An almost-perfect cuboid is defined as a cuboid that has 6 out of the 7 lengths as rational. Such cuboids can be sorted into three types, called Body, Edge, and Face cuboids. In the case of the Body cuboid, the body (space) diagonal g is irrational. For the Edge cuboid, one of the edges a, b, c is irrational. The Face cuboid has just one of the face diagonals d,e,f irrational. The Body cuboid is commonly referred to as the Euler cuboid in honor of Leonard Euler, who discussed this type of cuboid. He was also aware of Face cuboids, and provided the (104, 153, 672) example.
Face cuboids generationg fomula:
IF
m, n, p, q in Z
m, p > 0
n, q ≥ 0
m+n ≡ 1 (mod 2)
p+q ≡ 1 (mod 2)
m^2+n^2 > p^2+q^2
mp > nq
gcd((m^2+n^2)-(p^2+q^2), mp-nq, mq+np) = 1
THEN
a := (m^2+n^2)-(p^2+q^2)
b := 2*(mp-nq)
c := 2*(mq+np)
d := sqrt(a^2+b^2)
e := sqrt(b^2+c^2)
f := sqrt(c^2+a^2)
g := (m^2+n^2)+(p^2+q^2) = sqrt(a^2+b^2+c^2)
Primitive data:
#, m, n, p, q
1, 8, 19, 16, 4
2, 20, 11, 20, 2
3, 28, 0, 15, 8
4, 28, 4, 7, 16
5, 28, 16, 7, 4
6, 15, 32, 30, 4
7, 35, 28, 30, 24
8, 30, 40, 40, 9
9, 40, 42, 33, 0
10, 45, 24, 24, 10
11, 14, 46, 43, 8
12, 47, 8, 14, 14
13, 48, 18, 29, 4
14, 50, 36, 12, 5
15, 52, 47, 24, 6
16, 53, 8, 6, 24
17, 55, 48, 24, 10
18, 11, 60, 58, 0
19, 59, 60, 46, 24
20, 62, 40, 41, 44
21, 55, 44, 64, 2
22, 64, 52, 53, 8
23, 68, 1, 32, 44
24, 56, 70, 31, 8
25, 76, 45, 36, 30
26, 44, 77, 74, 32
27, 80, 39, 40, 42
28, 64, 80, 73, 40
29, 36, 84, 56, 15
30, 86, 64, 28, 7
31, 87, 84, 64, 8
32, 91, 28, 78, 24
33, 93, 24, 32, 40
34, 96, 18, 36, 73
35, 99, 20, 24, 70
36, 28, 101, 48, 6
37, 105, 88, 52, 0
38, 105, 56, 90, 56
39, 107, 20, 30, 24
40, 112, 15, 40, 42
41, 112, 15, 42, 40
42, 112, 68, 28, 17
43, 112, 15, 24, 70
44, 112, 15, 70, 24
45, 120, 22, 55, 48
46, 120, 22, 48, 55
47, 101, 120, 120, 60
48, 112, 126, 59, 12
49, 126, 120, 120, 35
50, 55, 132, 70, 24
51, 140, 51, 60, 32
52, 48, 140, 99, 0
53, 143, 16, 52, 44
54, 143, 44, 52, 16
55, 144, 60, 56, 105
56, 144, 50, 65, 108
57, 144, 64, 72, 129
58, 130, 144, 117, 44
59, 64, 148, 137, 4
60, 153, 104, 94, 0
61, 160, 46, 35, 28
62, 100, 160, 139, 80
63, 165, 144, 80, 60
64, 165, 164, 66, 4
65, 168, 49, 12, 16
66, 174, 110, 145, 132
67, 176, 128, 172, 41
68, 177, 116, 64, 12
69, 138, 184, 77, 36
70, 184, 138, 105, 36
71, 112, 180, 187, 0
72, 192, 80, 80, 39
73, 144, 192, 144, 17
74, 128, 204, 204, 17
75, 105, 208, 152, 0
76, 208, 105, 120, 182
77, 208, 105, 182, 120
78, 209, 120, 182, 0
79, 120, 182, 209, 0
80, 216, 66, 64, 177
81, 216, 63, 198, 40
82, 224, 28, 49, 128
83, 46, 226, 128, 13
84, 184, 230, 100, 43
85, 231, 160, 176, 210
86, 231, 160, 210, 176
87, 117, 240, 48, 20
88, 240, 102, 153, 100
89, 247, 64, 152, 104
90, 247, 104, 152, 64
91, 251, 16, 16, 4
92, 252, 115, 240, 70
93, 255, 32, 120, 90
94, 256, 224, 241, 112
95, 192, 258, 104, 59
96, 258, 152, 244, 51
97, 184, 235, 260, 124
98, 266, 86, 88, 53
99, 267, 248, 126, 56
100, 285, 152, 56, 90
101, 288, 175, 264, 110
102, 290, 66, 165, 116
103, 256, 295, 230, 184
104, 296, 0, 195, 28
105, 306, 136, 128, 3
106, 308, 33, 56, 6
107, 186, 314, 237, 32
