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User:Eric Chen

Primes of the form k*2^n+-1 or 2^n+-k

There are infinitely many odd k such that k*2^n+1 are composite for all integer n.

If k is negative, then we choose the absolute value of k*2^n+1, if n is negative, then we choose the numerator of k*2^n+1.

Thus, this list is about primes of the form k*2^n+1, k*2^n-1, 2^n+k, 2^n-k, and k-2^n.

Domain: k any odd integer (can be either positive or negative), n any nonzero integer.

Conjecture: Every row either contains infinitely many positive numbers and infinitely many negative numbers or is blank (such as rows 78557, 271129, and -509203, etc.)

This list lists all values of n (checked up to +-1500) of all -599 <= k <= 599 (odd k) such that k*2^n+1 is prime.

Related OEIS sequences:

Row n is blank (n>0): A076336

Row -n is blank (n>0): A101036

Row n and -n are both blank (n>0): A076335

Row n and -n both contain no numbers whose absolute value less than ${\displaystyle log_{2}n}$ (n>0): A256163

Least positive number in row n (n>0): A033809 A046067 (allow 0)

Corresponding primes: A057025 (allow 0)

Least positive number in row -n (n>0): A108129 A046069 (allow 0)

Corresponding primes: A057026 (allow 0)

Greatest negative number in row n (n>0): A067760

Corresponding primes: A123252

Greatest negative number in row -n (n>0): A252168 A096502 (with a condition that the absolute value of it is greater then ${\displaystyle log_{2}n}$)

Corresponding primes: A096822 (with a condition that the absolute value of the number in row -n is greater then ${\displaystyle log_{2}n}$)

