Max of 1,000

swhitt@bender:~/Code/personal$ ruby supermagical.rb 
..........(1, 1, 2), (3, 5, 6), (5, 13, 14), (7, 7, 10), (7, 25, 26), (9, 41, 42), (11, 19, 22), (11, 61, 62), (13, 27, 30), (13, 85, 86), (15, 113, 114), (17, 47, 50), (17, 145, 146), (19, 59, 62), (19, 181, 182), (21, 221, 222), (23, 25, 34), (23, 87, 90), (23, 265, 266), (25, 103, 106), (25, 313, 314), (27, 365, 366), (29, 139, 142), (29, 421, 422), (31, 49, 58), (31, 159, 162), (31, 481, 482), (33, 545, 546), (35, 203, 206), (35, 613, 614), (37, 227, 230), (37, 685, 686), (39, 761, 762), (41, 41, 58), (41, 71, 82), (41, 89, 98), (41, 279, 282), (41, 841, 842), (43, 307, 310), (43, 925, 926), (47, 95, 106), (47, 367, 370), (49, 129, 138), (49, 399, 402), (51, 59, 78), (53, 467, 470), (55, 503, 506), (59, 189, 198), (59, 579, 582), (61, 101, 118), (61, 619, 622), (63, 95, 114), (63, 175, 186), (65, 703, 706), (67, 245, 254), (67, 747, 750), (69, 211, 222), (71, 839, 842), (73, 887, 890), (75, 157, 174), (77, 325, 334), (77, 987, 990), (85, 93, 126), (85, 323, 334), (85, 397, 406), (89, 199, 218), (91, 109, 142), (91, 371, 382), (95, 257, 274), (95, 497, 506), (101, 259, 278), (103, 183, 210), (103, 585, 594), (107, 157, 190), (107, 515, 526), (109, 341, 358), (113, 127, 170), (113, 177, 210), (113, 223, 250), (113, 575, 586), (113, 705, 714), (121, 809, 818), (127, 415, 434), (129, 481, 498), (129, 751, 762), (131, 949, 958), (135, 823, 834), (139, 141, 198), (139, 499, 518), (143, 175, 226), (143, 593, 610), (145, 223, 266), (151, 329, 362), (153, 265, 306), (157, 357, 390), (157, 443, 470), (163, 235, 286), (163, 773, 790), (165, 707, 726), (167, 503, 530), (173, 437, 470), (175, 353, 394), (177, 815, 834), (177, 913, 930), (179, 469, 502), (181, 211, 278), (197, 355, 406), (199, 439, 482), (203, 333, 390), (207, 257, 330), (211, 411, 462), (211, 811, 838), (213, 355, 414), (215, 377, 434), (217, 697, 730), (221, 261, 342), (221, 331, 398), (221, 891, 918), (223, 737, 770), (227, 245, 334), (231, 329, 402), (231, 599, 642), (235, 653, 694), (239, 239, 338), (239, 849, 882), (241, 481, 538), (245, 563, 614), (245, 893, 926), (253, 533, 590), (257, 785, 826), (259, 539, 598), (265, 393, 474), (265, 663, 714), (283, 355, 454), (285, 923, 966), (299, 851, 902), (307, 485, 574), (311, 439, 538), (313, 377, 490), (313, 935, 986), (315, 707, 774), (317, 325, 454), (317, 347, 470), (317, 853, 910), (323, 587, 670), (329, 921, 978), (331, 899, 958), (341, 659, 742), (353, 817, 890), (355, 587, 686), (355, 907, 974), (365, 443, 574), (365, 533, 646), (367, 415, 554), (371, 469, 598), (371, 661, 758), (377, 937, 1010), (383, 865, 946), (397, 683, 790), (401, 449, 602), (403, 565, 694), (405, 797, 894), (405, 877, 966), (421, 611, 742), (421, 659, 782), (437, 915, 1014), (449, 481, 658), (457, 745, 874), (459, 499, 678), (459, 931, 1038), (465, 833, 954), (467, 715, 854), (471, 599, 