[was@modular hsia]$ [was@modular hsia]$ Magma V2.8-2 Thu Jan 17 2002 16:04:53 on modular [Seed = 4169398407] Type ? for help. Type -D to quit. Loading startup file "/home/was/magma/local/emacs.m" Loading "/home/was/magma/local/init.m" > C := HyperellipticCurve(x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 - 2*x + 1); > Q := C![0,-1]; > origin := C![0,1]; > function order(p) CC := ChangeRing(C,GF(p)); J := Jacobian(CC); return Order(J![CC!Q,CC!origin]); end function; > order(37); 1471 > P := [p : p in [2..200] | IsPrime(p) and p ne 2 and p ne 67]; > time ords := [order(p) : p in P]; Time: 1.050 > #Set([o : o in ords | o le 20]); 1 > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361 ] > P := [p : p in [2..500] | IsPrime(p) and p ne 2 and p ne 67]; > time ords := [order(p) : p in P]; Time: 3.570 > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361, 3153, 2309, 3077, 60259, 12991, 64231, 48169, 14761, 70969, 7821, 70339, 5861, 4579, 75349, 85669, 30543, 23059, 2013, 105289, 104371, 12938, 108289, 120979, 178, 123895, 189, 33571, 16245, 188, 162661, 38551, 179251, 52665, 14457, 8795, 202039, 161599, 190045, 66747, 210661, 187861, 231181, 6765, 25749, 207811, 53995, 224905, 75783, 525 ] > #Set([o : o in ords | o le 20]); 1 > #Set([o : o in ords | o le 100]); 7 > P := [p : p in [501..1000] | IsPrime(p) and p ne 2 and p ne 67]; > time ords := ords cat [order(p) : p in P]; Time: 10.080 > #Set([o : o in ords | o le 100]); 7 > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361, 3153, 2309, 3077, 60259, 12991, 64231, 48169, 14761, 70969, 7821, 70339, 5861, 4579, 75349, 85669, 30543, 23059, 2013, 105289, 104371, 12938, 108289, 120979, 178, 123895, 189, 33571, 16245, 188, 162661, 38551, 179251, 52665, 14457, 8795, 202039, 161599, 190045, 66747, 210661, 187861, 231181, 6765, 25749, 207811, 53995, 224905, 75783, 525, 221761, 22173, 135, 8569, 68599, 94485, 347509, 26787, 78649, 323779, 315799, 313009, 97339, 44102, 86629, 109983, 126015, 19509, 109219, 139287, 79211, 428269, 113905, 53462, 15989, 399019, 17067, 459559, 453601, 171, 116839, 1866, 455605, 350, 365, 539209, 552931, 529579, 537109, 387, 199677, 603229, 210615, 628111, 44547, 235065, 141119, 683845, 165241, 662191, 171151, 237423, 250503, 234177, 12333, 252165, 820831, 165, 798391, 869545, 306237, 305223, 848161, 846355, 312747, 20795, 178505, 332427, 914569, 979855, 108161, 905251, 1006891 ] > Sort(ords); [ 9, 27, 29, 33, 39, 61, 63, 109, 123, 135, 135, 139, 143, 153, 165, 171, 178, 188, 189, 295, 350, 365, 387, 421, 525, 839, 1069, 1471, 1795, 1866, 1891, 2013, 2309, 2539, 3057, 3077, 3079, 3153, 3747, 4189, 4351, 4579, 5673, 5861, 6481, 6765, 6871, 6897, 7821, 8095, 8311, 8569, 8795, 8929, 9505, 11311, 12333, 12421, 12938, 12991, 14457, 14761, 15989, 16245, 17067, 19509, 20795, 20959, 22173, 23059, 25749, 26787, 28045, 30543, 32569, 33571, 34309, 37411, 38005, 38551, 42361, 42829, 44102, 44547, 48169, 52665, 53462, 53995, 60259, 64231, 66747, 68599, 70339, 70969, 75349, 75783, 78649, 79211, 85669, 86629, 94485, 97339, 104371, 105289, 108161, 108289, 109219, 109983, 113905, 