108, 315, 80, 84, 80
109, 92, 320, 155, 40
110, 323, 36, 216, 162
111, 324, 130, 96, 195
112, 330, 36, 55, 216
113, 330, 216, 55, 36
114, 140, 336, 336, 45
115, 340, 189, 56, 42
116, 352, 15, 330, 16
117, 188, 353, 296, 74
118, 340, 353, 284, 80
119, 357, 88, 102, 308
120, 357, 308, 102, 88
121, 214, 366, 283, 48
122, 380, 171, 40, 18
123, 380, 18, 40, 171
124, 235, 384, 90, 24
125, 384, 12, 337, 40
126, 385, 44, 70, 8
127, 336, 389, 192, 112
128, 390, 56, 105, 208
129, 390, 56, 208, 105
130, 391, 120, 120, 160
131, 391, 276, 238, 168
132, 392, 93, 182, 312
133, 392, 260, 320, 217
134, 396, 128, 204, 289
135, 400, 254, 44, 55
136, 254, 400, 400, 115
137, 404, 256, 53, 8
138, 411, 240, 380, 240
139, 416, 234, 112, 63
140, 416, 19, 26, 304
141, 416, 87, 264, 198
142, 418, 240, 240, 275
143, 352, 420, 323, 0
144, 430, 56, 308, 155
145, 432, 57, 152, 162
146, 432, 57, 328, 96
147, 433, 336, 314, 378
148, 435, 232, 288, 330
149, 440, 170, 272, 275
150, 279, 440, 396, 80
151, 440, 275, 284, 400
152, 416, 384, 440, 45
153, 440, 384, 440, 99
154, 441, 112, 248, 186
155, 448, 27, 258, 56
156, 300, 455, 320, 156
157, 460, 391, 280, 238
158, 465, 120, 370, 32
159, 465, 368, 180, 112
160, 388, 470, 451, 160
161, 443, 472, 184, 46
162, 479, 300, 300, 2
163, 485, 20, 22, 32
164, 486, 48, 228, 209
165, 383, 488, 88, 32
166, 495, 156, 418, 240
167, 496, 155, 224, 70
168, 496, 70, 224, 155
169, 496, 62, 311, 112
170, 282, 490, 501, 84
171, 503, 148, 266, 326
172, 88, 507, 344, 6
173, 509, 344, 328, 82
174, 344, 509, 424, 64
175, 510, 64, 168, 315
176, 510, 14, 392, 135
177, 280, 511, 64, 2
178, 513, 76, 324, 48
179, 513, 324, 76, 48
180, 516, 43, 96, 298
181, 516, 90, 125, 396
182, 520, 110, 91, 104
183, 524, 260, 293, 260
184, 528, 121, 96, 216
185, 220, 528, 312, 25
186, 528, 33, 374, 184
187, 471, 528, 224, 140
188, 133, 532, 304, 26
189, 536, 134, 251, 16
190, 536, 274, 303, 192
191, 544, 408, 176, 57
192, 409, 544, 238, 140
193, 486, 546, 268, 217
194, 552, 230, 48, 55
195, 385, 552, 372, 0
196, 296, 555, 546, 272
197, 556, 209, 388, 190
198, 280, 547, 560, 196
199, 560, 476, 540, 459
200, 124, 565, 172, 10
201, 568, 340, 395, 520
202, 572, 136, 187, 416
203, 572, 416, 187, 136
204, 517, 572, 416, 236
205, 574, 154, 452, 127
206, 575, 296, 260, 208
207, 332, 576, 297, 36
208, 350, 576, 255, 136
209, 576, 582, 27, 4
210, 584, 141, 360, 160
211, 588, 53, 246, 244
212, 360, 598, 240, 117
213, 598, 120, 180, 507
214, 252, 601, 546, 208
215, 605, 528, 320, 156
216, 608, 105, 190, 336
217, 608, 105, 336, 190
218, 609, 200, 560, 192
219, 611, 64, 188, 208
220, 612, 416, 221, 60
221, 544, 612, 423, 204
222, 150, 616, 513, 0
223, 620, 403, 240, 156
224, 624, 50, 195, 216
225, 624, 50, 588, 91
226, 632, 205, 116, 10
227, 392, 601, 658, 64
228, 660, 255, 530, 136
229, 472, 678, 631, 276
230, 378, 680, 679, 0
231, 632, 682, 560, 35
232, 688, 86, 96, 597
233, 692, 655, 416, 260
234, 696, 0, 105, 88
235, 696, 177, 316, 222
236, 504, 550, 697, 0
237, 698, 22, 149, 176
238, 700, 123, 574, 150
239, 702, 92, 216, 299
240, 560, 702, 60, 25
241, 704, 366, 484, 129