762), (481, 591, 762), (481, 879, 1002), (497, 833, 970), (503, 583, 770), (503, 967, 1090), (503, 985, 1106), (507, 707, 870), (515, 523, 734), (517, 797, 950), (545, 673, 866), (545, 783, 954), (571, 989, 1142), (575, 593, 826), (583, 745, 946), (613, 877, 1070), (613, 973, 1150), (615, 967, 1146), (619, 931, 1118), (623, 865, 1066), (655, 737, 986), (673, 785, 1034), (685, 853, 1094), (693, 707, 990), (703, 833, 1090), (707, 907, 1150), (751, 801, 1098), (761, 951, 1218), (793, 935, 1226), (809, 889, 1202), (813, 923, 1230), (815, 817, 1154), (823, 887, 1210), (913, 945, 1314)

Max of 50,000

swhitt@bender:~/Code/personal$ ruby better_than_durian.rb 
....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(1, 1, 2), (3, 5, 6), (5, 13, 14), (7, 7, 10), (7, 25, 26), (9, 41, 42), (11, 19, 22), (11, 61, 62), (13, 27, 30), (13, 85, 86), (15, 113, 114), (17, 47, 50), (17, 145, 146), (19, 59, 62), (19, 181, 182), (21, 221, 222), (23, 25, 34), (23, 87, 90), (23, 265, 266), (25, 103, 106), (25, 313, 314), (27, 365, 366), (29, 139, 142), (29, 421, 422), (31, 49, 58), (31, 159, 162), (31, 481, 482), (33, 545, 546), (35, 203, 206), (35, 613, 614), (37, 227, 230), (37, 685, 686), (39, 761, 762), (41, 41, 58), (41, 71, 82), (41, 89, 98), (41, 279, 282), (41, 841, 842), (43, 307, 310), (43, 925, 926), (45, 1013, 1014), (47, 95, 106), (47, 367, 370), (47, 1105, 1106), (49, 129, 138), (49, 399, 402), (49, 1201, 1202), (51, 59, 78), (51, 1301, 1302), (53, 467, 470), (53, 1405, 1406), (55, 503, 506), (55, 1513, 1514), (57, 1625, 1626), (59, 189, 198), (59, 579, 582), (59, 1741, 1742), (61, 101, 118), (61, 619, 622), (61, 1861, 1862), (63, 95, 114), (63, 175, 186), (63, 1985, 1986), (65, 703, 706), (65, 2113, 2114), (67, 245, 254), (67, 747, 750), (67, 2245, 2246), (69, 211, 222), (69, 2381, 2382), (71, 839, 842), (71, 2521, 2522), (73, 887, 890), (73, 2665, 2666), (75, 157, 174), (75, 2813, 2814), (77, 325, 334), (77, 987, 990), (77, 2965, 2966), (79, 1039, 1042), (79, 3121, 3122), (81, 3281, 3282), (83, 1147, 1150), (83, 3445, 3446), (85, 93, 126), (85, 323, 334), (85, 397, 406), (85, 1203, 1206), (85, 3613, 3614), (87, 3785, 3786), (89, 199, 218), (89, 1319, 1322), (89, 3961, 3962), (91, 109, 142), (91, 371, 382), (91, 1379, 1382), (91, 4141, 4142), (93, 4325, 4326), (95, 257, 274), (95, 497, 506), (95, 1503, 1506), (95, 4513, 4514), (97, 1567, 1570), (97, 4705, 4706), (99, 4901, 4902), (101, 259, 278), (101, 1699, 1702), (101, 5101, 5102), (103, 183, 210), (103, 585, 594), (103, 1767, 1770), (103, 5305, 5306), (105, 5513, 5514), (107, 157, 190), (107, 515, 526), (107, 1907, 1910), (107, 5725, 5726), (109, 341, 358), (109, 1979, 1982), (109, 5941, 5942), (111, 6161, 6162), (113, 127, 170), (113, 177, 210), (113, 223, 250), (113, 575, 586), (113, 705, 714), (113, 2127, 2130), (113, 6385, 6386), (115, 2203, 2206), (115, 6613, 6614), (117, 6845, 6846), (119, 