 77 67 67 67 55 45 39 39 39 28 16 16 16 . . 84 77 77 77 66 60 50 50 50 34 34 34 23 16 . . . 82 76 76 76 60 60 60 43 43 43 34 23 23 23 . . . 90 88 81 75 68 65 52 52 52 42 33 33 33 21 15 . . 90 90 81 75 68 65 59 49 48 42 37 32 22 22 15 . . 89 89 80 74 64 58 58 47 48 41 31 31 31 20 14 . . 86 87 79 73 63 63 57 47 48 36 35 30 25 13 12 . . 86 86 71 73 62 62 62 47 46 35 35 29 19 18 12 . . 86 85 78 72 67 55 56 51 45 39 28 27 19 19 12 . . 84 84 77 70 61 61 54 44 40 40 27 27 17 11 11 . . 83 82 76 69 66 60 53 50 43 38 26 27 23 16 10 . . 82 82 76 66 66 66 53 50 43 38 34 24 24 24 10 . . 90 81 81 81 65 65 65 52 42 42 42 33 22 15 15 15 . 89 80 74 74 74 64 58 52 41 41 41 33 22 14 14 14 . 89 80 80 74 64 64 58 48 48 41 36 31 22 20 14 . . 89 80 73 73 73 64 58 47 47 36 36 31 20 20 20 . . 85 86 72 72 72 56 51 51 51 35 36 29 19 12 12 . . 85 85 70 72 61 56 56 51 44 40 29 29 29 17 11 . . 85 83 70 70 61 56 54 44 44 40 27 26 17 17 11 . . 83 83 70 69 61 54 54 54 44 40 26 26 24 17 11 . . 82 83 69 69 69 53 53 53 38 38 38 26 24 10 10 10 . the 3x9x35 box = A & B: 117108108108 92 92 92 81 69 69 69 58 47 47 47 38 32 22 20 . . part B 115107101101101 90 81 81 81 69 58 58 54 47 38 38 38 20 20 20 . 115107107101 90 90 79 73 73 73 63 58 52 41 36 30 30 30 19 13 . 115107100100100 90 79 79 73 66 63 51 52 41 36 36 30 19 19 13 . 112113 98 98 98 84 79 78 66 66 63 51 52 41 36 28 28 28 19 13 . 112112 97 98 88 84 76 76 76 66 61 51 49 44 34 27 28 17 17 17 . 112110 97 97 88 84 83 76 71 61 61 49 49 44 34 27 27 24 17 11 . 110110 97 96 88 83 83 83 71 64 61 55 49 44 34 27 24 24 24 . . 109110 96 96 96 82 82 82 71 64 55 55 55 39 39 39 23 23 23 . . 117116108102 95 92 86 81 70 70 70 54 54 54 42 38 32 22 20 15 . 117117108102 95 92 86 74 74 69 58 60 54 47 42 32 32 22 22 15 . 115115107101 90 85 80 80 68 68 68 59 53 46 37 31 31 31 21 14 . 113114106100 91 91 78 79 73 63 63 52 52 41 41 36 30 19 13 13 . 113113 99100 89 89 78 78 66 67 57 51 51 40 40 29 29 18 12 12 . 113112105 98 94 84 84 77 72 62 57 57 50 45 35 35 28 25 11 11 . 111111104 97 88 88 83 76 72 61 57 49 44 44 34 34 27 24 17 11 . 110109103 96 93 87 82 71 71 65 56 55 48 43 39 33 26 23 16 10 . 109109103 93 93 93 82 75 64 64 64 48 48 48 39 33 26 23 16 10 . 117116102102102 86 86 86 74 70 60 60 60 42 42 42 32 22 15 15 15 116116116 95 95 95 85 80 74 70 59 60 46 46 46 37 31 21 14 14 14 114106106106 91 85 85 80 74 68 59 59 53 46 37 37 31 21 21 14 . 114114106 99 91 89 85 80 67 68 59 53 53 53 40 37 29 21 18 12 . 114105 99 99 91 89 77 78 67 67 62 50 50 50 40 35 29 18 18 12 . 111105105 99 94 89 77 77 67 62 62 57 50 45 40 35 29 25 18 12 . 111105104 94 94 94 77 72 72 72 62 56 45 45 45 35 25 25 25 11 . 111104104104 93 87 75 75 75 65 56 56 48 43 33 33 33 16 16 16 . 109103103103 87 87 87 75 65 65 65 56 43 43 43 26 26 26 10 10 10 References: [1] Helmut Postl, many new prime boxes. letter from 9. July 1998