242, 707, 100, 326, 500
243, 376, 706, 708, 177
244, 713, 144, 372, 276
245, 713, 276, 372, 144
246, 714, 130, 364, 255
247, 717, 380, 240, 256
248, 720, 483, 672, 380
249, 672, 728, 513, 8
250, 252, 735, 624, 50
251, 391, 740, 370, 58
252, 740, 0, 231, 520
253, 740, 260, 481, 400
254, 740, 400, 481, 260
255, 757, 72, 96, 694
256, 758, 96, 324, 93
257, 758, 76, 643, 16
258, 759, 280, 120, 288
259, 760, 39, 150, 80
260, 764, 680, 336, 255
261, 768, 224, 224, 207
262, 432, 768, 516, 131
263, 770, 264, 315, 264
264, 528, 630, 775, 168
265, 777, 464, 504, 378
266, 780, 416, 315, 572
267, 731, 780, 366, 0
268, 784, 756, 579, 72
269, 588, 791, 108, 32
270, 792, 495, 730, 256
271, 792, 715, 608, 594
272, 798, 80, 105, 608
273, 798, 80, 608, 105
274, 801, 300, 320, 300
275, 805, 348, 670, 0
276, 720, 807, 500, 240
277, 812, 645, 110, 96
278, 815, 496, 730, 400
279, 695, 816, 510, 128
280, 824, 794, 287, 112
281, 828, 205, 720, 76
282, 836, 181, 148, 292
283, 838, 242, 428, 373
284, 840, 31, 564, 84
285, 840, 642, 220, 59
286, 495, 840, 840, 154
287, 840, 630, 605, 528
288, 841, 528, 696, 638
289, 845, 272, 526, 250
290, 336, 850, 473, 0
291, 850, 776, 792, 495
292, 855, 532, 782, 240
293, 855, 832, 680, 510
294, 864, 218, 148, 471
295, 360, 864, 575, 48
296, 870, 404, 604, 261
297, 874, 86, 272, 817
298, 580, 879, 564, 230
299, 880, 90, 429, 396
300, 840, 882, 667, 156
301, 121, 884, 656, 26
302, 888, 178, 109, 96
303, 888, 594, 148, 99
304, 888, 185, 624, 130
305, 888, 130, 624, 185
306, 712, 890, 620, 37
307, 892, 335, 336, 210
308, 780, 896, 780, 203
309, 897, 76, 456, 498
310, 828, 897, 568, 198
311, 614, 910, 585, 192
312, 912, 127, 244, 144
313, 892, 503, 916, 164
314, 920, 190, 232, 493
315, 920, 207, 570, 136
316, 920, 230, 361, 596
317, 920, 207, 816, 340
318, 924, 396, 409, 840
319, 840, 704, 925, 372
320, 935, 408, 770, 336
321, 936, 310, 624, 315
322, 845, 936, 660, 352
323, 942, 912, 424, 149
324, 944, 177, 216, 438
325, 945, 792, 230, 0
326, 945, 240, 448, 840
327, 949, 236, 64, 4
328, 950, 264, 285, 880
329, 950, 264, 880, 285
330, 952, 186, 527, 336
331, 495, 952, 520, 0
332, 495, 952, 644, 0
333, 172, 958, 604, 41
334, 960, 799, 884, 240
335, 960, 848, 900, 795
336, 960, 900, 848, 795
337, 968, 352, 383, 488
338, 977, 448, 212, 28
339, 980, 357, 576, 350
340, 689, 980, 560, 52
341, 943, 984, 984, 162
342, 436, 990, 968, 405
343, 635,1000, 428, 80
344, 904,1014, 368, 207
345,1016, 288, 336, 441
346,1020, 8, 255, 512
347,1022, 0, 111, 680
348,1032, 0, 455, 528
349,1032, 264, 473, 576
350,1032, 576, 473, 264
351, 931,1020,1038, 0
352,1040, 590, 416, 559
353, 462,1040, 969, 0
354,1050, 360, 608, 105
355,1060, 272, 100, 71
356,1070, 856, 824, 815
357, 930, 992,1076, 795
358,1068, 624,1079, 172
359,1080, 329, 672, 754
360,1080, 435,1028, 240
361,1083, 228, 184, 634
362,1084, 440, 776, 379
363, 840,1026,1085, 132
364, 984,1086, 493, 232
365,1088, 66, 540, 629
366, 740, 994,1108, 455
367,1112, 182, 24, 21
368,1136, 894, 924, 379
369, 735,1088,1140, 272
370, 80,1146, 636, 25
371,1152, 16, 636, 873
372,1157, 608, 494, 608
373, 560,1161, 560, 126