2359, 2362), (119, 7081, 7082), (121, 809, 818), (121, 2439, 2442), (121, 7321, 7322), (123, 7565, 7566), (125, 2603, 2606), (125, 7813, 7814), (127, 415, 434), (127, 2687, 2690), (127, 8065, 8066), (129, 481, 498), (129, 751, 762), (129, 8321, 8322), (131, 949, 958), (131, 2859, 2862), (131, 8581, 8582), (133, 2947, 2950), (133, 8845, 8846), (135, 823, 834), (135, 9113, 9114), (137, 3127, 3130), (137, 9385, 9386), (139, 141, 198), (139, 499, 518), (139, 1069, 1078), (139, 3219, 3222), (139, 9661, 9662), (141, 9941, 9942), (143, 175, 226), (143, 593, 610), (143, 3407, 3410), (143, 10225, 10226), (145, 223, 266), (145, 3503, 3506), (145, 10513, 10514), (147, 10805, 10806), (149, 1229, 1238), (149, 3699, 3702), (149, 11101, 11102), (151, 329, 362), (151, 1031, 1042), (151, 3799, 3802), (151, 11401, 11402), (153, 265, 306), (153, 11705, 11706), (155, 4003, 4006), (155, 12013, 12014), (157, 357, 390), (157, 443, 470), (157, 1115, 1126), (157, 1365, 1374), (157, 4107, 4110), (157, 12325, 12326), (159, 12641, 12642), (161, 4319, 4322), (161, 12961, 12962), (163, 235, 286), (163, 773, 790), (163, 4427, 4430), (163, 13285, 13286), (165, 707, 726), (165, 13613, 13614), (167, 503, 530), (167, 1545, 1554), (167, 4647, 4650), (167, 13945, 13946), (169, 4759, 4762), (169, 14281, 14282), (171, 14621, 14622), (173, 437, 470), (173, 1355, 1366), (173, 4987, 4990), (173, 14965, 14966), (175, 353, 394), (175, 1697, 1706), (175, 5103, 5106), (175, 15313, 15314), (177, 815, 834), (177, 913, 930), (177, 15665, 15666), (179, 469, 502), (179, 1451, 1462), (179, 5339, 5342), (179, 16021, 16022), (181, 211, 278), (181, 5459, 5462), (181, 16381, 16382), (183, 16745, 16746), (185, 1897, 1906), (185, 5703, 5706), (185, 17113, 17114), (187, 5827, 5830), (187, 17485, 17486), (189, 17861, 17862), (191, 6079, 6082), (191, 18241, 18242), (193, 2065, 2074), (193, 6207, 6210), (193, 18625, 18626), (195, 1723, 1734), (195, 19013, 19014), (197, 355, 406), (197, 1133, 1150), (197, 6467, 6470), (197, 19405, 19406), (199, 439, 482), (199, 6599, 6602), (199, 19801, 19802), (201, 1831, 1842), (201, 20201, 20202), (203, 333, 390), (203, 1075, 1094), (203, 2285, 2294), (203, 6867, 6870), (203, 20605, 20606), (205, 7003, 7006), (205, 21013, 21014), (207, 257, 330), (207, 21425, 21426), (209, 7279, 7282), (209, 21841, 21842), (211, 411, 462), (211, 811, 838), (211, 1301, 1318), (211, 2469, 2478), (211, 7419, 7422), (211, 22261, 22262), (213, 355, 414), (213, 22685, 22686), (215, 377, 434), (215, 1207, 1226), (215, 7703, 7706), (215, 23113, 23114), (217, 697, 730), (217, 2135, 2146), (217, 7847, 7850), (217, 23545, 23546), (219, 23981, 23982), (221, 261, 342), (221, 331, 398), (221, 891, 918), (221, 2709, 2718), (221, 8139, 8142), (221, 24421, 24422), (223, 737, 770), (223, 2255, 2266), (223, 8287, 8290), (223, 24865, 24866), (225, 25313, 25314), (227, 245, 334), (227, 8587, 8590), (227, 