Row n contains n (n>0): A005849

Corresponding primes: A050920

Row -n contains n (n>0): A002234

Corresponding primes: A050918

Row n contains -n (n>0): A052007

Corresponding primes: A129962

Row -n contains -n (n>0): A048744

Corresponding primes: A081296

k (odd) Values of n such that abs(numerator(k*2^n+1)) is prime (checked up to +-1500)
-599 -1060, -952, -40, -28, -16, 8, 20, 32, 80, 128
-597 -1250, -1131, -1064, -554, -416, -260, -156, -116, -84, -56, -44, -35, -27, -24, -20, -14, -12, -11, -2, 1, 4, 9, 16, 36, 60, 64, 70, 109, 129, 136, 240, 280, 369, 381, 484, 709, 981, 1029, 1288
-595 -1233, -953, -745, -601, -555, -441, -407, -353, -327, -267, -249, -233, -213, -141, -97, -69, -53, -31, -29, -25, -23, -17, -15, -11, -9, -7, -5, -3, -1, 3, 7, 11, 15, 25, 27, 31, 35, 49, 69, 79, 99, 107, 109, 143, 175, 177, 191, 249, 357, 409, 417, 1059, 1113
-593 -1470, -800, -750, -400, -286, -234, -118, -106, -98, -26, -24, -14, -10, -8, -4, 2, 6, 20, 22, 24, 30, 32, 74, 92, 102, 110, 266, 386, 474, 726, 1082
-591 -794, -597, -189, -167, -98, -69, -50, -45, -35, -10, -9, -7, -2, 1, 5, 15, 70, 83, 243, 281, 446, 553
-589 -1433, -1213, -661, -613, -473, -355, -343, -187, -163, -83, -31, -23, -17, -13, -11, -7, -5, -1, 7, 47, 55, 113, 115, 227, 265, 277, 283, 533
-587 -1416, -1294, -1114, -598, -486, -256, -220, -156, -104, -84, -74, -66, -58, -44, -36, -34, -30, -20, -18, -14, -8, -6, -4, 2, 4, 6, 32, 42, 60, 76, 140, 256, 790, 1004
-585 -1392, -1063, -903, -622, -604, -534, -424, -418, -409, -336, -295, -220, -202, -196, -168, -148, -142, -132, -130, -114, -96, -76, -75, -70, -57, -49, -40, -37, -33, -24, -16, -15, -13, -12, -10, -9, -7, -6, -4, -3, 2, 3, 5, 8, 14, 24, 26, 30, 32, 33, 47, 57, 74, 114, 177, 206, 240, 267, 327, 348, 375, 401, 440, 524, 575, 632, 932, 1175, 1346
-583 -1109, -525, -249, -189, -45, -21, -17, -9, 3, 7, 27, 351, 651, 1191
-581 -574, -234, -114, -62, -58, -18, -14, -10, -2, 18, 22, 26, 30, 62, 130, 322, 678, 790, 886
-579 -919, -819, -511, -473, -349, -125, -93, -69, -61, -60, -55, -51, -49, -36, -31, -20, -15, -12, -9, -5, -4, -3, -1, 11, 19, 35, 36, 231, 237, 261, 348, 355, 401, 564, 671, 785, 787, 975, 1236
-577 -807, -611, -167, -163, -127, -83, -79, -71, -39, -35, -15, -11, -7, -3, 1, 29, 33, 125, 269, 781, 1305, 1489
-575 -1424, -62, -44, -26, -14, -10, -2, 4, 16, 88, 106, 194, 1250
-573 -1468, -944, -565, -354, -226, -224, -221, -146, -101, -77, -66, -58, -56, -45, -42, -41, -9, -8, -6, -5, -4, -2, -1, 3, 6, 14, 32, 35, 46, 52, 102, 104, 116, 118, 172, 219, 251, 266, 344, 355, 382, 712, 826, 1375
-571 -991, -787, -247, -103, -93, -49, -39, -37, -31, -27, -19, -13, -9, -7, -3, -1, 3, 9, 21, 39, 41, 83, 137, 161, 293, 633, 807, 849, 879, 1353, 1367, 1481
-569 -1496, -728, -512, -344, -236, -180, -68, -48, -20, -12, -8, 4, 24, 48, 60, 108, 172, 204, 940, 1384
-567 -1402, -1176, -1044, -587, -554, -464, -383, -288, -264, -246, -232, -206, -174, -91, -72, -66, -54, -48, -36, -20, -18, -16, -14, -12, -11, -10, -8, -7, -6, -2, 2, 5, 10, 12, 16, 20, 29, 38, 42, 54, 82, 92, 113, 146, 166, 168, 174, 210, 414, 497, 544, 632, 746, 773, 840, 1014, 1214, 1394
-565 -651, -229, -121, -119, -111, -49, -33, -27, -15, -11, -9, -3, -1, 1, 3, 13, 21, 25, 41, 49, 51, 63, 89, 97, 157, 185, 277, 313, 327, 707, 865, 1237, 1393
-563 -1216, -642, -498, -438, -404, -372, -208, -178, -176, -124, -118, -88, -84, -66, -56, -40, -20, -18, -12, -10, -8, -6, -4, 2, 4, 14, 16, 18, 20, 56, 66, 72, 76, 100, 114, 204, 392, 954, 1052
-561 -1442, -1379, -1195, -922, -905, -515, -343, -259, -235, -95, -83, -77, -26, -22, -14, -11, -10, -7, -2, 2, 7, 14, 26, 31, 38, 70, 238, 493, 583, 877, 907, 1330
-559 -1491, -1391, -961, -847, -449, -441, -407, -231, -71, -51, -19, -17, -11, -9, -7, -1, 1, 7, 13, 17, 23, 39, 49, 77, 101, 173, 349, 481, 647, 821, 959, 1129
-557 -996, -984, -282, -178, -76, -60, -52, -42, -24, -18, -12, -10, -4, 8, 14, 44, 60, 200, 224, 270, 350, 1110
-555 -1419, -1277, -1247, -867, -717, -570, -467, -441, -350, -267, -210, -153, -137, -120, -117, -98, -95, -90, -87, -72, -66, -36, -35, -27, -21, -17, -15, -12, -11, -9, -6, -5, -3, 1, 7, 9, 12, 24, 27, 30, 31, 43, 67, 150, 238, 282, 307, 357, 694, 793, 909, 918, 1101, 1272, 1437
-553 -1493, -1021, -977, -801, -405, -153, -137, -93, -81, -53, -45, -25, -21, -13, -9, -5, 3, 7, 39, 63, 87, 95, 235, 567, 603, 975, 1487
-551 -782, -114, -98, -46, -26, -22, -18, -6, -2, 2, 34, 66, 162, 226, 442, 778, 1238
-549 -1407, -1291, -1149, -1001, -668, -591, -459, -439, -437, -416, -393, -303, -252, -228, -223, -80, -69, -63, -48, -39, -29, -23, -20, -17, -13, -12, -11, -9, -8, -7, -3, -1, 1, 3, 4, 7, 11, 12, 23, 28, 33, 39, 43, 48, 81, 147, 177, 324, 373, 384, 411, 1084, 1361, 1380
-547 -1367, -971, -35, -19, -7, 1, 653
-545 -1228, -1018, -772, -108, -74, -50, -22, -10, -2, 2, 4, 20, 34, 38, 158, 292, 298, 476, 878, 886, 1390
-543 -1317, -160, -145, -96, -33, -18, -13, -9, -6, -1, 15, 27, 47, 63, 90, 104, 363, 1007, 1304
-541 -1067, -885, -869, -665, -407, -357, -335, -117, -105, -47, -17, -9, -5, 3, 7, 13, 25, 55, 61, 85, 135, 303, 307, 361, 475, 493, 1093, 1351
-539 -1040, -520, -472, -300, -152, -116, -76, -68, -44, -36, -16, -12, -8, -4, 4, 8, 16, 24, 36, 40, 92, 136, 140, 340, 384, 492, 704, 1248, 1356
-537 -1351, -1020, -991, -815, -724, -648, -644, -547, -479, -354, -235, -228, -172, -114, -112, -92, -79, -43, -39, -30, -24, -23, -12, -11, -10, -8, -7, -4, 5, 6, 9, 13, 16, 21, 26, 28, 32, 48, 61, 76, 77, 100, 102, 121, 126, 208, 241, 245, 440, 581, 748, 845, 1221, 1357
-535 -569, -279, -159, -69, -65, -15, -9, -5, 1, 9, 15, 51, 129, 151, 175, 225, 735, 1385
-533 -1462, -1238, -1118, -286, -226, -212, -196, -176, -110, -86, -26, -20, -16, -10, -8, 2, 4, 8, 10, 22, 44, 112, 118, 310, 320, 430, 484, 572, 622, 1478
-531 -1473, -1081, -961, -521, -454, -395, -329, -249, -239, -233, -229, -173, -121, -110, -85, -75, -61, -41, -39, -35, -25, -21, -15, -9, -6, -5, -3, 1, 7, 11, 15, 57, 739, 897, 1199, 1387, 1434
-529 -1285, -759, -703, -663, -87, -63, -55, -39, -27, -19, -9, -7, -3, 3, 5, 11, 17, 21, 27, 41, 51, 93, 165, 1155
-527 -608, -344, -242, -192, -174, -158, -132, -98, -90, -74, -48, -44, -42, -36, -32, -24, -20, -8, -6, -2, 4, 12, 22, 54, 78, 108, 112, 120, 144, 150, 628, 640
-525 -1432, -1219, -1067, -980, -919, -728, -682, -625, -531, -388, -354, -288, -247, -172, -170, -98, -84, -48, -41, -38, -31, -24, -20, -19, -18, -17, -16, -14, -12, -11, -10, -9, -8, -7, -6, -4, -2, -1, 1, 2, 6, 8, 10, 12, 16, 18, 22, 26, 29, 33, 34, 44, 45, 48, 69, 71, 72, 84, 85, 96, 98, 101, 146, 188, 190, 221, 242, 314, 333, 383, 409, 685, 812, 838, 1013, 1231, 1306
-523 -353, -317, -301, -141, -73, -33, -25, -21, -13, -9, -5, -1, 7, 15, 23, 27, 39, 63, 79, 183, 363, 459
-521 -534, -286, -254, -86, -10, -6, 2, 6, 30, 34, 50, 54, 66, 170, 482
-519 -1237, -947, -833, -820, -673, -605, -584, -413, -376, -217, -112, -92, -85, -49, -37, -35, -28, -17, -13, -9, -8, -5, -4, 5, 7, 8, 11, 13, 16, 28, 47, 55, 67, 187, 200, 212, 251, 316, 548, 944, 1475
-517 -1111, -707, -675, -267, -207, -151, -139, -79, -63, -59, -55, -39, -23, -19, -15, -11, -9, -7, -3, 1, 13, 17, 33, 37, 57, 61, 77, 149, 165, 181, 201, 365
-515 -1192, -1102, -508, -294, -262, -120, -40, -30, -28, -22, -12, -10, -9, -4, 8, 20, 36, 38, 56, 230, 266, 410, 540, 566, 668, 986, 1496
-513 -1413, -945, -794, -684, -672, -588, -462, -350, -236, -213, -138, -66, -48, -45, -38, -30, -26, -21, -20, -18, -12, -8, -6, -2, 6, 12, 18, 39, 42, 51, 96, 135, 190, 255, 267, 268, 306, 495, 526, 558, 1324, 1347, 1468, 1486
-511 -1231, -857, -809, -805, -643, -639, -577, -565, -467, -377, -335, -307, -295, -233, -187, -181, -173, -165, -155, -127, -87, -79, -75, -55, -53, -51, -45, -31, -29, -19, -15, -13, -7, -5, -3, -1, 1, 7, 9, 11, 15, 23, 31, 67, 103, 105, 113, 121, 127, 149, 231, 357, 471, 573, 627, 765, 1135
-509 -1312, -736, -16, -9, 8, 648
-507 -895, -786, -783, -366, -316, -243, -196, -179, -147, -127, -114, -87, -78, -42, -28, -27, -18, -16, -15, -14, -9, -8, -7, -6, -4, -3, -2, 1, 2, 4, 5, 9, 14, 18, 26, 28, 29, 38, 52, 54, 108, 126, 129, 141, 272, 482, 577, 1009, 1049, 1246
-505 -1441, -697, -77, -13, -11, -9, -1, 1, 11, 31, 47, 241, 1363
-503 -1374, -1192, -1068, -880, -798, -640, -552, -504, -306, -290, -282, -234, -210, -124, -96, -76, -66, -64, -34, -24, -22, -18, -16, -14, -12, -10, -6, -4, -2, 2, 6, 8, 12, 24, 26, 34, 42, 58, 62, 80, 110, 264, 270, 294, 394, 540, 744, 966, 1206, 1332, 1404
-501 -1342, -694, -450, -445, -343, -165, -145, -73, -34, -33, -22, -18, -13, -10, -9, -7, -1, 2, 3, 6, 14, 194, 195, 329, 579, 1386, 1467
-499 -639, -425, -155, -77, -35, -23, -11, -9, -5, -3, 1, 9, 13, 33, 37, 129, 187, 259, 571, 621, 1053, 1159
-497 -1028, -526, -212, -206, -118, -92, -46, -24, -22, -14, -8, -6, 2, 4, 18, 24, 72, 74, 218, 268, 456, 826, 1466