374, 560,1161, 560, 192
375, 823,1164,1080, 486
376,1171, 856, 376, 436
377, 220,1177, 740, 64
378, 722,1192, 916, 229
379,1196, 317, 554, 248
380,1200, 49, 210, 280
381,1200, 49, 280, 210
382,1200, 61, 540, 2
383,1204, 560, 485, 644
384, 844, 935,1208, 220
385,1188,1209, 624, 182
386,1216, 210, 341, 420
387, 988,1216, 824, 461
388,1224, 7, 36, 238
389,1224, 238, 36, 7
390,1224, 70,1015, 348
391,1224,1105, 960, 468
392,1114,1016,1228, 637
393,1229, 596, 692, 542
394,1232, 300, 429, 460
395,1232, 287, 328,1078
396, 561,1240, 198, 40
397,1240, 369, 558, 820
398,1248, 754, 336, 203
399, 806,1254,1097, 492
400,1256, 785, 680, 158
401,1136,1259,1042, 82
402,1260, 797, 840, 942
403, 869,1264,1172, 608
404, 280,1273, 560, 64
405,1276, 745, 832, 550
406,1288, 922, 476, 499
407,1042,1296, 209, 132
408, 978,1296, 988, 285
409,1076,1300,1300,1003
410,1303, 492, 406, 336
411,1304, 356, 472, 467
412,1304, 606,1169, 84
413,1305, 592, 360, 480
414,1305, 52, 884, 450
415,1320, 550, 912, 215
416, 385,1320,1320, 126
417,1324, 121, 748, 898
418,1330, 864, 700, 255
419,1345,1052, 624, 390
420,1360, 663, 280, 294
421, 980,1360, 112, 35
422,1360, 222,1095, 584
423,1048,1362,1183, 672
424,1368, 951,1072, 402
425, 360,1371, 720, 100
426,1264,1027,1376, 268
427,1378, 208, 172, 433
428, 476,1379, 928, 58
429,1386, 280, 280, 165
430,1391,1004,1118, 998
431,1393, 224, 584, 122
432,1394, 368, 656,1207
433,1404, 465, 570, 136
434, 960,1405, 136, 6
435,1408, 33, 726, 64
436,1368,1413,1118, 424
437,1420, 227, 800, 634
438,1420, 504, 603, 980
439,1422, 492,1339, 316
440,1432, 587, 888, 732
441,1432, 999, 846, 752
442,1439, 504,1320, 504
443,1440, 93,1020, 544
444, 944,1441, 882, 528
445, 817,1444, 448, 196
446,1444, 932, 773, 44
447,1460, 238,1241, 280
448,1462, 702, 884,1161
449,1463, 272, 532, 748
450,1463, 748, 532, 272
451,1464, 66, 629, 296
452,1349,1464, 586, 384
453,1470,1400, 992, 705
454, 504,1470,1472, 495
455,1480, 969,1002,1336
456,1484,1309, 424, 374
457,1488, 385, 682, 840
458,1488, 385, 840, 682
459,1496, 153,1232, 126
460,1220,1502, 389, 160
461,1504, 564,1197, 896
462,1504,1222,1077, 228
463,1507, 572, 548, 208
464,1278,1508,1508, 585
465,1509, 888, 448, 476
466,1512, 242, 528, 693
467,1512, 55,1120, 384
468,1365,1512,1480,1110
469,1515, 808, 870, 616
470,1110,1520,1188, 363
471,1044,1520,1320, 385
472,1520,1239,1482,1160
473,1536, 996, 376, 179
474,1536, 525, 648, 700
475,1543, 188, 244, 976
476,1547, 372,1054, 546
477,1548, 513, 382, 282
478, 864,1548, 584, 141
479,1552, 284, 136, 187
480,1330,1560, 992, 705
481,1566, 804,1148,1057
482, 768,1568,1340, 255
483,1572, 856, 648, 449
484,1579, 852,1128, 544
485,1580,1264, 976, 625
486,1584, 396, 808,1069
487,1584,1084, 828, 883
488,1586, 76, 104,1159
489,1588, 88, 295, 760
490,1590, 190, 636,1301
491, 560,1518,1593, 0
492,1594, 876, 699,1004
493, 528,1596,1483, 76
494,1600, 399, 920, 966
495,1600, 880,1321, 440
496,1220,1600,1555, 712
497,1602,1488,1464, 101
498, 728,1603,1222, 128
499,1604, 461, 322, 368
500,1608, 626, 264, 83
501,1610,1372,1400,1415
502,1614, 324, 437,1388
503,1616,1339, 890, 520