25765, 25766), (229, 2909, 2918), (229, 8739, 8742), (229, 26221, 26222), (231, 329, 402), (231, 599, 642), (231, 1561, 1578), (231, 26681, 26682), (233, 9047, 9050), (233, 27145, 27146), (235, 653, 694), (235, 9203, 9206), (235, 27613, 27614), (237, 28085, 28086), (239, 239, 338), (239, 849, 882), (239, 2591, 2602), (239, 3169, 3178), (239, 9519, 9522), (239, 28561, 28562), (241, 481, 538), (241, 1519, 1538), (241, 9679, 9682), (241, 29041, 29042), (243, 29525, 29526), (245, 563, 614), (245, 893, 926), (245, 1757, 1774), (245, 2723, 2734), (245, 10003, 10006), (245, 30013, 30014), (247, 3385, 3394), (247, 10167, 10170), (247, 30505, 30506), (249, 31001, 31002), (251, 10499, 10502), (251, 31501, 31502), (253, 533, 590), (253, 1675, 1694), (253, 10667, 10670), (253, 32005, 32006), (255, 32513, 32514), (257, 785, 826), (257, 3665, 3674), (257, 11007, 11010), (257, 33025, 33026), (259, 539, 598), (259, 11179, 11182), (259, 33541, 33542), (261, 3091, 3102), (261, 34061, 34062), (263, 11527, 11530), (263, 34585, 34586), (265, 393, 474), (265, 663, 714), (265, 1287, 1314), (265, 2057, 2074), (265, 3897, 3906), (265, 11703, 11706), (265, 35113, 35114), (267, 3235, 3246), (267, 35645, 35646), (269, 12059, 12062), (269, 36181, 36182), (271, 12239, 12242), (271, 36721, 36722), (273, 37265, 37266), (275, 1387, 1414), (275, 4197, 4206), (275, 12603, 12606), (275, 37813, 37814), (277, 12787, 12790), (277, 38365, 38366), (279, 2039, 2058), (279, 2281, 2298), (279, 38921, 38922), (281, 13159, 13162), (281, 39481, 39482), (283, 355, 454), (283, 1197, 1230), (283, 3635, 3646), (283, 4445, 4454), (283, 13347, 13350), (283, 40045, 40046), (285, 923, 966), (285, 40613, 40614), (287, 13727, 13730), (287, 41185, 41186), (289, 1249, 1282), (289, 3791, 3802), (289, 13919, 13922), (289, 41761, 41762), (291, 2219, 2238), (291, 42341, 42342), (293, 4765, 4774), (293, 14307, 14310), (293, 42925, 42926), (295, 14503, 14506), (295, 43513, 43514), (297, 44105, 44106), (299, 851, 902), (299, 2621, 2638), (299, 14899, 14902), (299, 44701, 44702), (301, 5029, 5038), (301, 15099, 15102), (301, 45301, 45302), (303, 45905, 45906), (305, 1393, 1426), (305, 4223, 4234), (305, 15503, 15506), (305, 46513, 46514), (307, 485, 574), (307, 15707, 15710), (307, 47125, 47126), (309, 47741, 47742), (311, 439, 538), (311, 1449, 1482), (311, 4391, 4402), (311, 5369, 5378), (311, 16119, 16122), (311, 48361, 48362), (313, 377, 490), (313, 935, 986), (313, 2873, 2890), (313, 16327, 16330), (313, 48985, 48986), (315, 707, 774), (315, 49613, 49614), (317, 325, 454), (317, 347, 470), (317, 853, 910), (317, 1147, 1190), (317, 1205, 1246), (317, 2635, 2654), (317, 16747, 16750), (319, 1871, 1898), (319, 5649, 5658), (319, 16959, 16962), (323, 587, 670), (323, 17387, 17390), (325, 17603, 17606), (327, 4855, 4866), (329, 921, 978), (329, 1991, 2018), (329, 2839, 2858), (329, 6009, 6018), (329, 