-495 -1355, -1290, -1252, -1196, -1106, -1094, -970, -803, -770, -682, -464, -452, -374, -370, -343, -211, -203, -176, -134, -117, -66, -62, -56, -52, -51, -44, -30, -28, -26, -23, -19, -14, -11, -9, -8, -7, -6, -5, -4, -3, -2, 2, 4, 8, 9, 16, 21, 33, 44, 59, 65, 91, 93, 114, 140, 149, 182, 280, 283, 294, 302, 328, 332, 347, 403, 532, 712, 717, 982, 985, 1294
-493 -769, -517, -365, -345, -309, -289, -257, -209, -161, -109, -101, -65, -33, -17, -13, -9, -5, -1, 3, 7, 19, 39, 71, 111, 223, 1027, 1319, 1387, 1495
-491 -26, -2, 46, 178, 922, 934
-489 -1453, -1365, -1300, -1188, -1116, -957, -937, -848, -769, -712, -652, -521, -517, -373, -353, -329, -265, -245, -225, -192, -107, -93, -68, -56, -36, -33, -13, -12, -11, -9, -8, -5, -1, 1, 3, 4, 5, 7, 8, 17, 20, 31, 32, 39, 41, 48, 51, 63, 75, 99, 151, 187, 228, 229, 275, 312, 347, 391, 419, 697, 723, 1049, 1323, 1331, 1447
-487 -1111, -543, -367, -111, -55, -39, -19, -7, -3, 5, 29, 161, 173
-485 -954, -666, -558, -468, -248, -198, -186, -164, -92, -72, -24, -8, -6, 4, 6, 28, 36, 108, 366
-483 -1386, -1188, -1106, -1088, -922, -898, -778, -732, -730, -678, -594, -578, -557, -388, -380, -333, -300, -298, -276, -246, -220, -116, -114, -108, -102, -101, -88, -68, -62, -53, -41, -40, -32, -17, -16, -14, -12, -10, -9, -8, -6, -4, -2, 2, 3, 4, 6, 10, 18, 22, 27, 32, 38, 50, 54, 64, 76, 104, 110, 116, 126, 127, 146, 176, 186, 208, 262, 300, 318, 319, 330, 342, 376, 379, 414, 532, 578, 764, 1166
-481 -1121, -895, -877, -845, -697, -511, -267, -231, -211, -207, -201, -145, -81, -27, -11, -9, -7, -5, -1, 3, 5, 9, 13, 15, 33, 55, 69, 75, 285, 439, 835, 895, 909, 1095, 1105, 1109
-479 -720, -216, -212, -136, -100, -68, -40, -36, -28, -12, -8, -4, 12, 20, 28, 36, 48, 72, 92, 108, 128, 164, 172, 256, 320, 332, 348, 496, 932, 1008
-477 -1330, -964, -638, -187, -79, -76, -31, -28, -26, -14, -11, -10, -7, -4, 1, 2, 5, 13, 22, 49, 70, 77, 437, 529, 566, 641, 673, 769, 1004, 1262
-475 -775, -653, -565, -345, -255, -243, -229, -159, -133, -73, -49, -33, -13, -9, -7, -5, -3, 5, 11, 15, 21, 35, 105, 141, 151, 185, 191, 355, 365, 943
-473 -760, -684, -660, -412, -376, -276, -220, -144, -114, -102, -96, -72, -70, -52, -34, -16, -12, -6, -4, 6, 36, 60, 66, 68, 140, 200, 738
-471 -1407, -1233, -1130, -1031, -963, -765, -714, -383, -311, -219, -179, -167, -143, -123, -111, -98, -63, -51, -41, -39, -38, -27, -21, -18, -15, -14, -9, -5, -3, -2, 1, 3, 13, 15, 37, 49, 70, 99, 135, 159, 193, 199, 310, 379, 402, 415, 442, 687, 987, 1201
-469 -1221, -493, -189, -179, -143, -105, -85, -45, -31, -15, -13, -11, -9, -3, -1, 1, 51, 267, 295, 451, 879, 1385
-467 -1402, -1348, -868, -722, -412, -338, -240, -110, -108, -40, -38, -32, -10, -8, -2, 2, 8, 10, 12, 112, 142, 322, 382, 480
-465 -1261, -1100, -1083, -1061, -945, -880, -823, -723, -524, -484, -401, -315, -251, -174, -160, -151, -143, -132, -126, -74, -71, -69, -61, -57, -54, -51, -43, -42, -41, -36, -25, -21, -16, -15, -14, -13, -12, -11, -9, -7, -6, -5, -4, -3, -2, -1, 1, 3, 5, 6, 8, 9, 13, 16, 17, 34, 43, 44, 51, 53, 54, 55, 61, 65, 81, 89, 90, 96, 99, 126, 131, 160, 171, 179, 180, 188, 241, 251, 289, 291, 381, 390, 426, 433, 498, 585, 695, 697, 714, 781, 785, 801, 895, 991, 1015, 1057, 1078, 1185, 1303
-463 -581, -397, -113, -77, -53, -37, -25, -5, -1, 7, 43, 367, 1195
-461 -822, -454, -434, -414, -390, -86, -74, -42, -14, -10, -6, -2, 10, 54, 58, 358, 562, 1486
-459 -1359, -1095, -856, -616, -331, -295, -207, -199, -196, -159, -75, -57, -51, -48, -28, -21, -19, -15, -12, -9, -7, -4, -1, 3, 8, 9, 11, 24, 32, 123, 153, 155, 209, 269, 333, 449, 471, 515, 780, 785, 1349
-457 -635, -63, -3, 9, 33, 37, 93, 145, 273, 345, 865, 1437
-455 -1448, -788, -690, -628, -564, -506, -410, -236, -228, -176, -130, -88, -40, -36, -34, -10, -8, -4, 20, 24, 30, 62, 94, 102, 112, 270, 640, 756, 1172
-453 -1317, -1254, -1002, -788, -656, -570, -533, -446, -416, -414, -314, -305, -276, -262, -145, -142, -133, -97, -82, -65, -64, -60, -54, -45, -38, -33, -30, -24, -20, -17, -12, -10, -9, -8, -6, -5, -2, 2, 3, 4, 11, 15, 31, 38, 47, 48, 70, 71, 76, 78, 103, 123, 147, 234, 243, 466, 528, 775, 880, 938, 1126, 1160, 1222
-451 -1331, -945, -347, -251, -235, -209, -157, -153, -117, -77, -57, -53, -41, -35, -33, -27, -17, -13, -11, -9, -5, -3, -1, 3, 5, 7, 15, 37, 79, 343, 379, 543, 957, 995, 1149, 1165
-449 -1048, -620, -28, -20, -8, -4, 112, 200, 1192, 1480
-447 -1030, -898, -844, -836, -696, -535, -394, -378, -214, -180, -162, -139, -130, -118, -102, -96, -95, -79, -70, -58, -50, -28, -20, -18, -16, -15, -14, -11, -10, -8, -6, -4, -3, -2, 2, 4, 5, 6, 12, 14, 18, 20, 22, 30, 38, 45, 56, 60, 69, 78, 106, 132, 174, 224, 232, 445, 572, 621, 674, 1182, 1500
-445 -1417, -843, -513, -369, -225, -199, -151, -49, -43, -15, -9, -7, -1, 3, 11, 17, 81, 479, 983
-443 -510, -282, -116, -110, -66, -62, -30, -6, -2, 6, 10, 34, 66, 70, 118, 186, 214, 298, 406, 438, 1474
-441 -1473, -1347, -1035, -883, -873, -861, -857, -815, -633, -611, -583, -553, -463, -447, -271, -227, -217, -205, -173, -159, -155, -107, -103, -95, -89, -71, -67, -49, -45, -33, -25, -19, -17, -15, -11, -9, -7, -5, -3, -1, 1, 3, 13, 19, 23, 35, 39, 45, 83, 151, 179, 181, 287, 293, 417, 499, 525, 663, 813, 839, 1301, 1327, 1337, 1375, 1409
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211 -680, -560, -448, -124, -8, -4, 20, 28, 32, 192, 380, 1408
213 -1498, -1476, -1399, -864, -538, -450, -438, -204, -103, -94, -66, -60, -58, -36, -30, -28, -10, -6, -4, 2, 6, 14, 17, 36, 62, 80, 84, 156, 726, 866
215 -1053, -297, -183, -153, -93, -45, -33, -27, -15, -9, -3, 1, 3, 171, 585, 1161
217 -220, -214, -142, -126, -32, -20, -6, -4, 66, 84, 880
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229 -678, -206, -30, -6, -2, 6, 82, 186, 334, 690, 838, 1146, 1482
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237 -1166, -868, -481, -236, -157, -85, -77, -13, -5, -2, -1, 4, 10, 52, 58, 59, 68, 82, 115, 247, 647
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241 -768, -616, -348, -336, -48, -28, -16, -12, -4, 36, 72, 288
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251 -1249, -787, -229, -215, -167, -127, -53, -13, -7, -5, 1, 11, 13, 17, 35, 77, 155, 325
253 -1390, -1328, -608, -584, -564, -396, -158, -152, -148, -124, -108, -96, -80, -62, -60, -48, -40, -36, -32, -30, -24, -20, -16, -12, -10, -8, -6, -4, -2, 2, 4, 6, 16, 32, 48, 50, 52, 64, 66, 72, 86, 108, 130, 164, 304, 356, 482, 486, 712, 772, 834, 1196
255 -1494, -1479, -1408, -1284, -1261, -643, -514, -382, -234, -223, -99, -94, -87, -78, -72, -63, -61, -42, -39, -37, -28, -22, -18, -15, -13, -10, -7, -4, -3, -1, 2, 5, 32, 36, 38, 41, 57, 69, 71, 72, 116, 137, 156, 197, 237, 336, 353, 489, 545, 678, 1040, 1137, 1217, 1451
257 -441, -209, -9, 279, 415, 711
259 -138, -26, -10, -2, 38, 70
261 -1493, -1464, -912, -835, -611, -571, -549, -536, -513, -452, -421, -396, -320, -301, -241, -212, -209, -204, -156, -152, -109, -95, -87, -85, -76, -75, -65, -59, -49, -36, -29, -27, -25, -20, -15, -12, -11, -9, -7, -5, -4, -3, -1, 1, 3, 4, 5, 7, 9, 11, 27, 29, 37, 57, 59, 67, 71, 73, 101, 117, 155, 157, 160, 193, 195, 208, 273, 303, 328, 357, 433, 443, 444, 479, 587, 1095, 1101, 1149, 1291, 1319
263 -115, -11, -3, 29, 85, 605, 1293
265 -1406, -1382, -758, -712, -602, -404, -368, -310, -182, -172, -134, -110, -94, -92, -50, -38, -32, -14, -10, -8, -4, -2, 2, 4, 16, 58, 70, 80, 158, 202, 322, 356, 616
267 -1460, -1394, -1186, -1012, -976, -952, -770, -745, -618, -444, -408, -394, -386, -277, -218, -206, -152, -102, -97, -86, -32, -30, -28, -26, -25, -18, -14, -12, -10, -8, -6, -4, -2, -1, 2, 3, 4, 12, 34, 40, 46, 70, 82, 102, 118, 119, 192, 202, 300, 434, 508, 515, 516, 612, 690, 718, 795, 846, 1112
269 -1215, -675, -445, -343, -247, -63, -57, -37, -21, -15, -13, -7, -3, -1, 3, 5, 15, 27, 53, 137, 153, 155, 185, 239, 717, 735, 789, 1343
271 -1340, -20, 4, 84
273 -1214, -1144, -1062, -834, -730, -619, -559, -422, -323, -287, -247, -242, -155, -154, -139, -138, -128, -127, -115, -88, -78, -67, -66, -59, -47, -46, -35, -32, -23, -16, -14, -10, -7, -6, -3, -2, 1, 2, 5, 10, 13, 40, 41, 45, 56, 64, 72, 86, 94, 121, 160, 213, 338, 352, 833, 1014, 1072, 1098, 1297, 1381
275 -873, -339, -255, -145, -51, -45, -21, -13, -9, -5, -3, -1, 7, 15, 21, 25, 27, 69, 71, 105, 207, 285, 611, 635, 647, 969, 1127, 1159
277 -1452, -1062, -580, -314, -198, -190, -184, -170, -162, -122, -100, -94, -62, -60, -52, -42, -40, -22, -14, -12, -10, -4, -2, 2, 6, 8, 18, 20, 22, 36, 62, 108, 120, 162, 180, 222, 450, 530, 706, 1028, 1200, 1296, 1362
279 -1370, -1225, -790, -721, -598, -533, -313, -106, -49, -38, -29, -22, -10, -5, -2, -1, 2, 5, 10, 67, 70, 185, 218, 254, 530, 539, 587, 767, 806, 1142, 1169