504,1290,1624,1008, 135
505,1344,1624,1084, 129
506, 240,1627, 480, 36
507,1630,1304, 695, 64
508,1632, 850, 701, 60
509,1632, 276,1415, 368
510,1642, 444, 417, 444
511,1653, 720, 624, 260
512,1656, 690,1080, 329
513,1656, 414, 988, 893
514,1661,1004,1474, 16
515,1664, 275,1300, 352
516,1088,1583,1666, 280
517,1672, 911, 664, 902
518,1672,1575, 576, 240
519, 832,1673, 862, 182
520,1679, 920, 740, 64
521,1680, 116,1015, 192
522,1680, 116, 192,1015
523,1680, 260, 975, 448
524,1680, 260, 448, 975
525,1159,1680, 638, 0
526, 819,1680,1680, 260
527,1680, 900, 840,1459
528, 984,1681,1416, 162
529,1688,1266,1368, 651
530,1692, 431,1368, 114
531,1698, 162,1016, 221
532,1700, 544, 215, 620
533,1701, 960, 562, 380
534,1702, 840,1053, 840
535,1702, 912, 912,1291
536,1711, 660, 870,1298
537,1712, 188, 609, 336
538, 677,1712,1670, 460
539,1716, 19, 962, 888
540,1665,1716, 320, 156
541,1716,1190,1309,1560
542,1720, 996,1473, 872
543,1290,1720,1360, 663
544,1725, 144, 200,1242
545,1725, 144,1242, 200
546,1733, 932, 566, 514
547,1736, 434,1651, 536
548,1740, 19, 58, 570
549,1744, 92,1084, 337
550,1746,1304,1476, 241
551,1754, 40, 155, 40
552,1760,1555, 952, 448
553,1760,1320,1320, 689
554,1358,1760,1631,1100
555,1763, 84, 464, 870
556,1764,1344,1579, 672
557,1440,1769,1440, 768
558,1780, 960,1389,1080
559,1339,1784, 848, 212
560, 744,1789,1690, 576
561,1796, 469, 868,1568
562,1800, 485, 224, 210
563,1800, 768,1060, 9
564,1260,1819,1260, 142
565,1820, 624, 624, 315
566,1824,1080,1137, 160
567,1824,1419,1496, 704
568,1415,1828,1810,1312
569,1829, 372, 272, 306
570, 192,1833,1664, 76
571,1836, 543, 544, 612
572,1842,1096,1476, 123
573,1632,1852, 880, 561
574,1859, 128, 416, 572
575,1859, 44, 728, 896
576, 840,1870, 407, 0
577,1870, 52,1768, 55
578,1880, 269, 904, 356
579,1109,1880,1640, 82
580,1884,1143, 398, 96
581,1888, 472, 716, 689
582,1890, 496, 728, 615
583,1892, 183, 930, 880
584,1906, 46,1427, 248
585,1288,1920,1785, 688
586,1734,1224,1923, 848
587,1924, 690, 711,1744
588,1924, 925,1872, 900
589,1925, 924, 450, 216
590,1929,1656, 472, 18
591,1932,1561, 248, 114
592,1943, 300, 402,1450
593,1944,1021, 608, 228
594,1563,1944,1558, 984
595,1846,1946,1148, 143
596,1948, 723, 192, 248
597,1961, 184,1862, 322
598,1632,1524,1961, 212
599,1962, 378,1152,1243
600,1975,1356,1884, 950
601,1976, 741, 608,1542
602, 678,1978, 731, 36
603,1980, 624, 715, 624
604,1980,1728, 825, 232
605,1980,1015, 912,1710
606,1985, 432, 636,1130
607, 743,1968,1986, 254
608,1992,1494,1368, 935
609,2012, 64, 556,1807
610,2013, 732, 826,1496
611,1770,2016,1955,1388
612,2024, 90,1071, 728
613,2024, 595, 644,1870
614,2024,1870, 644, 595
615,1892,2027,1376,1210
616,2028, 177, 694,1456
617,2032,1793,1052, 508
618,2036, 560,1120, 875
619,1940,2037,2030, 384
620,2032,2038,1636, 239
621,2040, 374, 999, 320
622,2040,1530, 368, 465
623,2023,2040, 966, 88
624,2040,1754,2040, 753
625,2041,1700,1700,1958
626,1384,2042,1949,1012
627,2051,1344,1936, 726
628,2052, 673, 432, 362
629,2052, 133,1296, 84
630,2056,1789, 312, 282
631, 793,2060,1664, 100
632,2064,1110,1652, 805
633, 585,2072,1708, 0
634,1352,2080,1145, 536