18039, 18042), (331, 899, 958), (331, 18259, 18262), (333, 3253, 3270), (333, 5035, 5046), (335, 18703, 18706), (337, 6305, 6314), (337, 18927, 18930), (339, 1381, 1422), (341, 659, 742), (341, 19379, 19382), (343, 19607, 19610), (347, 1155, 1206), (347, 3533, 3550), (347, 6685, 6694), (347, 20067, 20070), (349, 1829, 1862), (349, 5531, 5542), (349, 20299, 20302), (353, 817, 890), (353, 20767, 20770), (355, 587, 686), (355, 907, 974), (355, 1077, 1134), (355, 1893, 1926), (355, 3307, 3326), (355, 5723, 5734), (355, 6997, 7006), (355, 21003, 21006), (359, 21479, 21482), (361, 21719, 21722), (365, 443, 574), (365, 533, 646), (365, 7397, 7406), (365, 22203, 22206), (367, 415, 554), (367, 1153, 1210), (367, 1295, 1346), (367, 3535, 3554), (367, 3953, 3970), (367, 22447, 22450), (371, 469, 598), (371, 661, 758), (371, 1579, 1622), (371, 2069, 2102), (371, 6251, 6262), (371, 22939, 22942), (373, 2563, 2590), (373, 7725, 7734), (373, 23187, 23190), (377, 937, 1010), (377, 1175, 1234), (377, 2137, 2170), (377, 6455, 6466), (377, 23687, 23690), (379, 23939, 23942), (381, 4261, 4278), (383, 865, 946), (383, 2703, 2730), (383, 8145, 8154), (383, 24447, 24450), (385, 24703, 24706), (389, 25219, 25222), (391, 8489, 8498), (391, 25479, 25482), (393, 4055, 4074), (393, 7015, 7026), (395, 26003, 26006), (397, 683, 790), (397, 26267, 26270), (399, 1921, 1962), (399, 7231, 7242), (401, 449, 602), (401, 1551, 1602), (401, 4721, 4738), (401, 8929, 8938), (401, 26799, 26802), (403, 565, 694), (403, 1867, 1910), (403, 27067, 27070), (405, 797, 894), (405, 877, 966), (405, 4307, 4326), (407, 27607, 27610), (409, 9289, 9298), (409, 27879, 27882), (413, 28427, 28430), (415, 1663, 1714), (415, 2593, 2626), (415, 5057, 5074), (415, 7823, 7834), (415, 28703, 28706), (419, 9749, 9758), (419, 29259, 29262), (421, 611, 742), (421, 659, 782), (421, 2141, 2182), (421, 2669, 2702), (421, 8051, 8062), (421, 29539, 29542), (425, 30103, 30106), (427, 1085, 1166), (427, 3363, 3390), (427, 10125, 10134), (427, 30387, 30390), (431, 1601, 1658), (431, 4879, 4898), (431, 30959, 30962), (433, 31247, 31250), (435, 5557, 5574), (437, 915, 1014), (437, 2877, 2910), (437, 3523, 3550), (437, 8675, 8686), (437, 10605, 10614), (437, 31827, 31830), (439, 32119, 32122), (443, 1693, 1750), (443, 2957, 2990), (443, 5155, 5174), (443, 8915, 8926), (443, 32707, 32710), (445, 10997, 11006), (445, 33003, 33006), (449, 481, 658), (449, 1471, 1538), (449, 1679, 1738), (449, 1951, 2002), (449, 5921, 5938), (449, 33599, 33602), (451, 33899, 33902), (455, 11497, 11506), (455, 34503, 34506), (457, 745, 874), (457, 2407, 2450), (457, 34807, 34810), (459, 499, 678), (459, 931, 1038), (459, 9571, 9582), (461, 35419, 35422), (463, 11905, 11914), (463, 35727, 35730), (465, 833, 954), (465, 9823, 9834), (467, 715, 854), (467, 36347, 36350), (469, 1901, 1958), (469, 2131, 2182), (469, 5779, 5798), (469, 6461, 