116839, 120979, 123895, 126015, 139287, 141119, 161599, 162661, 165241, 171151, 178505, 179251, 187861, 190045, 199677, 202039, 207811, 210615, 210661, 221761, 224905, 231181, 234177, 235065, 237423, 250503, 252165, 305223, 306237, 312747, 313009, 315799, 323779, 332427, 347509, 399019, 428269, 453601, 455605, 459559, 529579, 537109, 539209, 552931, 603229, 628111, 662191, 683845, 798391, 820831, 846355, 848161, 869545, 905251, 914569, 979855, 1006891 ] > order(2003); 3937459 > order(NextPrime(2003)); 1026901 > order(NextPrime(3000)); 9191899 > order(NextPrime(4000)); 15455161 > order(NextPrime(5000)); 8246757 > order(NextPrime(6000)); 36326659 > order(NextPrime(7000)); 3116779 > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361, 3153, 2309, 3077, 60259, 12991, 64231, 48169, 14761, 70969, 7821, 70339, 5861, 4579, 75349, 85669, 30543, 23059, 2013, 105289, 104371, 12938, 108289, 120979, 178, 123895, 189, 33571, 16245, 188, 162661, 38551, 179251, 52665, 14457, 8795, 202039, 161599, 190045, 66747, 210661, 187861, 231181, 6765, 25749, 207811, 53995, 224905, 75783, 525, 221761, 22173, 135, 8569, 68599, 94485, 347509, 26787, 78649, 323779, 315799, 313009, 97339, 44102, 86629, 109983, 126015, 19509, 109219, 139287, 79211, 428269, 113905, 53462, 15989, 399019, 17067, 459559, 453601, 171, 116839, 1866, 455605, 350, 365, 539209, 552931, 529579, 537109, 387, 199677, 603229, 210615, 628111, 44547, 235065, 141119, 683845, 165241, 662191, 171151, 237423, 250503, 234177, 12333, 252165, 820831, 165, 798391, 869545, 306237, 305223, 848161, 846355, 312747, 20795, 178505, 332427, 914569, 979855, 108161, 905251, 1006891 ] > E := EllipticCurve(CremonaDatabase(),"37A"); > G,f := MordellWeilGroup(E); > Q := f(G.1); > P := [p : p in [2..3000] | IsPrime(p) and Conductor(E) mod p ne 0]; > time ords := [Order(ChangeRing(E,GF(p))!Q) : p in P]; Time: 4.540 > ords; [ 5, 7, 8, 9, 17, 16, 18, 20, 11, 12, 18, 51, 14, 57, 53, 13, 35, 30, 63, 75, 76, 33, 86, 47, 33, 86, 20, 126, 33, 127, 144, 72, 17, 155, 68, 15, 182, 36, 55, 81, 177, 49, 220, 39, 99, 45, 241, 122, 223, 38, 123, 114, 254, 129, 49, 138, 303, 133, 135, 28, 74, 325, 104, 292, 148, 167, 121, 179, 172, 346, 375, 180, 393, 73, 91, 193, 403, 384, 195, 413, 446, 154, 425, 103, 443, 414, 440, 432, 243, 47, 233, 512, 260, 61, 488, 541, 555, 546, 261, 270, 144, 594, 297, 565, 578, 620, 599, 599, 156, 640, 599, 601, 207, 660, 643, 315, 656, 339, 135, 690, 647, 689, 74, 178, 119, 134, 227, 712, 727, 749, 723, 727, 202, 797, 93, 783, 793, 373, 404, 255, 869, 35, 403, 417, 398, 138, 302, 880, 444, 414, 448, 209, 863, 428, 886, 978, 228, 53, 476, 936, 893, 491, 490, 475, 25, 202, 520, 1057, 978, 974, 1084, 518, 1031, 1099, 527, 356, 562, 1057, 110, 538, 59, 565, 531, 556, 1145, 155, 191, 360, 1177, 1136, 150, 597, 75, 1221, 1205, 1158, 1226, 1259, 199, 1278, 417, 64, 1263, 626, 217, 152, 220, 1242, 1257, 1336, 1272, 96, 106, 1324, 1287, 1330, 1296, 653, 688, 1319, 1425, 1411, 486, 1459, 1454, 31, 1493, 1505, 1430, 469, 1497, 1473, 1469, 1523, 1491, 63, 248, 1566, 1542, 766, 1516, 103, 1564, 154, 89, 259, 520, 1549, 814, 1570, 