635,2084,1344,1659,1512
636,2090,1200,2035, 828
637,2091, 460,1824, 430
638,2108, 138, 816, 831
639,2112, 396, 257, 396
640,2112, 65, 208, 660
641,2112, 65, 660, 208
642,2020,2121, 680, 378
643, 660,2128,1139, 0
644,2132,1005, 630,1248
645,2134, 520,1900, 335
646,2139,1900,1170, 624
647, 668,2144, 731, 68
648,2144,1048, 584, 73
649,2145, 752, 392, 0
650,2145, 192, 910,1654
651,2145,1568,2040,1134
652,2160, 871, 600, 250
653, 576,2160,1000, 135
654,2170, 264, 385,1488
655,2170, 264,1488, 385
656,2170, 0, 935,1368
657,2180, 627,2090, 654
658,2184, 737, 486, 648
659,2184, 0, 935,1368
660,1440,2184,2184, 175
661,2186, 920, 448, 455
662,2190, 182, 780, 511
663,2192, 243, 496, 306
664,2192,1340, 609, 840
665,1376,2193,1632, 136
666,2200,1050,1288,1263
667,2201,2040,1958, 0
668,2204, 960, 765, 96
669,2208, 230, 868,1449
670,2209, 288, 846, 752
671,2214, 952,1272, 371
672, 720,2217,1440, 256
673,2160,1860,2229, 520
674,2239, 436,1016,1304
675, 562,2248, 832, 149
676,1772,1888,2256, 921
677,2257, 784,1708,1036
678,2257,1036,1708, 784
679,2268,1376,1649, 504
680,2279, 344, 494, 344
681,2280,1216, 465, 368
682,2280,1078,2244, 585
683,1304,2282, 784, 397
684,1260,2288,1387, 0
685,2110,2288,1300,1133
686,2295, 288, 952, 186
687,2296,1230, 812, 435
688,2296,1722,1593,1376
689,2303, 64, 392, 376
690,2303, 376, 392, 64
691, 435,2304,1644, 176
692,2136,2314,1709, 156
693,2320, 231,1218, 440
694,2325,1240,1980,1056
695,2325,1980,1240,1056
696,1074,2328,1064, 133
697,2328, 970,1537, 984
698,2332, 583, 896,1414
699,2337,1980, 930, 496
700,2340, 880, 880, 429
701,2344,1536, 639, 48
702,1632,2345,1650, 520
703,1977,2348,1674, 496
704,1470,2176,2349, 168
705,2354, 178, 397, 164
706,2356,1333, 912, 516
707,2361, 244, 198,1464
708, 790,2366,1855, 148
709,2368, 176, 48, 75
710,2376, 490,1155,1008
711,2376, 490,1008,1155
712,2376, 480,1705,1488
713,2145,2376,1040, 276
714, 840,2378,1740, 59
715,1696,2381,1696, 596
716,2384, 188, 389, 824
717,2384, 763,1162, 784
718,2392,1157,1884,1764
719,2088,2175,2394, 392
720,2396,1005, 490, 672
721,2400,1798, 961,1080
722,2035,1864,2400, 384
723,1428,2405,2346, 720
724,2412,1667,1114,1194
725,2412,1005,1886,1152
726,2431, 408, 852,1136
727,2432, 532,1376, 301
728, 964,2435,1840, 250
729,2436, 800,1176,2257
730,2440,1205,1168,1460
731,2442, 280, 387, 516
732,2086,1800,2445, 196
733,1020,2448,2205, 560
734,2448, 861, 952,2214
735,2448,1161,1462,1944
736,2457,1960,1248, 520
737,2464, 600,1008, 135
738,2464,1799,1352, 286
739,2464,2392,1757,1136
740,2472, 838, 971,1464
741,2475,1860,1320, 992
742,2476,2393, 944, 590
743,2479, 268, 272, 254
744,2479,1560,1560,1170
745,1112,2479,2272, 284
746,2480,1122, 279, 440
747, 615,2484,1150, 96
748,2484,1539, 368, 228
749, 852,2485,2030, 384
750,2493, 668,1314,1796
751,2281,2500,1160, 58
752,1152,2508, 599, 264
753,2516,2160,1476,1357
754,1802,2520,2520, 567
755,2522,1360,1580,1937
756, 532,2527,1426, 176
757,2530, 920, 844,1789
758,2530, 970,1288,1717
759,2534,2072,2072, 521
760,2541,1056,1528,1538
761,2552,1095,1680, 308
762,2552,2466,1904, 357
763,2235,2568,1774, 250
764,2576, 510,1591, 240