281 -1391, -509, -361, -319, -113, -111, -71, -47, -37, -31, -15, -7, -5, -1, 1, 7, 9, 11, 33, 81, 113, 143, 185, 227, 359, 393, 631, 1123, 1273, 1351
283 -706, -310, -24, -10, -6, 30, 264, 486
285 -1019, -1016, -824, -687, -575, -512, -459, -333, -305, -143, -111, -71, -69, -45, -38, -17, -15, -11, -9, -8, -6, -5, -3, 1, 3, 4, 15, 18, 21, 27, 37, 45, 55, 58, 69, 73, 87, 171, 201, 232, 307, 375, 567, 882
287 -1141, -53, -37, -29, 3, 27, 59, 291, 699, 1259
289 -794, -450, -374, -78, -30, -18, -14, -6, -2, 10, 22, 34, 42, 150
291 -644, -393, -340, -295, -188, -160, -107, -84, -83, -73, -35, -28, -24, -20, -17, -16, -11, -8, -7, -4, -1, 4, 12, 16, 20, 24, 39, 40, 65, 77, 95, 240, 256, 303, 376, 416, 596, 760, 1037, 1045
293 -907, -403, -319, -263, -191, -43, -23, -11, -7, 1, 5, 181, 257, 469
295 -1480, -1060, -754, -436, -330, -274, -154, -138, -132, -52, -34, -28, -22, -16, -12, -10, -6, -4, 2, 4, 8, 30, 52, 68, 128, 140, 170, 182, 186, 294, 332, 498, 516, 528, 534, 1106
297 -1488, -1425, -1116, -1000, -736, -612, -322, -274, -256, -225, -213, -136, -112, -48, -33, -22, -21, -10, -9, -4, 3, 6, 14, 15, 20, 27, 38, 123, 276, 327, 380, 411, 546, 819, 1155, 1274
299 -1251, -671, -419, -165, -159, -87, -41, -33, -21, -17, -11, -9, -5, -3, 1, 3, 7, 9, 45, 57, 73, 79, 81, 91, 141, 177, 193, 241, 267, 493, 777, 921, 1167, 1179, 1191
301 -1196, -452, -376, -256, -72, -32, -28, -20, -16, -12, -8, -4, 4, 184, 344, 352, 392, 1060
303 -1456, -1263, -1227, -831, -686, -640, -587, -516, -436, -339, -311, -286, -279, -243, -235, -187, -183, -142, -127, -119, -110, -75, -70, -62, -40, -38, -31, -27, -26, -19, -16, -15, -11, -10, -7, -6, -3, -2, 1, 2, 5, 8, 9, 10, 13, 17, 21, 30, 38, 93, 125, 140, 170, 178, 181, 394, 453, 588, 1161, 1221
305 -1399, -1365, -1209, -1131, -313, -291, -217, -147, -139, -87, -85, -73, -67, -61, -43, -25, -19, -15, -7, -5, -3, -1, 3, 7, 21, 23, 29, 35, 53, 87, 91, 95, 115, 165, 179, 233, 367, 419, 609, 791
307 -1376, -1256, -694, -314, -302, -104, -86, -64, -26, -16, -14, -8, -2, 2, 8, 16, 26, 34, 112, 182, 226, 304, 782
309 -1243, -1183, -1161, -883, -786, -714, -503, -474, -423, -407, -366, -363, -267, -214, -213, -179, -131, -81, -78, -69, -39, -27, -21, -17, -14, -13, -11, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 21, 51, 53, 57, 67, 69, 106, 143, 163, 193, 194, 231, 338, 343, 1197, 1314
311 -597, -261, -135, -129, -75, -55, -45, -27, -25, -19, -9, -7, -1, 9, 29, 35, 105, 125, 131, 179, 359
313 -1112, -956, -596, -360, -116, -92, -26, -20, -12, -8, -2, 4, 10, 16, 24, 70, 184, 250, 432, 460, 792
315 -1350, -1319, -1276, -1218, -1217, -785, -720, -717, -594, -573, -477, -414, -325, -253, -249, -247, -245, -217, -191, -186, -133, -108, -104, -97, -88, -60, -48, -45, -41, -24, -23, -20, -18, -16, -15, -14, -9, -8, -7, -6, -5, -4, -1, 1, 3, 6, 9, 20, 22, 27, 32, 72, 97, 99, 104, 107, 120, 140, 142, 151, 180, 304, 305, 342, 440, 489, 521, 635, 665, 673, 767, 876, 1040, 1313, 1359
317 -413, -317, -245, -177, -133, -89, -77, -9, -5, 7, 11, 243, 291, 327, 1211
319 -238, -94, -46, -14, -6, 2, 10, 18, 274, 314, 522, 562, 578, 594, 602, 930, 1074
321 -1300, -1028, -701, -581, -500, -461, -301, -167, -125, -101, -68, -35, -29, -23, -20, -13, -8, -7, -5, -4, 1, 5, 32, 68, 109, 128, 133, 212, 241, 653, 776, 1339
323 -1155, -679, -599, -415, -295, -211, -83, -59, -39, -35, -15, -11, -3, 1, 5, 145, 329, 381, 465
325 -886, -510, -408, -240, -166, -138, -130, -102, -72, -60, -42, -36, -18, -12, -6, 2, 14, 18, 32, 42, 72, 144, 174, 282, 318, 828, 1338
327 -1416, -1133, -1002, -704, -473, -393, -125, -114, -104, -84, -57, -42, -26, -21, -12, -9, -5, -2, 3, 4, 6, 15, 30, 64, 99, 108, 135, 363, 414, 531, 576, 811, 1326, 1414, 1476
329 -1435, -1237, -1195, -915, -799, -727, -649, -483, -467, -425, -371, -353, -253, -111, -105, -89, -75, -51, -49, -35, -27, -25, -21, -13, -11, -7, -3, -1, 1, 3, 5, 9, 11, 15, 27, 55, 87, 105, 111, 163, 225, 311, 487, 537, 723, 735, 771
331 -1492, -844, -748, -664, -532, -384, -376, -188, -104, -100, -72, -64, -44, -32, -16, -8, -4, 4, 8, 12, 20, 28, 36, 120, 184, 200, 756, 788, 1304
333 -1140, -1131, -1092, -972, -760, -592, -579, -484, -411, -255, -102, -60, -52, -51, -42, -39, -35, -22, -20, -11, -7, -6, -4, -2, 5, 6, 9, 18, 25, 33, 50, 54, 69, 70, 101, 153, 176, 245, 401, 448, 745, 768, 806, 840, 1338
335 -935, -791, -551, -433, -353, -215, -151, -95, -35, -13, -11, -7, -5, -1, 19, 23, 29, 173, 263, 295, 659, 803, 1075, 1087, 1129, 1189
337 -950, -710, -604, -436, -246, -126, -116, -104, -50, -46, -38, -26, -10, -8, -6, -4, 4, 6, 10, 26, 64, 66, 70, 102, 322, 370, 570
339 -502, -195, -105, -82, -70, -55, -37, -34, -25, -22, -15, -7, -3, 3, 11, 17, 21, 26, 50, 62, 125, 165, 278, 290, 1227, 1275, 1325
341 -819, -795, -303, -171, -159, -137, -83, -53, -33, -27, -23, -17, -11, -9, -5, -3, 1, 3, 7, 19, 21, 33, 43, 99, 183, 235, 499, 579, 1137, 1225
343 -1300, -1180, -934, -502, -344, -284, -80, -62, -52, -40, -32, -20, -10, -8, -4, -2, 2, 20, 22, 46, 58, 226
345 -921, -779, -740, -731, -555, -538, -522, -489, -486, -480, -428, -411, -351, -335, -286, -241, -186, -162, -156, -153, -140, -121, -103, -93, -88, -75, -68, -56, -54, -50, -39, -38, -31, -30, -26, -23, -19, -18, -16, -15, -14, -13, -12, -11, -9, -8, -6, -3, -2, -1, 1, 2, 4, 8, 9, 11, 15, 18, 20, 24, 30, 40, 47, 87, 88, 150, 154, 166, 195, 264, 360, 412, 438, 546, 569, 621, 625, 778, 814, 1041, 1189, 1302, 1356, 1397, 1465
347 -1433, -933, -873, -573, -357, -161, -105, -89, -77, -57, -41, -29, -21, -13, -9, -5, -1, 3, 7, 15, 23, 27, 175, 259, 391, 607, 679, 863, 927, 999, 1339, 1371
349 -1346, -370, -314, -10, -2, 10, 26, 38, 46, 1114
351 -1464, -1303, -1204, -1184, -648, -564, -507, -392, -201, -185, -121, -84, -79, -44, -31, -29, -21, -15, -13, -12, -11, -9, -8, -7, -5, -4, -3, -1, 12, 13, 15, 31, 36, 45, 53, 123, 153, 155, 172, 223, 247, 269, 287, 353, 1416
353 -27, 21, 369
355 -1394, -254, -228, -168, -90, -24, -12, -6, -2, 6, 12, 24, 34, 46, 138, 174, 816, 1164
357 -1130, -928, -677, -557, -517, -386, -286, -256, -232, -172, -160, -148, -116, -112, -53, -37, -33, -32, -28, -26, -25, -22, -18, -14, -10, -8, -6, -5, -4, -1, 2, 3, 7, 8, 10, 14, 18, 23, 26, 27, 35, 44, 46, 50, 55, 56, 59, 67, 80, 115, 138, 248, 280, 319, 372, 416, 454, 624, 662, 686, 702, 707, 806, 847, 866, 1422
359 -1313, -1227, -895, -817, -507, -143, -97, -87, -83, -79, -63, -43, -31, -17, -7, -3, 1, 5, 7, 9, 47, 55, 65, 69, 97, 103, 273, 1231
361 -1392, -72, -24, -12, -8, 28, 36, 100, 312, 568
363 -1475, -1238, -1087, -1084, -706, -275, -254, -179, -95, -74, -56, -34, -26, -23, -16, -14, -11, -8, -7, -4, -2, 1, 2, 5, 16, 29, 61, 136, 145, 157, 178, 560, 581, 1001, 1234, 1325, 1370, 1405
365 -771, -757, -693, -667, -355, -273, -267, -253, -157, -133, -61, -51, -37, -21, -17, -9, -5, -3, -1, 5, 11, 19, 63, 93, 95, 103, 147, 275, 293, 539, 623, 1115, 1181
367 -804, -342, -186, -168, -48, -42, -28, -18, -12, -6, -4, 12, 48, 72, 84, 228, 306, 360, 404, 524, 1062
369 -1463, -1113, -866, -690, -609, -569, -461, -383, -258, -191, -170, -126, -62, -41, -26, -18, -17, -11, -9, -6, -5, -2, 1, 3, 13, 39, 61, 99, 111, 121, 142, 385
371 -937, -459, -393, -287, -263, -189, -157, -97, -87, -79, -61, -21, -13, -9, -7, -3, -1, 1, 3, 23, 27, 39, 41, 97, 101, 123, 183, 201, 311, 411, 519, 551, 557, 867
373 -1258, -154, -54, -46, -22, -4, 2, 6, 14, 36, 62, 92, 122, 292, 758
375 -1353, -1230, -1171, -531, -523, -498, -494, -470, -456, -454, -410, -366, -319, -306, -283, -262, -248, -208, -153, -122, -110, -82, -71, -67, -62, -27, -22, -18, -17, -14, -11, -10, -9, -8, -7, -6, -3, -2, 1, 3, 6, 8, 10, 13, 14, 16, 17, 21, 22, 26, 30, 32, 33, 39, 49, 53, 152, 162, 181, 233, 328, 576, 629, 666, 824, 850, 919, 1131
377 -557, -505, -361, -349, -41, -17, -5, -1, 11, 143, 619
379 -786, -46, -42, -30, -26, -14, -6, -2, 14, 26, 30, 94, 334, 498, 714, 1446
381 -727, -528, -409, -363, -231, -183, -168, -151, -148, -145, -115, -109, -108, -75, -51, -37, -24, -21, -19, -15, -13, -7, -4, -3, -1, 3, 15, 17, 20, 21, 41, 44, 51, 113, 140, 179, 219, 249, 323, 461, 521, 671, 680, 692, 695, 716, 809, 825, 887, 897, 1055, 1439
383 -15
385 -1266, -858, -668, -650, -412, -408, -316, -300, -286, -202, -150, -128, -112, -106, -70, -62, -50, -40, -38, -32, -30, -24, -16, -12, -10, -8, -6, -4, -2, 8, 10, 14, 16, 36, 62, 76, 88, 114, 138, 258, 278, 338, 416, 538, 590, 736, 1074, 1154, 1262
387 -1153, -1040, -813, -425, -397, -273, -260, -142, -110, -72, -62, -60, -53, -21, -20, -12, -8, -5, -1, 2, 7, 15, 27, 28, 60, 67, 82, 88, 122, 179, 202, 235, 298, 519, 655
389 -1229, -643, -173, -149, -115, -83, -75, -31, -29, -13, -11, -5, -3, 11, 57, 59, 115, 299, 347, 715
391 -640, -632, -320, -272, -188, -68, -52, -32, -16, -8, 4, 20, 28, 40, 88, 92, 328, 1052, 1420