103, 128, 538, 1668, 87, 1605, 836, 1585, 421, 207, 1720, 808, 878, 813, 545, 1713, 1762, 1729, 845, 1674, 344, 872, 1738, 92, 874, 896, 1806, 1799, 889, 1833, 955, 27, 1781, 933, 1889, 44, 116, 650, 1824, 981, 1966, 639, 1923, 1981, 1931, 665, 507, 137, 2053, 656, 1921, 1961, 664, 188, 127, 2098, 284, 655, 2092, 2135, 2029, 2153, 2093, 525, 2054, 2155, 1052, 2157, 2172, 1100, 2075, 1058, 1102, 2197, 2162, 528, 544, 1125, 555, 2193, 2270, 2202, 2244, 2200, 1160, 2341, 2283, 774, 566, 2333, 2287, 2352, 568, 2384, 250, 2281, 2359, 2316, 2311, 1166, 2407, 818, 1185, 410, 54, 132, 2460, 2371, 2470, 317, 273, 814, 50, 2409, 305, 412, 1211, 2492, 2450, 2554, 638, 1242, 2570, 2521, 646, 2553, 1322, 2600, 2665, 41, 1339, 896, 1298, 2584, 881, 2569, 2708, 546, 2598, 113, 272, 457, 1357, 2691, 678, 2652, 297, 919, 346, 2789, 691, 180, 669, 685, 2781, 699, 227, 172, 2809, 2855, 2859, 2798, 1412, 1463, 178, 738, 2827, 484, 376, 2846, 370, 132, 2903, 188, 3051, 370, 979, 1508, 986 ] > M := ModularSymbols("67B"); > M; Modular symbols space of level 67, weight 2, and dimension 4 > M := ModularSymbols("67B",+1); > M; Modular symbols space of level 67, weight 2, and dimension 2 > Factorization(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,19)),20)); >> Factorization(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,19)),2 ^ Runtime error in 'Factorization': Bad argument types Argument types given: FldRatElt > factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,19)),20)); [ <3, 2>, <41, 1> ] > p := 19; factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,p)),p+1)); [ <3, 2>, <41, 1> ] > p := 31; factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,p)),p+1)); [ <3, 2>, <11, 2> ] > p := 37; factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,p)),p+1)); [ <1471, 1> ] > p := 41; factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,p)),p+1)); [ <31, 1>, <61, 1> ] > p := 997; factor(Evaluate(CharacteristicPolynomial(DualHeckeOperator(M,p)),p+1)); [ <1006891, 1> ] > P := [p : p in [2..3000] | IsPrime(p) and p ne 2 and p ne 67]; > order(P[5]); 295 > ords := []; for p in P do print "trying p = ", p; time o := order(p); Append(~ords,o); end for; trying p = 3 29 Time: 0.010 trying p = 5 9 Time: 0.000 trying p = 7 61 Time: 0.000 trying p = 11 139 Time: 0.010 trying p = 13 295 Time: 0.000 trying p = 17 109 Time: 0.010 trying p = 19 123 Time: 0.000 trying p = 23 421 Time: 0.000 trying p = 29 1069 Time: 0.010 trying p = 31 33 Time: 0.000 trying p = 37 1471 Time: 0.010 trying p = 41 1891 Time: 0.000 trying p = 43 1795 Time: 0.000 trying p = 47 3079 Time: 0.010 trying p = 53 63 Time: 0.000 trying p = 59 27 Time: 0.010 trying p = 61 4189 Time: 0.000 trying p = 71 4351 Time: 0.010 trying p = 73 39 Time: 0.000 trying p = 79 6871 Time: 0.010 trying p = 83 8311 Time: 0.000 trying p = 89 8095 Time: 0.010 trying p = 97 839 Time: 0.010 trying p = 101 11311 Time: 0.000 trying p = 103 3747 Time: 0.010 trying p = 107 3057 Time: 0.000 trying p = 109 12421 Time: 0.010 trying p = 113 9505 Time: 0.000 trying p = 127 5673 Time: 0.010 trying p = 131 135 Time: 