765,2268,2576,1725,1336
766,2589, 300,1880, 658
767,2479,1560,2604, 0
768,2609,1032, 478, 864
769,2610,1184,1677,2236
770,2616, 419,1792, 42
771,2408,2620,2275, 40
772,2627,1836, 762,1016
773,1231,2628,1686, 648
774,2631,1724,1002, 142
775,2633,1876,1876,1072
776,2392,1563,2634, 670
777,2640, 855, 510, 64
778,2640,1287, 760, 522
779,2640, 252,1680,1925
780,2646,1672,2079,2128
781,2648, 61,2200, 128
782,2648,2602, 576, 9
783,2649,2220, 860, 662
784,2656,1784, 855, 360
785,2656, 308,2191, 604
786,2600,2669,1580,1088
787,2672,2182,1287, 792
788,2676,1979,1960, 960
789,2679, 520,1248, 520
790,2490,2680, 936, 169
791,2685, 580,1256, 540
792,2695, 312,2016, 270
793,2695, 312,1288,2070
794,2695,1736,1760,2552
795,2699, 832, 894,2544
796,1816,2538,2704,1521
797,2713, 568, 994,2086
798,1248,2717,1198, 528
799,2717,1560,1248, 814
800,2720, 187, 440, 898
801,2720, 408,1167, 400
802,1872,2380,2739, 0
803,2740, 170,1139, 80
804,2760, 621,1056, 680
805,2760, 805,1120, 408
806,2760, 805, 672,1080
807,2784,1212,1325,2332
808,2790,1736,1848, 305
809,2792,1047,1096,1506
810,1716,2800,1763, 0
811,2800, 308,2700, 297
812,2816, 326,1668, 267
813,2820,1504, 840, 833
814,2824, 927, 288, 344
815,2829,2484,1806, 424
816,2304,2251,2832,1062
817,2606,2844,2028, 607
818,2850, 792,1485,1520
819,2856,1430,2380, 69
820,2856,1050,2788,1025
821,2858,2240,2040, 969
822,2860,1760,1344,1311
823,2860,2288,2537, 160
824,2860,2775,2378, 840
825,2871, 160,1044, 440
826,2871, 440,1044, 160
827,2872,1077,1422, 296
828,2880,1008, 295, 440
829,2880,1001,1260,2288
830,2880,1001,2288,1260
831,2880,2022,2040, 103
832,2397,2880,1960, 672
833,2881,1320,1520, 342
834,2448,2550,2891,1260
835,1569,2896, 660, 160
836,1134,2896,2716, 471
837,2900,1051,2350, 302
838,2901, 360, 80, 108
839,2904, 990,2475,1384
840,2909,1172,2172,1776
841,2911, 528,1704, 902
842,2911, 660,2130, 902
843,2912,1384,1313, 392
844,2912, 938,1157,2792
845,2460,2912,2380, 69
846,2913, 744,1536,1058
847,2920, 0,1071,1840
848,2920, 920,1679,1600
849,2920,1600,1679, 920
850,2922,1096,1232, 693
851,2924, 234,1677, 408
852,2925,1344,1100,1008
853,1568,2926,1419, 660
854,2013,2928, 970, 40
855,1856,2929,2670,1560
856,2943,2616,2664,2368
857,2943,2664,2616,2368
858,2944, 416,1120,2035
859,2952, 385,1710,1064
860,2092,2957,2734,1646
861,2960, 161, 920, 518
862,2960, 231, 518,1320
863,2960, 231,1320, 518
864,2960, 666,1612, 285
865,2960, 231, 280,2442
866,2960, 231,2442, 280
867,2960,1443,2200, 282
868,2046,2976,1373, 352
869,2984, 288,1521,2496
870,2988, 28,2712, 777
871,3000,2357, 856, 60
872,3003,1540, 702, 360
873,1254,3006,2252, 487
874,3008,1351,1798,1736
875,2190,3014,2811, 160
876,1564,3015,2448, 690
877,3015,1232,2850, 0
878,2772,2640,3015,1232
879,3020,2293,2222, 500
880,3024, 110, 693, 480
881,3024, 110, 480, 693
882,3024, 882, 736, 273
883,3024,2796, 673, 708
884,2868,3024,1253, 168
885,3025,2992,2750, 584
886,3029,1976,1864,1216
887,3045, 160,1218,2500
888,3050, 46,2300, 61
889,2596,3051, 576, 184
890,3070,1816,2011,2420
891,1482,3080,2193, 0
892,3080,1440,2079,1440
893,3086, 376,1120,1505
894,3094,1590,2756,1785