393 -1020, -912, -604, -546, -539, -519, -455, -332, -272, -187, -135, -126, -64, -55, -52, -51, -43, -39, -31, -23, -19, -16, -15, -11, -7, -6, -4, -3, -2, 1, 5, 6, 8, 13, 17, 21, 24, 25, 37, 41, 46, 173, 185, 285, 313, 344, 368, 421, 550, 558, 669, 709, 749, 781, 956, 1009, 1141, 1165, 1441, 1461
395 -385, -169, -127, -67, -31, -19, -9, -7, -1, 5, 11, 23, 41, 221, 485, 839
397 -1286, -1256, -1170, -912, -680, -476, -324, -260, -228, -188, -126, -50, -44, -18, -12, -8, -6, -2, 4, 6, 16, 24, 30, 36, 40, 52, 60, 78, 132, 204, 352, 556
399 -1365, -1314, -1225, -1206, -661, -581, -546, -409, -234, -169, -101, -90, -85, -78, -58, -49, -34, -30, -29, -25, -18, -11, -10, -9, -6, -5, -1, 2, 6, 11, 14, 15, 42, 59, 66, 75, 91, 102, 126, 131, 195, 795, 811, 1410
401 -285, -177, -105, -43, -5, -3, 3, 7, 57, 123, 615
403 -1376, -1358, -996, -984, -688, -536, -296, -294, -236, -234, -210, -170, -130, -96, -90, -78, -56, -54, -46, -24, -14, -10, -8, -6, -4, 2, 4, 6, 14, 16, 32, 40, 74, 110, 134, 252, 280, 306, 356, 410, 692, 760, 1220, 1286
405 -1115, -740, -695, -593, -589, -517, -406, -209, -182, -118, -106, -70, -52, -35, -32, -26, -17, -13, -10, -8, -4, -2, 1, 2, 4, 8, 10, 14, 32, 43, 46, 58, 80, 163, 184, 227, 262, 361, 592, 602, 623, 638
407 -1089, -709, -693, -585, -361, -185, -177, -149, -125, -105, -101, -97, -77, -57, -49, -45, -29, -25, -21, -17, -13, -9, -5, -1, 3, 11, 15, 23, 75, 119, 159, 215, 227, 235, 931, 979, 1147
409 -1258, -658, -498, -250, -30, -22, -18, -10, 2, 6, 18, 110, 186, 318, 398
411 -1395, -735, -531, -413, -125, -48, -39, -35, -23, -15, -12, -11, -5, -3, 1, 4, 7, 19, 37, 55, 72, 79, 81, 136, 139, 955, 976, 979
413 -1335, -1015, -931, -639, -623, -351, -323, -191, -91, -51, -39, -31, -19, -15, -7, -3, 1, 5, 9, 13, 25, 85, 113, 133, 185, 217, 269, 285, 469, 1025
415 -1382, -1264, -934, -754, -644, -562, -392, -284, -126, -74, -70, -62, -54, -46, -40, -22, -20, -16, -10, -6, -4, -2, 6, 10, 26, 30, 40, 50, 68, 94, 106, 114, 140, 328, 386, 438
417 -826, -818, -804, -793, -752, -741, -613, -554, -384, -358, -329, -317, -266, -237, -161, -122, -49, -46, -45, -41, -34, -33, -28, -26, -25, -24, -17, -13, -12, -9, -8, -5, -4, -2, -1, 2, 4, 7, 8, 11, 12, 15, 16, 19, 24, 28, 51, 59, 62, 63, 64, 75, 79, 132, 338, 355, 518, 692, 806, 1287
419 -1003, -911, -311, -29, -23, -19, -11, -7, -1, 1, 7, 11, 19, 53, 91, 133, 187, 211, 263, 281, 331, 437, 793, 1151
421 -836, -540, -252, -160, -128, -68, -16, -12, -8, 4, 8, 12, 16, 24, 36, 72, 196, 576, 928
423 -1251, -1162, -898, -802, -466, -426, -424, -342, -250, -216, -195, -138, -123, -118, -114, -96, -87, -82, -72, -67, -34, -28, -24, -18, -15, -12, -10, -6, -4, -3, 2, 5, 6, 8, 9, 12, 17, 24, 44, 48, 57, 68, 74, 125, 204, 272, 306, 345, 378, 488, 528, 678, 750, 974, 1140
425 -437, -225, -149, -129, -113, -93, -83, -59, -45, -29, -27, -17, -11, -9, -5, -3, 7, 27, 31, 43, 79, 169, 193, 241, 511, 987, 1273
427 -1448, -1376, -1300, -1264, -1154, -1134, -964, -946, -842, -768, -758, -566, -524, -350, -190, -188, -182, -176, -148, -134, -122, -116, -114, -84, -68, -62, -46, -32, -26, -24, -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 12, 20, 22, 56, 66, 94, 136, 142, 174, 186, 200, 286, 352, 362, 512, 582, 842, 1056, 1080, 1144, 1242
429 -1387, -981, -383, -343, -269, -253, -231, -195, -138, -122, -61, -51, -41, -35, -17, -11, -10, -9, -7, -5, -2, -1, 1, 3, 5, 6, 9, 11, 21, 27, 37, 54, 55, 113, 147, 181, 185, 222, 313, 317, 695, 1003, 1270, 1385, 1483
431 -1187, -975, -513, -419, -351, -239, -237, -233, -173, -137, -87, -37, -27, -23, -15, -13, -5, -3, -1, 1, 3, 9, 15, 23, 45, 47, 95, 225, 309, 363, 923, 1425, 1473
433 -454, -388, -328, -118, -34, -28, -4, 2, 8, 32, 38, 46, 58, 92, 212, 242, 332, 494, 1088
435 -1429, -1371, -963, -946, -927, -902, -818, -697, -549, -446, -413, -400, -388, -377, -355, -332, -330, -259, -246, -190, -123, -116, -110, -86, -80, -63, -60, -50, -46, -40, -31, -30, -26, -25, -22, -20, -17, -15, -13, -10, -9, -8, -7, -6, -5, -3, -2, 2, 4, 5, 7, 11, 18, 19, 33, 51, 68, 69, 82, 93, 99, 101, 113, 132, 138, 141, 198, 201, 255, 298, 522, 528, 533, 537, 547, 790, 903, 1032, 1195, 1365
437 -745, -217, -37, -13, -1, 23, 83, 467
439 -1362, -666, -542, -426, -138, -18, -14, -6, -2, 6, 18, 34, 54, 58, 454, 538, 994, 1122
441 -1121, -347, -231, -197, -193, -179, -71, -69, -27, -21, -9, -7, -4, -3, -1, 1, 3, 4, 13, 17, 21, 47, 76, 91, 137, 167, 181, 211, 347, 353, 407, 479, 553, 591, 747, 981, 1407
443 -1135, -495, -487, -299, -255, -99, -55, -27, -19, -15, -7, 1, 5, 9, 33, 45, 245, 401, 565
445 -1288, -916, -806, -758, -680, -652, -590, -566, -472, -112, -68, -62, -40, -36, -16, -14, -8, -6, -4, -2, 4, 8, 10, 22, 40, 52, 56, 58, 136, 152, 154, 208, 316, 356, 364, 472, 752, 1006, 1244
447 -398, -310, -269, -248, -100, -89, -86, -58, -34, -20, -17, -16, -14, -10, -5, -4, -1, 2, 16, 19, 20, 23, 50, 52, 71, 116, 286, 379, 391, 395, 410, 454, 476, 700, 716, 1340, 1442
449 -817, -357, -63, -43, -37, -35, -23, -13, -7, -3, 3, 5, 17, 25, 53, 65, 75, 93, 227, 263, 265, 455, 627, 805, 1187, 1253
451 -1080, -1012, -624, -424, -396, -120, -72, -40, -12, -4, 12, 24
453 -1490, -894, -870, -548, -407, -327, -272, -248, -222, -192, -158, -138, -123, -119, -110, -87, -63, -47, -44, -39, -30, -27, -24, -23, -18, -12, -8, -3, -2, 1, 10, 16, 18, 21, 33, 37, 48, 57, 66, 96, 108, 133, 198, 262, 480, 550, 673, 858, 988, 1065
455 -1413, -1385, -1181, -1169, -985, -325, -303, -299, -273, -199, -165, -115, -105, -103, -93, -69, -41, -29, -23, -19, -15, -13, -11, -9, -5, -3, -1, 1, 5, 9, 15, 17, 37, 111, 139, 185, 287, 297, 561, 705, 769, 1187
457 -1212, -540, -216, -182, -112, -86, -80, -62, -26, -22, -16, -10, -6, -2, 8, 28, 34, 70, 90, 158, 280, 320, 448, 1240
459 -1169, -1021, -970, -563, -449, -423, -345, -301, -239, -229, -159, -151, -123, -109, -102, -101, -71, -70, -61, -49, -46, -43, -41, -26, -25, -21, -14, -10, -9, -7, -6, -5, -3, -2, -1, 1, 3, 9, 18, 19, 21, 29, 35, 51, 53, 57, 75, 111, 150, 175, 273, 279, 306, 317, 475, 669, 717, 750, 1291, 1326, 1449, 1483
461 -1135, -505, -289, -121, -91, -73, -65, -55, -49, -31, -1, 5, 7, 17, 41, 175
463 -1082, -1048, -708, -412, -378, -312, -298, -272, -220, -128, -114, -92, -82, -32, -24, -20, -10, -8, -4, -2, 6, 8, 30, 62, 96, 118, 222, 332, 472, 528, 1086, 1388
465 -948, -538, -277, -258, -144, -85, -78, -67, -66, -48, -37, -30, -24, -22, -21, -12, -10, -9, -7, -1, 2, 6, 9, 21, 41, 50, 74, 105, 119, 161, 191, 246, 255, 402, 419, 540, 941, 1085, 1245, 1250, 1415
467 -557, -353, -41, -5, 19, 247, 547
469 -1438, -98, -10, 2, 190, 242, 326
471 -1357, -963, -957, -940, -809, -360, -196, -189, -184, -160, -149, -105, -104, -48, -44, -37, -36, -35, -27, -25, -23, -17, -13, -12, -9, -8, -7, -5, -4, -3, 3, 4, 5, 7, 8, 11, 17, 20, 36, 40, 43, 47, 53, 71, 107, 123, 225, 345, 368, 460, 468, 625, 652, 807, 1036, 1107, 1285
473 -1235, -1075, -839, -715, -647, -259, -155, -23, -11, -7, 1, 5, 37, 109
475 -1054, -980, -482, -374, -130, -34, -20, -10, -4, -2, 2, 26, 38, 100, 340, 686
477 -1233, -721, -606, -585, -544, -258, -241, -225, -186, -133, -126, -112, -72, -61, -54, -48, -45, -41, -29, -22, -21, -18, -13, -8, -6, -5, -1, 6, 7, 14, 15, 18, 27, 39, 42, 50, 54, 71, 88, 99, 102, 104, 138, 168, 275, 306, 615, 1274, 1375
479 -463, -127, -51, -39, -15, -9, -7, -3, 3, 5, 21, 45, 123, 209, 297, 401, 489, 761
481 -20, 64, 196
483 -1216, -1131, -1064, -626, -366, -338, -268, -251, -248, -227, -218, -136, -118, -106, -92, -74, -72, -62, -58, -46, -39, -38, -32, -24, -18, -11, -8, -6, -4, -3, -2, 1, 2, 13, 14, 18, 21, 22, 26, 56, 73, 74, 121, 133, 169, 192, 193, 226, 242, 282, 346, 356, 416, 517, 812
485 -1497, -1353, -1101, -989, -677, -607, -431, -399, -349, -127, -113, -63, -33, -23, -13, -9, -7, -1, 1, 3, 7, 19, 31, 111, 147, 257, 259, 307, 313, 383, 401, 451, 481, 483, 519
487 -1078, -552, -450, -260, -256, -182, -172, -124, -110, -104, -84, -70, -54, -52, -36, -32, -20, -14, -12, -10, -8, -4, -2, 2, 4, 8, 10, 14, 16, 18, 24, 26, 28, 36, 44, 62, 64, 94, 110, 136, 220, 352, 538, 546, 836, 1104, 1364
489 -1447, -1214, -577, -427, -350, -343, -331, -233, -223, -121, -113, -101, -41, -35, -22, -17, -13, -7, -5, -1, 5, 13, 19, 37, 49, 50, 65, 119, 599, 803, 919, 1045, 1106
491 -1335, -1247, -1163, -743, -735, -459, -397, -351, -347, -293, -255, -123, -119, -79, -71, -63, -61, -47, -45, -39, -35, -23, -21, -11, -7, -5, -3, 1, 3, 9, 25, 29, 73, 85, 89, 161, 169, 233, 241, 261, 273, 859, 1197
493 -826, -748, -580, -258, -244, -136, -102, -66, -64, -16, -6, -4, 2, 680, 798, 1112
495 -1409, -1124, -851, -434, -417, -204, -122, -107, -56, -41, -38, -32, -24, -23, -14, -12, -11, -8, -3, -2, 1, 7, 16, 24, 28, 33, 39, 46, 49, 73, 84, 127, 223, 271, 276, 591, 636, 663, 973, 1248
497 -1489, -1405, -1021, -645, -581, -453, -425, -53, -25, -13, -9, -1, 7, 11, 19, 31, 35, 71, 79, 235, 319, 1391