0.010 trying p = 137 6897 Time: 0.000 trying p = 139 143 Time: 0.020 trying p = 149 20959 Time: 0.000 trying p = 151 153 Time: 0.010 trying p = 157 2539 Time: 0.010 trying p = 163 28045 Time: 0.010 trying p = 167 6481 Time: 0.000 trying p = 173 37411 Time: 0.010 trying p = 179 8929 Time: 0.010 trying p = 181 34309 Time: 0.010 trying p = 191 38005 Time: 0.010 trying p = 193 32569 Time: 0.000 trying p = 197 42829 Time: 0.010 trying p = 199 42361 Time: 0.010 trying p = 211 3153 Time: 0.010 trying p = 223 2309 Time: 0.020 trying p = 227 3077 Time: 0.010 trying p = 229 60259 Time: 0.010 trying p = 233 12991 Time: 0.010 trying p = 239 64231 Time: 0.010 trying p = 241 48169 Time: 0.010 trying p = 251 14761 Time: 0.010 trying p = 257 70969 Time: 0.010 trying p = 263 7821 Time: 0.000 trying p = 269 70339 Time: 0.000 trying p = 271 5861 Time: 0.000 trying p = 277 4579 Time: 0.000 trying p = 281 75349 Time: 0.000 trying p = 283 85669 Time: 0.000 trying p = 293 30543 Time: 0.000 trying p = 307 23059 Time: 0.010 trying p = 311 2013 Time: 0.000 trying p = 313 105289 Time: 0.000 trying p = 317 104371 Time: 0.010 trying p = 331 12938 Time: 0.000 trying p = 337 108289 Time: 0.000 trying p = 347 120979 Time: 0.000 trying p = 349 178 Time: 0.010 trying p = 353 123895 Time: 0.000 trying p = 359 189 Time: 0.000 trying p = 367 33571 Time: 0.000 trying p = 373 16245 Time: 0.010 trying p = 379 188 Time: 0.000 trying p = 383 162661 Time: 0.000 trying p = 389 38551 Time: 0.010 trying p = 397 179251 Time: 0.000 trying p = 401 52665 Time: 0.000 trying p = 409 14457 Time: 0.000 trying p = 419 8795 Time: 0.010 trying p = 421 202039 Time: 0.000 trying p = 431 161599 Time: 0.000 trying p = 433 190045 Time: 0.000 trying p = 439 66747 Time: 0.010 trying p = 443 210661 Time: 0.000 trying p = 449 187861 Time: 0.000 trying p = 457 231181 Time: 0.010 trying p = 461 6765 Time: 0.000 trying p = 463 25749 Time: 0.000 trying p = 467 207811 Time: 0.010 trying p = 479 53995 Time: 0.000 trying p = 487 224905 Time: 0.000 trying p = 491 75783 Time: 0.000 trying p = 499 525 Time: 0.010 trying p = 503 221761 Time: 0.010 trying p = 509 22173 Time: 0.000 trying p = 521 135 Time: 0.000 trying p = 523 8569 Time: 0.000 trying p = 541 68599 Time: 0.000 trying p = 547 94485 Time: 0.010 trying p = 557 347509 Time: 0.000 trying p = 563 26787 Time: 0.000 trying p = 569 78649 Time: 0.000 trying p = 571 323779 Time: 0.010 trying p = 577 315799 Time: 0.000 trying p = 587 313009 Time: 0.000 trying p = 593 97339 Time: 0.000 trying p = 599 44102 Time: 0.010 trying p = 601 86629 Time: 0.000 trying p = 607 109983 Time: 0.000 trying p = 613 126015 Time: 0.010 trying p = 617 19509 Time: 0.000 trying p = 619 109219 Time: 0.000 trying p = 631 139287 Time: 0.000 trying p = 641 79211 Time: 0.010 trying p = 643 428269 Time: 0.000 trying p = 647 113905 Time: 0.010 trying p = 653 53462 Time: 0.000 trying p = 659 15989 Time: 0.000 trying p = 661 399019 Time: 0.010 trying p = 673 17067 Time: 0.000 trying p = 677 459559 Time: 0.000 trying p = 683 453601 Time: 0.000 trying p = 691 171 Time: 0.000 trying p = 701 116839 Time: 0.010 