6478), (469, 36659, 36662), (471, 599, 762), (473, 12425, 12434), (473, 37287, 37290), (475, 37603, 37606), (479, 38239, 38242), (481, 591, 762), (481, 879, 1002), (481, 1119, 1218), (481, 2001, 2058), (481, 2801, 2842), (481, 3489, 3522), (481, 4271, 4298), (481, 6079, 6098), (481, 10511, 10522), (481, 12849, 12858), (481, 38559, 38562), (483, 6853, 6870), (485, 1277, 1366), (485, 39203, 39206), (487, 3577, 3610), (487, 10775, 10786), (487, 39527, 39530), (489, 1399, 1482), (489, 1751, 1818), (489, 2759, 2802), (491, 4451, 4478), (491, 13389, 13398), (491, 40179, 40182), (493, 40507, 40510), (495, 2047, 2106), (497, 833, 970), (497, 41167, 41170), (499, 1669, 1742), (499, 13829, 13838), (499, 41499, 41502), (503, 583, 770), (503, 967, 1090), (503, 985, 1106), (503, 2455, 2506), (503, 3065, 3106), (503, 3817, 3850), (503, 7433, 7450), (503, 11495, 11506), (503, 42167, 42170), (505, 42503, 42506), (507, 707, 870), (507, 1507, 1590), (507, 6755, 6774), (509, 1259, 1358), (509, 3909, 3942), (509, 11771, 11782), (509, 14389, 14398), (509, 43179, 43182), (511, 43519, 43522), (515, 523, 734), (515, 44203, 44206), (517, 797, 950), (517, 2595, 2646), (517, 7853, 7870), (517, 14845, 14854), (517, 44547, 44550), (519, 7079, 7098), (521, 45239, 45242), (523, 1837, 1910), (523, 45587, 45590), (525, 12523, 12534), (527, 15425, 15434), (527, 46287, 46290), (529, 46639, 46642), (531, 12811, 12822), (533, 47347, 47350), (535, 5287, 5314), (535, 15897, 15906), (535, 47703, 47706), (537, 8473, 8490), (539, 1229, 1342), (539, 48419, 48422), (541, 48779, 48782), (543, 3407, 3450), (545, 673, 866), (545, 783, 954), (545, 1793, 1874), (545, 2577, 2634), (545, 5487, 5514), (545, 7807, 7826), (545, 16497, 16506), (545, 49503, 49506), (547, 4517, 4550), (547, 13595, 13606), (547, 49867, 49870), (551, 2951, 3002), (551, 8921, 8938), (553, 1495, 1594), (553, 4617, 4650), (553, 13895, 13906), (553, 16985, 16994), (557, 2693, 2750), (557, 8155, 8174), (563, 1227, 1350), (563, 3845, 3886), (563, 17605, 17614), (565, 1597, 1694), (567, 2695, 2754), (569, 4889, 4922), (569, 14711, 14722), (571, 989, 1142), (571, 3171, 3222), (571, 9581, 9598), (571, 18109, 18118), (575, 593, 826), (575, 1217, 1346), (575, 3823, 3866), (575, 4993, 5026), (575, 15023, 15034), (581, 18749, 18758), (583, 745, 946), (583, 1865, 1954), (583, 2503, 2570), (583, 2953, 3010), (583, 8935, 8954), (585, 4153, 4194), (585, 10057, 10074), (589, 2101, 2182), (589, 6411, 6438), (589, 19269, 19278), (591, 1489, 1602), (591, 15871, 15882), (595, 3077, 3134), (595, 9307, 9326), (597, 16195, 16206), (599, 1241, 1378), (599, 1801, 1898), (599, 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61726), (43025, 48447, 64794), (43061, 45379, 62558), (43101, 49451, 65598), (43105, 44767, 62146), (43105, 46593, 63474), (43145, 45017, 62354), (43155, 43403, 61206), (43225, 45703, 62906), (43313, 45873, 63090), (43389, 