499 -1158, -538, -466, -386, -162, -74, -54, -50, -46, -26, -18, -14, -10, -6, -2, 2, 18, 58, 94, 146, 362, 610, 714, 898, 994
501 -1371, -1320, -961, -787, -261, -179, -160, -156, -155, -131, -112, -88, -67, -48, -32, -21, -20, -19, -16, -13, -12, -11, -9, -8, -3, -1, 4, 5, 8, 12, 13, 37, 40, 45, 53, 60, 61, 77, 120, 125, 152, 159, 205, 269, 323, 344, 351, 629, 992, 1484
503 -559, -295, -127, -91, -43, -23, -11, -7, 5, 13, 17, 277, 461, 1205
505 -808, -728, -706, -402, -196, -186, -108, -106, -98, -86, -74, -58, -38, -28, -24, -18, -16, -14, -8, -6, -4, -2, 4, 6, 8, 14, 32, 36, 38, 42, 54, 68, 96, 138, 158, 182, 214, 386, 684, 754, 964, 1214
507 -1186, -904, -414, -381, -366, -361, -334, -316, -286, -208, -142, -76, -60, -57, -24, -18, -13, -12, -10, -9, -6, -4, -1, 2, 3, 8, 11, 20, 23, 26, 30, 32, 72, 74, 92, 180, 200, 236, 251, 342, 360, 563, 702, 962, 1340, 1398
509 -1467, -1421, -1065, -717, -605, -597, -527, -485, -441, -347, -285, -257, -225, -221, -165, -159, -149, -107, -99, -89, -81, -71, -45, -39, -35, -29, -27, -17, -11, -9, -5, 1, 3, 9, 13, 31, 33, 39, 51, 105, 121, 241, 369, 531, 1459
511 -192, -48, -16, 8, 264, 1392
513 -1278, -1147, -951, -694, -680, -520, -284, -283, -216, -188, -88, -75, -55, -34, -31, -24, -20, -19, -18, -8, -7, -6, -3, 2, 4, 5, 6, 9, 10, 12, 14, 17, 22, 26, 30, 33, 45, 66, 110, 116, 126, 153, 165, 174, 220, 230, 234, 294, 362, 404
515 -1359, -1079, -1019, -995, -833, -713, -689, -265, -245, -207, -137, -113, -109, -89, -85, -73, -67, -65, -59, -43, -39, -37, -35, -29, -27, -23, -19, -13, -7, -5, -3, 1, 5, 7, 11, 17, 31, 65, 77, 81, 93, 127, 131, 265, 401, 671, 751, 815, 1123, 1271
517 -392, -238, -194, -154, -92, -86, -74, -20, -14, -8, -2, 2, 4, 22, 40, 50, 64, 148, 244, 310, 466, 532, 626, 1186
519 -950, -831, -742, -697, -687, -559, -501, -487, -479, -457, -357, -247, -242, -225, -177, -174, -134, -102, -85, -81, -74, -57, -49, -31, -30, -25, -22, -21, -17, -15, -14, -10, -9, -7, -2, -1, 1, 3, 9, 10, 11, 15, 26, 38, 55, 63, 70, 73, 75, 129, 145, 166, 186, 239, 310, 311, 370, 503, 585, 638, 675, 879, 961, 1103, 1110, 1139, 1150
521 -1063, -991, -301, -249, -141, -115, -75, -55, -45, -21, -15, -13, -9, -1, 5, 11, 21, 29, 39, 47, 65, 71, 89, 119, 869
523 -596, -38, -6, 4, 250, 300
525 -854, -572, -342, -320, -284, -197, -174, -152, -139, -120, -102, -100, -94, -85, -84, -70, -62, -52, -45, -34, -32, -20, -12, -10, -7, -5, -4, 1, 3, 6, 8, 11, 13, 26, 28, 35, 56, 125, 170, 190, 245, 315, 368, 666, 1006, 1148
527 -253, -57, -37, -25, -21, -13, -9, 3, 11, 47, 71, 179, 431
529 -310, -258, -78, -66, -58, -30, -10, -6, 6, 14, 26, 62, 66, 102, 122, 126, 230, 234, 246, 410
531 -1292, -1268, -1136, -1076, -844, -719, -557, -367, -319, -284, -176, -89, -56, -44, -28, -16, -11, -8, -7, -5, -4, 1, 5, 8, 28, 41, 49, 52, 53, 76, 80, 124, 136, 209, 329, 584, 700, 944
533 -443, -75, -23, -15, -7, -3, 13, 29, 229, 237, 1245, 1349, 1357
535 -1450, -1416, -804, -700, -384, -126, -108, -24, -16, -10, -6, 2, 26, 90, 210, 242, 260, 606
537 -1118, -1026, -762, -549, -422, -414, -366, -282, -105, -65, -42, -38, -30, -29, -18, -14, -9, -6, -5, -2, 3, 6, 7, 18, 24, 30, 34, 82, 102, 106, 142, 178, 250, 406, 534, 907, 1071, 1182, 1476
539 -1273, -405, -389, -283, -273, -255, -207, -201, -157, -153, -113, -61, -49, -45, -37, -25, -19, -17, -13, -9, -5, -3, -1, 7, 9, 11, 33, 35, 53, 55, 65, 151, 159, 167, 197, 233, 251, 293, 461, 545, 1403
541 -1108, -880, -808, -532, -348, -288, -88, -72, -64, -60, -20, -12, -8, -4, 8, 16, 36, 56, 120, 272, 328, 560, 900, 1160
543 -1255, -1239, -1063, -806, -439, -420, -303, -286, -210, -179, -106, -63, -62, -55, -26, -22, -19, -15, -14, -12, -11, -10, -6, -2, 1, 4, 5, 9, 18, 21, 26, 29, 36, 41, 45, 46, 65, 85, 125, 181, 460, 481, 689
545 -1187, -1039, -859, -857, -799, -607, -431, -275, -143, -127, -71, -61, -49, -25, -23, -17, -13, -11, -7, -5, -1, 1, 7, 13, 17, 31, 35, 67, 73, 109, 221, 293, 325, 341, 395, 397, 439, 541, 583
547 -1436, -1416, -964, -502, -280, -132, -94, -40, -34, -22, -16, -14, -12, -10, -4, 4, 24, 36, 74, 76, 104, 228, 764, 1148
549 -1425, -1269, -1237, -655, -553, -493, -247, -183, -79, -49, -42, -33, -31, -18, -15, -13, -9, -7, -6, -3, 5, 11, 21, 42, 65, 155, 231, 273, 275, 285, 1437
551 -621, -233, -113, -47, -29, -23, -9, 1, 3, 7, 13, 19, 469, 631, 1291
553 -844, -624, -500, -438, -434, -380, -290, -242, -196, -156, -146, -134, -122, -72, -58, -54, -40, -26, -22, -20, -18, -16, -14, -12, -8, -6, -4, -2, 2, 4, 6, 10, 22, 24, 30, 42, 46, 50, 56, 60, 64, 84, 182, 190, 202, 204, 214, 256, 322, 382, 384, 402, 768, 1100
555 -1436, -1347, -1191, -1076, -917, -742, -666, -657, -656, -634, -627, -622, -572, -528, -503, -501, -370, -363, -288, -262, -258, -234, -213, -195, -162, -145, -132, -125, -115, -108, -90, -80, -67, -55, -52, -48, -40, -36, -34, -33, -31, -28, -23, -20, -17, -13, -12, -10, -8, -7, -6, -5, -4, -3, -1, 2, 3, 5, 6, 9, 14, 16, 17, 18, 20, 27, 33, 44, 48, 52, 60, 62, 65, 73, 84, 99, 112, 132, 184, 189, 217, 282, 360, 365, 412, 444, 553, 588, 739, 756, 1084, 1184
557 -377, -21, -9, 3, 39, 63, 451, 1011
559 -1342, -670, -638, -542, -506, -502, -442, -278, -122, -82, -62, -34, -22, -14, -10, -2, 2, 10, 22, 70, 74, 202, 226, 314, 338, 382, 506, 530, 710, 1154
561 -1321, -1285, -1220, -1180, -1152, -984, -884, -731, -593, -515, -452, -435, -363, -352, -321, -320, -197, -84, -83, -69, -41, -39, -32, -27, -25, -24, -21, -20, -15, -13, -12, -11, -5, -4, -3, -1, 1, 7, 8, 9, 12, 13, 15, 16, 39, 40, 44, 49, 51, 67, 72, 81, 93, 105, 108, 117, 124, 195, 235, 248, 275, 277, 324, 443, 472, 484, 588, 589, 815, 1415
563 -1291, -579, -451, -367, -259, -199, -39, -27, -15, -7, -3, 9, 41, 53, 57, 185, 417, 549, 609
565 -1452, -1106, -888, -794, -290, -260, -210, -192, -50, -36, -32, -24, -20, -18, -8, -2, 4, 6, 12, 22, 28, 48, 168, 204, 256, 294, 372, 424, 556, 990
567 -1153, -1073, -978, -796, -786, -756, -529, -462, -436, -281, -197, -170, -101, -98, -86, -76, -37, -30, -26, -22, -20, -17, -16, -12, -8, -6, -5, -2, -1, 2, 7, 11, 24, 34, 64, 78, 120, 138, 191, 220, 299, 372, 378, 450, 478, 582, 680, 974, 1004, 1183
569 -979, -717, -649, -499, -253, -157, -89, -69, -59, -43, -37, -35, -33, -29, -19, -17, -13, -11, -5, -3, -1, 15, 27, 39, 43, 51, 85, 111, 151, 275, 831, 903, 919, 1391, 1499
571 -1148, -292, -136, -32, -16, -8, -4, 4, 16, 32, 44, 56, 404
573 -1208, -1070, -646, -370, -223, -163, -158, -128, -106, -62, -31, -16, -11, -10, -8, -7, -2, 2, 13, 17, 22, 89, 92, 193, 269, 314, 344, 377, 814, 1190
575 -1479, -867, -595, -447, -369, -141, -139, -127, -119, -99, -85, -69, -65, -57, -49, -35, -31, -27, -21, -19, -15, -9, -5, -1, 1, 5, 15, 21, 35, 39, 43, 51, 53, 61, 81, 93, 103, 111, 131, 133, 165, 181, 291, 319, 323
577 -1038, -762, -378, -342, -316, -202, -178, -106, -100, -94, -82, -58, -36, -34, -12, -10, -6, -4, 2, 6, 12, 14, 18, 20, 92, 98, 102, 156, 290, 330, 524
579 -1470, -615, -375, -330, -267, -246, -201, -129, -39, -38, -33, -30, -27, -26, -23, -18, -15, -14, -9, -6, -3, 6, 10, 21, 45, 46, 69, 99, 273, 346, 537, 630, 1110
581 -1455, -997, -967, -235, -205, -187, -167, -127, -97, -79, -67, -45, -19, -15, -9, -7, -5, 1, 3, 5, 13, 21, 31, 43, 55, 75, 91, 93, 203, 271, 315, 605, 613, 853, 1101
583 -1232, -1018, -672, -496, -478, -406, -260, -256, -184, -74, -56, -40, -38, -22, -12, -10, -8, -6, -4, -2, 2, 6, 8, 12, 30, 48, 66, 134, 316, 366, 476, 530, 554, 646, 710, 1184, 1428, 1478
585 -1260, -1235, -981, -893, -790, -498, -465, -459, -450, -445, -374, -373, -199, -111, -103, -98, -90, -63, -59, -50, -48, -41, -34, -31, -28, -19, -15, -11, -10, -9, -5, -4, -3, -1, 1, 2, 6, 9, 11, 17, 19, 32, 45, 57, 61, 66, 86, 95, 162, 217, 230, 339, 399, 456, 812, 1441, 1469
587 -553, -409, -169, -85, -29, -25, -13, -5, 227
589 -578, -482, -190, -86, -18, -10, -6, -2, 2, 22, 34, 62, 102, 310, 318, 542
591 -1221, -1063, -637, -249, -141, -132, -129, -127, -85, -75, -37, -33, -31, -24, -21, -15, -13, -9, -7, -4, -3, -1, 3, 5, 9, 11, 41, 53, 56, 93, 195, 245, 249, 411, 651, 993
593 -423, -399, -75, -23, -3, 1, 9, 33, 117, 141, 1129, 1345
595 -1368, -1294, -1050, -782, -776, -334, -170, -154, -146, -130, -114, -110, -104, -54, -34, -32, -24, -20, -18, -14, -12, -10, -6, -2, 2, 4, 12, 16, 38, 46, 54, 66, 72, 84, 106, 130, 144, 232, 262, 312, 450, 470, 546, 554, 690, 750, 844, 1270, 1278
597 -1217, -1168, -500, -448, -241, -234, -161, -80, -64, -57, -50, -28, -20, -18, -14, -10, -9, -8, -6, -4, -2, -1, 2, 8, 14, 18, 28, 70, 82, 116, 190, 196, 218, 270, 316, 382, 534, 674, 710
599 -877, -721, -707, -617, -497, -291, -253, -231, -177, -147, -115, -63, -57, -55, -43, -27, -17, -11, -7, -5, -3, -1, 3, 7, 9, 13, 17, 27, 35, 53, 65, 97, 115, 143, 327, 379, 447, 517, 545, 679, 787, 815, 823