trying p = 709 1866 Time: 0.000 trying p = 719 455605 Time: 0.000 trying p = 727 350 Time: 0.010 trying p = 733 365 Time: 0.000 trying p = 739 539209 Time: 0.000 trying p = 743 552931 Time: 0.010 trying p = 751 529579 Time: 0.000 trying p = 757 537109 Time: 0.000 trying p = 761 387 Time: 0.000 trying p = 769 199677 Time: 0.010 trying p = 773 603229 Time: 0.000 trying p = 787 210615 Time: 0.010 trying p = 797 628111 Time: 0.000 trying p = 809 44547 Time: 0.010 trying p = 811 235065 Time: 0.000 trying p = 821 141119 Time: 0.000 trying p = 823 683845 Time: 0.000 trying p = 827 165241 Time: 0.000 trying p = 829 662191 Time: 0.010 trying p = 839 171151 Time: 0.000 trying p = 853 237423 Time: 0.000 trying p = 857 250503 Time: 0.000 trying p = 859 234177 Time: 0.010 trying p = 863 12333 Time: 0.000 trying p = 877 252165 Time: 0.010 trying p = 881 820831 Time: 0.000 trying p = 883 165 Time: 0.010 trying p = 887 798391 Time: 0.010 trying p = 907 869545 Time: 0.000 trying p = 911 306237 Time: 0.000 trying p = 919 305223 Time: 0.010 trying p = 929 848161 Time: 0.000 trying p = 937 846355 Time: 0.000 trying p = 941 312747 Time: 0.010 trying p = 947 20795 Time: 0.000 trying p = 953 178505 Time: 0.010 trying p = 967 332427 Time: 0.000 trying p = 971 914569 Time: 0.000 trying p = 977 979855 Time: 0.010 trying p = 983 108161 Time: 0.000 trying p = 991 905251 Time: 0.010 trying p = 997 1006891 Time: 0.000 trying p = 1009 1017901 Time: 0.020 trying p = 1013 325527 Time: 0.040 trying p = 1019 365163 Time: 0.020 trying p = 1021 66315 Time: 0.330 trying p = 1031 201905 Time: 0.030 trying p = 1033 1097179 Time: 0.020 trying p = 1039 1168381 Time: 0.030 trying p = 1049 1076839 Time: 0.020 trying p = 1051 1157941 Time: 0.060 trying p = 1061 1143679 Time: 0.060 trying p = 1063 282979 Time: 0.040 trying p = 1069 270355 Time: 0.030 trying p = 1087 1253179 Time: 0.040 trying p = 1091 1209781 Time: 0.020 trying p = 1093 76684 Time: 0.030 trying p = 1097 1224949 Time: 0.030 trying p = 1103 1268341 Time: 0.060 trying p = 1109 256505 Time: 0.050 trying p = 1117 113201 Time: 0.060 trying p = 1123 96657 Time: 0.040 trying p = 1129 437637 Time: 0.020 trying p = 1151 197533 Time: 0.030 trying p = 1153 1289371 Time: 0.010 trying p = 1163 82021 Time: 0.020 trying p = 1171 591 Time: 0.150 trying p = 1181 606 Time: 0.130 trying p = 1187 1442551 Time: 0.050 trying p = 1193 1394479 Time: 0.020 trying p = 1201 1473751 Time: 0.030 trying p = 1213 482343 Time: 0.030 trying p = 1217 357841 Time: 0.030 trying p = 1223 1516561 Time: 0.060 trying p = 1229 1472581 Time: 0.040 trying p = 1231 308705 Time: 0.060 trying p = 1237 89689 Time: 0.030 trying p = 1249 2937 Time: 0.310 trying p = 1259 171809 Time: 0.040 trying p = 1277 1742155 Time: 0.030 trying p = 1279 1662529 Time: 0.050 trying p = 1283 1575919 Time: 0.040 trying p = 1289 1624645 Time: 0.030 trying p = 1291 84491 Time: 0.060 trying p = 1297 410971 Time: 0.030 trying p = 1301 1636669 Time: 0.040 trying p = 1303 560985 Time: 0.050 trying p = 1307 1678171 Time: 0.030 trying p = 1319 54440 Time: 0.040 trying p = 1321 624993 Time: 0.050 