895,1120,3102,2860, 273
896, 623,3108, 632, 18
897,3120, 448,2576, 345
898,3120,2660,1680, 819
899,1386,3120,2952, 385
900,3120,2631,1548,1430
901,1035,3120,3120, 886
902,3128, 838, 272, 17
903,3135, 112, 330,1064
904,3135, 112,1064, 330
905,3136, 37, 224, 518
906,3136,1498, 759,1452
907,3136,1817,1888, 616
908,3136,1456,2521, 728
909,3142,1912,2041,1816
910,3148, 960,3000, 405
911,3160,1049,1390,1114
912,3162,1640,1575,1672
913,3168, 396,1379,2228
914,3176,2286, 296, 111
915,1984,3179,2972,1462
916,3180, 583, 560,1518
917,3192, 741, 464,1052
918,3192, 993,1064,2894
919,3212, 983,1824,1254
920,3226,2370,2668,1125
921,2257,3228,1296, 486
922, 690,3228,2932, 135
923,3228,2385,1500,1600
924,3232,2517, 332, 222
925,2428,3232,3133,2032
926,2788,3233, 880, 20
927,3234, 984,1117, 308
928,3234,1312,1357,1476
929,1328,3207,3236,1086
930,3248,2580,2920, 657
931,1744,3270,2805, 212
932,3271,3040, 504, 90
933,3280, 574,2323, 860
934,3280,1639,2542,2420
935,3288,2286, 847, 924
936,3290,1128,2200,1311
937,3298,1470,1940,2499
938,3300,1411, 752,1410
939,3300,1760,2565,2496
940,3319,1004, 302, 152
941,3326,2354, 671, 436
942,3328,2704,2983,2888
943,3336,1390,2552,1095
944,1825,3340,1700, 544
945,3344,2164, 957, 48
946,3360,2254,1479, 880
947,2640,2772,3360, 925
948,3366,2640,2193,1720
949,1538,3368, 739, 104
950,3372,2219,1694,2508
951,2296,3381,2208,1382
952,1958,3272,3385,1280
953,3396,1072,1548,1721
954,3409,1688,2856, 366
955,3416, 448, 452,2231
956,3416,2303,1592, 256
957,1158,3418,1916, 291
958,3420,1824,2040,2201
959,3436,2864, 725, 584
960,3440, 892, 395,1264
961,3444, 0, 765, 520
962,3453, 696, 808,1696
963,3456,2100,1533,1460
964,3465,1952,1072, 0
965,3200,3471, 980, 336
966,3472, 320,1024,1085
967,3472,1085,1670,1400
968,3472,2373,1936,2046
969,3475, 320,2224, 500
970,3478,1504,1779,1212
971,2834,3390,3480,2543
972,3484,1159,1586,2546
973,3486, 116,1812, 783
974, 184,3488,1763, 56
975,3489,1620,2050,1968
976,1830,3496,1240, 561
977,3496,1311,2532,1424
978,1232,3499,2464, 484
979,3504, 366, 143, 352
980,3196,3506,3140, 85
981,3510, 504, 455, 504
982,2520,3515,2520,1568
983,3520, 792,1431,1040
984,3520,3072,3520,2001
985,3524, 928,1251,1692
986,3536,2720,1864,1075
987,3546, 72, 937,2384
988,3551, 840, 840, 306
989,3266,1994,3551, 664
990,3553,1632, 648, 702
991,3560,1439,1240,1798
992,2170,3560,2407, 232
993,3569, 516, 542,2112
994,3570,1254,2772,1615
995,3576,2166,1961, 296
996,3576, 130,2615,1668
997, 739,3596, 672, 42
998,3600,1204, 120, 119
999,3604, 667, 306, 288
1000,3608,2394, 728, 429
1001,3615, 728,2730, 964
1002,3616,1024,1055,2740
1003,1092,3623,3458, 948
1004,3626,2072,2564,2273
1005,2148,3639,2240, 248
1006, 819,3640,3640, 270
1007,2821,3660,1290, 688
1008,2850,2624,3660, 671
1009,2396,3670,3404,1465
1010,3672, 518, 999,1904
1011,1326,3672,3479, 168
1012,3680,2760, 912, 215
1013,3680, 828,1200,2755
1014,3696, 172, 704, 903
1015,3696,1197,2646,1672
1016,3696,1782,1764,2783
1017,3700, 259, 600, 42
英語で検索される可能性があったので、ウィキペディアの英文をそのままコピーしておく。
OEISとかにも、1000個超えのデータなんてものがなかったので作ってみた。
1ヶ月半も掛かってしまったが、有意義なデータだと思う。
さて、次はオイラーのレンガを1000個以上を目指そうか。
ではでは