Primes of the form (m^p+-n^p)/(m+-n)

Consider a generalized repunit with p 1s to "base" b, while b is a positive integer (>1), the value of it is ${\displaystyle {\frac {b^{p}-1}{b-1}}}$, we can generalized to b be any rational number with absolute value greater than 1 (if the absolute value of it is lesser than 1, we can choose the multiplicative inverse of it), if the value of the generalized "repunit" number to the "base" b is negative, then we choose the absolute value of it, and if the value of the generalized "repunit" number to the "base" b is not an integer, then we choose the numerator of it. Thus, let b = ${\displaystyle {\frac {m}{n}}}$ (m and n are coprime integers, m > 1, -m < n < m), then the repunit number with p 1s in base b is ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$, if p is odd, then it also equals ${\displaystyle {\frac {m^{p}+(-n)^{p}}{m+(-n)}}}$. (Of course, if it is prime, then p needs to be prime)

Conjecture: there are infinitely many generalized "repunit" prime in every rational number "base" except perfect power (rational number of the form ${\displaystyle ({\frac {a}{b}})^{n}}$, with a positive integer, b integer, n an integer greater then 1). However, there are many bases which are not perfect powers without known generalized "repunit" prime or PRP, such as 152, -97, ${\displaystyle {\frac {140}{139}}}$, ${\displaystyle {\frac {91}{89}}}$, etc.

The list is about the least generalized "repunit" prime (with at least 3 1s, a repunit with 2 1s in base b is the absolute value of the numerator of b+1) in base ${\displaystyle {\frac {m}{n}}}$ (or ${\displaystyle -{\frac {m}{n}}}$), with "???" if no known generalized repunit prime in this base. Thus, this list is about primes of the form ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$ or ${\displaystyle {\frac {m^{p}+n^{p}}{m+n}}}$ with coprime m and n. (0 < n < m <= 50) There are no existing OEIS sequences for primes of the form ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$ or ${\displaystyle {\frac {m^{p}+n^{p}}{m+n}}}$ when m - n > 1 and n > 5.

See also A084740 (least repunit prime in base n), A128164 (least repunit prime in base n with at least 3 1s), A084742 (least repunit prime in base -n with at least 3 1s), A058013 (least repunit prime in base ${\displaystyle {\frac {n+1}{n}}}$), A125713 (least repunit prime in base ${\displaystyle {\frac {n+1}{n}}}$ with at least 3 1s), A247244 (least repunit prime in base ${\displaystyle -{\frac {n+1}{n}}}$), A125954 (least repunit prime in base ${\displaystyle {\frac {2n+1}{2}}}$), A125958 (least repunit prime in base ${\displaystyle -{\frac {2n-1}{2}}}$ with at least 3 1s), A128033 (least repunit prime in base ${\displaystyle {\frac {n+3}{3}}}$), A128049 (least repunit prime in base ${\displaystyle -{\frac {n-3}{3}}}$), A122478 (least repunit prime in base ${\displaystyle {\frac {2n+1}{2n-1}}}$), A247093 (least repunit prime in base ${\displaystyle {\frac {m}{n}}}$).

m n Least odd prime p such that ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$ is prime (repunit prime in base ${\displaystyle {\frac {m}{n}}}$) Sequence in database for primes p such that ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$ is prime (repunit prime in base ${\displaystyle {\frac {m}{n}}}$) Least odd prime p such that ${\displaystyle {\frac {m^{p}+n^{p}}{m+n}}}$ is prime (repunit prime in base ${\displaystyle -{\frac {m}{n}}}$) Sequence in database for primes p such that ${\displaystyle {\frac {m^{p}+n^{p}}{m+n}}}$ is prime (repunit prime in base ${\displaystyle -{\frac {m}{n}}}$)
2 1 3 A000043 3 A000978
3 1 3 A028491 3 A007658
3 2 3 A057468 3 A057469
4 1 0 (Algebra factorization) 3 (Algebra factorization)
4 3 3 A059801 3 A128066
5 1 3 A004061 5 A057171
5 2 5 A082182 3 A082387
5 3 13 A121877 3 A122853
5 4 3 A059802 5 A128335
6 1 3 A004062 3 A057172
6 5 5 A062572 3 A128336
7 1 5 A004063 3 A057173
7 2 3 A215487 5 A125955
7 3 3 A128024 3 A128067
7 4 5 A213073 3 A218373
7 5 3 A128344 11 A128337
7 6 3 A062573 3 A187805
8 1 3 (Algebra factorization) 0 (Algebra factorization)
8 3 3 A128025 5 A128068
8 5 19 A128345 7 A128338
8 7 7 A062574 7 A181141
9 1 0 (Algebra factorization) 3 A057175
9 2 3 A173718 3 A125956
9 4 0 (Algebra factorization) 3 A211409
9 5 3 A128346 3 A128339
9 7 3 A?????? 3 A??????
9 8 7 A059803 3 A187819
10 1 19 A004023 5 A001562
10 3 3 A128026 3 A128069
10 7 31 A?????? 3 A??????
10 9 3 A062576 7 A217095
11 1 17 A005808 5 A057177
11 2 5 A210506 3 A125957
11 3 3 A128027 3 A128070
11 4 3 A216181 7 A224501
11 5 5 A128347 7 A128340
11 6 3 A?????? 5 A??????
11 7 5 A?????? 7 A??????
11 8 7 A?????? 3 A??????
11 9 5 A?????? 3 A??????
11 10 3 A062577 53 A185239
12 1 3 A004064 5 A057178
12 5 3 A128348 3 A128341
12 7 3 A?????? 3 A??????
12 11 3 A062578 47 A213216