47749, 64518), (43411, 49371, 65742), (43447, 46985, 63994), (43457, 43695, 61626), (43511, 47209, 64202), (43519, 45279, 62802), (43569, 48991, 65562), (43593, 45607, 63090), (43597, 48875, 65494), (43601, 46689, 63882), (43615, 44897, 62594), (43621, 44371, 62222), (43623, 44105, 62034), (43631, 48689, 65378), (43637, 44445, 62286), (43673, 45175, 62834), (43729, 45521, 63122), (43823, 48095, 65066), (43981, 46469, 63982), (43999, 49679, 66362), (44011, 44941, 62902), (44041, 48729, 65682), (44091, 44941, 62958), (44167, 47703, 65010), (44267, 49853, 66670), (44291, 48821, 65918), (44309, 46621, 64318), (44325, 47507, 64974), (44365, 44907, 63126), (44399, 48479, 65738), (44481, 48001, 65442), (44491, 48019, 65462), (44543, 47407, 65050), (44549, 49181, 66358), (44663, 48823, 66170), (44785, 46703, 64706), (44855, 45193, 63674), (44887, 49625, 66914), (45001, 45959, 64322), (45029, 48829, 66422), (45033, 46553, 64770), (45077, 49987, 67310), (45115, 46813, 65014), (45131, 47219, 65318), (45131, 48429, 66198), (45185, 48143, 66026), (45241, 45689, 64298), (45245, 49163, 66814), (45301, 45939, 64518), (45515, 47693, 65926), (45617, 48703, 66730), (45663, 46273, 65010), (45875, 49877, 67766), (45961, 49159, 67298), (46043, 46093, 65150), (46103, 47655, 66306), (46145, 48623, 67034), (46175, 49583, 67754), (46233, 46553, 65610), (46291, 47131, 66062), (46323, 47525, 66366), (46469, 47539, 66478), (46529, 48289, 67058), (46643, 47995, 66926), (46735, 46753, 66106), (46757, 47357, 66550), (46913, 48095, 67186), (47011, 49461, 68238), (47101, 48821, 67838), (47179, 48109, 67382), (47219, 47451, 66942), (47227, 49155, 68166), (47239, 49271, 68258), (47321, 47321, 66922), (47359, 48431, 67738), (47453, 49115, 68294), (47635, 49717, 68854), (47779, 47819, 67598), (47915, 49213, 68686), (48293, 49805, 69374), (48595, 49387, 69286), (48601, 49991, 69722), (48719, 49169, 69218), (48961, 49919, 69922), (49011, 49189, 69438), (49171, 49819, 69998), (49179, 49901, 70062), (49469, 49749, 70158)

super_steve.rb

MIN_VAL = 1
MAX_VAL = 2000
valid = (MIN_VAL..MAX_VAL)
i = 0
results = []
result_count = {}


puts "Determining integer solutions to `a^2 + b^2 + 2 = c^2`, in the range #{MIN_VAL} to #{MAX_VAL}"

valid.each do |a|
  (a..MAX_VAL).each do |b|
    c = ((a ** 2) + (b ** 2) + 2) ** 0.5
    if c.floor == c
      results << "(#{a}, #{b}, #{c.to_i})" 
      result_count[c.to_i] ||= 0
      result_count[c.to_i]+=1
    end
  end
  i += 1
  print '.' if (i % 100 == 0)
end

print 'bang.'
puts
puts
top_num_hits = result_count.sort{|a,b| b[1]<=>a[1]}[0][1]
top_hits = result_count.find_all{|o| o[1] == top_num_hits}

most_popular_cs = top_hits.map{|o| o[0]}
most_popular_hit_count = top_hits[0][1]

puts "Most common 'c' values (with #{most_popular_hit_count} appearances): #{most_popular_cs.join(', ')}"
puts
puts 'Solutions (a, b, c):'
puts results.join(', ')