m n Least odd prime p such that ${\displaystyle {\frac {m^{p}-n^{p}}{m-n}}}$ is prime (repunit prime in base ${\displaystyle {\frac {m}{n}}}$) Least odd prime p such that ${\displaystyle {\frac {m^{p}+n^{p}}{m+n}}}$ is prime (repunit prime in base ${\displaystyle -{\frac {m}{n}}}$)
13 1 5 3
13 2 3 7
13 3 7 3
13 4 5 7
13 5 5 13
13 6 3 3
13 7 7 3
13 8 3 17
13 9 3 1217
13 10 251 3
13 11 3 7
13 12 17 3
14 1 3 7
14 3 5 3
14 5 151 3
14 9 59 3
14 11 5 3
14 13 3 7
15 1 3 3
15 2 5 3
15 4 1097 3
15 7 3 5
15 8 3 17
15 11 7 3
15 13 17 3
15 14 3 3
16 1 0 3
16 3 3 5
16 5 7 31
16 7 5 3
16 9 0 3
16 11 13 7
16 13 41 89
16 15 43 3
17 1 3 7
17 2 83 5
17 3 3 37
17 4 3 13
17 5 5 3
17 6 29 3
17 7 3 353
17 8 7 23
17 9 3 43
17 10 23 11
17 11 5 3
17 12 19 3
17 13 487 7
17 14 139 11
17 15 3 17
17 16 5 41
18 1 25667 3
18 5 3 61
18 7 3 7
18 11 3 79
18 13 3 5
18 17 3 3
19 1 19 17
19 2 11 5
19 3 73 3
19 4 7 7
19 5 5 11
19 6 19 3
19 7 7 3
19 8 3 5
19 9 3 3
19 10 17 3
19 11 3 13
19 12 3 3
19 13 7 3
19 14 3 5
19 15 5 139
19 16 5 3
19 17 163 11
19 18 1607 5
20 1 3 5
20 3 43 3
20 7 5 7
20 9 3 13
20 11 5 5
20 13 3 163
20 17 5 3
20 19 5 11
21 1 3 3
21 2 3 11
21 4 3 3
21 5 3 73
21 8 3 3
21 10 3 3
21 11 31 3
21 13 3 3
21 16 3 7
21 17 3 3
21 19 3 7
21 20 19 3
22 1 5 3
22 3 5 2617
22 5 3 31
22 7 43 3
22 9 5 3
22 13 17 3
22 15 3 3
22 17 587 7
22 19 7 11
22 21 127 3
23 1 5 11
23 2 5 3
23 3 3 1153
23 4 7 457
23 5 53 3
23 6 5 7
23 7 3 7
23 8 7 3
23 9 349 5
23 10 3 7
23 11 7 3
23 12 5 3
23 13 3 127
23 14 31 5
23 15 17 3
23 16 3 7
23 17 491 7
23 18 7 3
23 19 3 17
23 20 17 5
23 21 3 3
23 22 229 11
24 1 3 7
24 5 5 163
24 7 29 3
24 11 11 3
24 13 19 3
24 17 17 3
24 19 7 7
24 23 3 11
25 1 0 3
25 2 11 19
25 3 3 83
25 4 0 3
25 6 3 79
25 7 563 3
25 8 5 5
25 9 0 11
25 11 3 5
25 12 3 17
25 13 5 17
25 14 3 479
25 16 0 5
25 17 5 19
25 18 3 3
25 19 11 7
25 21 179 3
25 22 13 5
25 23 109 5
25 24 3 3
26 1 7 11
26 3 31 3
26 5 79 3
26 7 3 5
26 9 3 3
26 11 47 67
26 15 3 5
26 17 7 3
26 19 3 13
26 21 3 3
26 23 11 3
26 25 3 5
27 1 3 0
27 2 3 11
27 4 3 5
27 5 5 3
27 7 3 157
27 8 3 3
27 10 5 43
27 11 5 5
27 13 3 3
27 14 3 3
27 16 5 7
27 17 11 13
27 19 13 3
27 20 3 97
27 22 409 3
27 23 3 7
27 25 3 5
27 26 13 103
28 1 5 3
28 3 3 3
28 5 17 13
28 9 3 3
28 11 3 281
28 13 61 31
28 15 3 37
28 17 3 23
28 19 31 3
28 23 47 109
28 25 7 3
28 27 3 3
29 1 5 7
29 2 7 3
29 3 3 11
29 4 7 7
29 5 199 7
29 6 3 19
29 7 3 5
29 8 13 3
29 9 7 3
29 10 3 5
29 11 5 3
29 12 13 13
29 13 7 31
29 14 7 3
29 15 163 3
29 16 5 83
29 17 19 73
29 18 5 3
29 19 3 5
29 20 17 3
29 21 157 3
29 22 461 5
29 23 11 7
29 24 3 5
29 25 5 19
29 26 5 23
29 27 13 3
29 28 3 37
30 1 5 139
30 7 373 3
30 11 5 3
30 13 3 53
30 17 3 17
30 19 3 3
30 23 47 3
30 29 149 17
31 1 7 109
31 2 5 229
31 3 3 3
31 4 7 3
31 5 7 971
31 6 6961 3
31 7 5 881
31 8 7 809
31 9 3 43
31 10 139 3
31 11 3 31
31 12 7 3
31 13 227 3
31 14 11 283
31 15 13 13
31 16 7 7
31 17 3 7
31 18 5 3
31 19 11 3
31 20 5 113
31 21 3 3
31 22 11 7
31 23 3 5
31 24 3 13
31 25 7 3
31 26 47 151
31 27 19 3
31 28 7 3
31 29 19 19
31 30 3 7
32 1 0 0
32 3 3 3
32 5 5 ???
32 7 3 7
32 9 5 7
32 11 5 5
32 13 3 7
32 15 5 3
32 17 83 3
32 19 3 5
32 21 3 2269
32 23 17 337
32 25 5 7
32 27 3 11
32 29 53 3
32 31 5 13
33 1 3 5
33 2 71 47
33 4 3 5
33 5 3 43
33 7 7 3
33 8 7 71
33 10 5 3
33 13 127 3
33 14 3 3
33 16 3 31
33 17 19 7
33 19 5 3
33 20 17 3
33 23 3 3
33 25 3 53
33 26 5 3
33 28 3 5
33 29 3 5
33 31 5 5
33 32 3 37
34 1 13 3
34 3 337 3
34 5 19 11
34 7 13 3
34 9 3 5
34 11 43 11
34 13 149 3
34 15 53 19
34 19 13 251
34 21 3 3
34 23 3 5
34 25 11 17
34 27 3 3
34 29 853 37
34 31 19 3
34 33 23 3
35 1 313 11
35 2 17 5
35 3 5 3
35 4 3 19
35 6 3 3
35 8 13 3
35 9 3 3
35 11 433 5
35 12 3 227
35 13 5 5
35 16 37 71
35 17 11 3
35 18 3 3
35 19 3 13
35 22 61 17
35 23 13 11
35 24 7 5
35 26 19 3
35 27 19 3
35 29 7 3
35 31 3 5
35 32 19 3
35 33 3 5
35 34 3 269
36 1 0 31
36 5 11 5
36 7 3 3
36 11 11 3
36 13 3 3
36 17 5 13
36 19 3 13
36 23 11 3
36 25 0 3
36 29 3 3
36 31 3 59
36 35 5 17
37 1 13 5
37 2 3 257
37 3 3 557
37 4 7 3
37 5 3 11
37 6 3 13
37 7 7 7
37 8 7 139
37 9 3 3
37 10 127 11
37 11 7 5
37 12 11 3
37 13 37 29
37 14 3 13
37 15 5 3
37 16 13 3
37 17 3 43
37 18 17 37
37 19 13 13
37 20 73 11
37 21 5 3
37 22 2621 3
37 23 3 11
37 24 3 227
37 25 3271 3
37 26 5 13
37 27 317 5
37 28 43 3
37 29 7 5
37 30 31 7
37 31 7 31
37 32 11 29
37 33 17 3
37 34 ??? 5
37 35 3 59
37 36 83 5
38 1 3 5
38 3 3 19
38 5 5 3
38 7 3 16747
38 9 3 5
38 11 1249 5
38 13 31 31
38 15 3 5
38 17 5 3
38 21 3 3
38 23 53 13
38 25 3 5
38 27 79 17
38 29 5 47
38 31 3 31
38 33 1097 3
38 35 5 7
38 37 3 17
39 1 349 3
39 2 229 3
39 4 3 3
39 5 3 5
39 7 7 3
39 8 967 5
39 10 3 3
39 11 241 3
39 14 191 3
39 16 71 3
39 17 3 5
39 19 7 19
39 20 11 31
39 22 31 5
39 23 5 3
39 25 3 3
39 28 5 3
39 29 17 3
39 31 3 31
39 32 3 3
39 34 3 7
39 35 3 3
39 37 1879 3
39 38 3 3
40 1 5 53
40 3 5 3
40 7 7 439
40 9 5 3
40 11 3 11
40 13 113 3
40 17 317 5
40 19 ??? 3
40 21 13 3
40 23 3 13
40 27 907 3
40 29 5 5
40 31 61 3
40 33 5 11
40 37 31 3
40 39 37 5
41 1 3 17
41 2 41 19
41 3 401 3
41 4 3 41
41 5 79 7
41 6 19 3
41 7 3 5
41 8 5 17
41 9 3 11
41 10 13 5
41 11 47 17
41 12 7 7
41 13 3 599
41 14 31 3
41 15 3 3
41 16 3 7
41 17 7 7
41 18 1259 5
41 19 5 43
41 20 19 127
41 21 61 5
41 22 3 337
41 23 5 7
41 24 13 7
41 25 3 ???
41 26 19 3
41 27 3 3
41 28 3 5
41 29 7 29
41 30 5 7
41 31 7 11
41 32 19 5
41 33 7 5
41 34 3 37
41 35 17 3
41 36 23 5
41 37 3 227
41 38 5 3
41 39 3 11
41 40 7 139
42 1 1319 3
42 5 3 3
42 11 3 3
42 13 19 271
42 17 3 7
42 19 113 3
42 23 3 3
42 25 7 43
42 29 3 7
42 31 3 3
42 37 19 3
42 41 3 3
43 1 5 5
43 2 167 31
43 3 3 7
43 4 17 3
43 5 3 11
43 6 3 3
43 7 ??? 3
43 8 17 29
43 9 37 3
43 10 19 23
43 11 617 5
43 12 11 ???
43 13 11 3
43 14 3 7
43 15 3 3
43 16 5 311
43 17 73 7
43 18 67 3
43 19 19 5
43 20 3 17
43 21 1873 13
43 22 5 7
43 23 41 19
43 24 3 7
43 25 5 3
43 26 3 11
43 27 3 ???
43 28 7 3
43 29 887 5
43 30 241 3
43 31 11 7
43 32 61 19
43 33 3 ???
43 34 149 3
43 35 29 5
43 36 19 3
43 37 37 3
43 38 17 79
43 39 71 3
43 40 67 421
43 41 13 13
43 42 3 11
44 1 5 7
44 3 5 ???
44 5 547 3
44 7 3 7
44 9 499 3
44 13 3 5
44 15 5 5
44 17 7 5
44 19 13 23
44 21 3 3
44 23 271 3
44 25 7 7
44 27 3 5
44 29 13 19
44 31 3 61
44 35 73 3
44 37 3 7
44 39 13 3
44 41 5 13
44 43 37 ???
45 1 19 103
45 2 7 17
45 4 3 3
45 7 3 3
45 8 5 73
45 11 41 859
45 13 5 3
45 14 3 137
45 16 3 13
45 17 3 3
45 19 313 3
45 22 3 29
45 23 47 5
45 26 11 3
45 28 137 3
45 29 5 7
45 31 101 79
45 32 17 3
45 34 5 19
45 37 3 11
45 38 3 3
45 41 5 3
45 43 379 7
45 44 5 5
46 1 7 7
46 3 5 3
46 5 3 13
46 7 37 7
46 9 7 3
46 11 13 ???
46 13 7 307
46 15 5 157
46 17 3 5
46 19 151 29
46 21 43 5
46 25 5 7
46 27 7 193
46 29 113 89
46 31 ??? 5
46 33 3 23
46 35 3 23
46 37 5 3
46 39 3 31
46 41 3 107
46 43 139 3
46 45 3 17
47 1 127 5
47 2 17 11
47 3 5 631
47 4 7 53
47 5 29 3
47 6 5 7
47 7 11 919
47 8 139 19
47 9 3 3
47 10 241 29
47 11 11 127
47 12 3 3
47 13 5 11
47 14 7 3
47 15 373 983
47 16 3 5
47 17 19 3
47 18 5 7
47 19 3 31
47 20 7 3
47 21 3 3
47 22 3 499
47 23 ??? 3
47 24 5 3
47 25 19 31
47 26 211 3
47 27 31 3
47 28 5 7
47 29 7 7
47 30 3 3
47 31 7 5
47 32 7 41
47 33 ??? 3
47 34 19 31
47 35 383 3
47 36 3 19
47 37 151 ???
47 38 13 3
47 39 3 463
47 40 3 227
47 41 5 5
47 42 7 3
47 43 3 ???
47 44 5 5
47 45 7 7
47 46 5 3671
48 1 19 5
48 5 109 3
48 7 3 3
48 11 3 7
48 13 43 17
48 17 5 3
48 19 19 3
48 23 7 31
48 25 3 317
48 29 ??? 3
48 31 53 3
48 35 3 7
48 37 3 ???
48 41 3 3
48 43 3 3
48 47 58543 13
49 1 0 7
49 2 3 13
49 3 3 5
49 4 0 3
49 5 3 ???
49 6 3 3
49 8 3 17
49 9 0 5
49 10 17 3
49 11 3 7
49 12 17 5
49 13 5 3
49 15 3 5
49 16 0 3
49 17 5 7
49 18 3 7
49 19 7 3
49 20 11 29
49 22 313 59
49 23 3 7
49 24 3 3
49 25 0 3
49 26 37 13
49 27 409 13
49 29 3 11
49 30 5 3
49 31 13 7
49 32 3 11
49 33 3 3
49 34 7 5
49 36 0 3
49 37 7 5
49 38 ??? 5
49 39 19 3
49 40 13 7
49 41 3 19
49 43 5 3
49 44 11 5
49 45 37 3
49 46 ??? ???
49 47 1531 7
49 48 3 491
50 1 3 1153
50 3 3 43
50 7 103 59
50 9 17 3
50 11 5 109
50 13 3 31
50 17 5 17
50 19 59 5
50 21 7 5
50 23 7 3
50 27 5 3
50 29 31 7
50 31 3 17
50 33 23 17
50 37 31 ???
50 39 13 5
50 41 7 3
50 43 19 ???
50 47 5 41
50 49 3 5