trying p = 1327 156633 Time: 0.050 trying p = 1361 437581 Time: 0.040 trying p = 1367 1856371 Time: 0.050 trying p = 1373 166199 Time: 0.030 trying p = 1381 608757 Time: 0.040 trying p = 1399 1974631 Time: 0.030 trying p = 1409 1944745 Time: 0.030 trying p = 1423 1911205 Time: 0.030 trying p = 1427 2214139 Time: 0.030 trying p = 1429 497629 Time: 0.040 trying p = 1433 1937659 Time: 0.020 trying p = 1439 427475 Time: 0.060 trying p = 1447 73473 Time: 0.460 trying p = 1451 546829 Time: 0.040 trying p = 1453 135691 Time: 0.020 trying p = 1459 2228869 Time: 0.040 trying p = 1471 532069 Time: 0.030 trying p = 1481 2149669 Time: 0.020 trying p = 1483 2225659 Time: 0.020 trying p = 1487 2212339 Time: 0.030 trying p = 1489 2219695 Time: 0.030 trying p = 1493 2281459 Time: 0.060 trying p = 1499 44283 Time: 0.570 trying p = 1511 572755 Time: 0.050 trying p = 1523 2313361 Time: 0.030 trying p = 1531 757515 Time: 0.040 trying p = 1543 196473 Time: 0.050 trying p = 1549 2434879 Time: 0.050 trying p = 1553 622441 Time: 0.040 trying p = 1559 2590429 Time: 0.040 trying p = 1567 798753 Time: 0.030 trying p = 1571 2599795 Time: 0.060 trying p = 1579 507155 Time: 0.050 trying p = 1583 70479 Time: 0.040 trying p = 1597 162165 Time: 0.550 trying p = 1601 2499481 Time: 0.030 trying p = 1607 288905 Time: 0.050 trying p = 1609 2678149 Time: 0.030 trying p = 1613 27714 Time: 0.350 trying p = 1619 644005 Time: 0.060 trying p = 1621 2669059 Time: 0.040 trying p = 1627 858615 Time: 0.070 trying p = 1637 2707459 Time: 0.060 trying p = 1657 886173 Time: 0.050 trying p = 1663 2709601 Time: 0.040 trying p = 1667 945843 Time: 0.040 trying p = 1669 314149 Time: 0.070 trying p = 1693 302495 Time: 0.030 trying p = 1697 242727 Time: 0.040 trying p = 1699 25113 Time: 0.590 trying p = 1709 2989639 Time: 0.060 trying p = 1721 176380 Time: 0.030 trying p = 1723 2860261 Time: 0.050 trying p = 1733 265485 Time: 0.040 trying p = 1741 771481 Time: 0.030 trying p = 1747 717229 Time: 0.030 trying p = 1753 3119161 Time: 0.050 trying p = 1759 395690 Time: 0.030 trying p = 1777 70205 Time: 0.050 trying p = 1783 161045 Time: 0.040 trying p = 1787 1054707 Time: 0.040 trying p = 1789 352831 Time: 0.020 trying p = 1801 3314611 Time: 0.060 trying p = 1811 3288781 Time: 0.050 trying p = 1823 74099 Time: 0.050 trying p = 1831 3474091 Time: 0.040 trying p = 1847 3321505 Time: 0.080 trying p = 1861 216589 Time: 0.040 trying p = 1867 185261 Time: 0.040 trying p = 1871 3550459 Time: 0.040 trying p = 1873 3585331 Time: 0.050 trying p = 1877 1194423 Time: 0.020 trying p = 1879 135465 Time: 0.700 trying p = 1889 742961 Time: 0.050 trying p = 1901 1206687 Time: 0.050 trying p = 1907 3442429 Time: 0.040 trying p = 1913 3884821 Time: 0.040 trying p = 1931 977071 Time: 0.040 trying p = 1933 3706999 Time: 0.050 trying p = 1949 227524 Time: 0.040 trying p = 1951 3754531 Time: 0.040 trying p = 1973 4046101 Time: 0.050 trying p = 1979 4069255 Time: 0.050 trying p = 1987 1845 Time: 0.040 trying p = 1993 4019845 Time: 0.040 trying p = 1997 4007695 Time: 0.040 trying p = 1999 3730591 Time: 0.040 trying p = 2003 3937459 Time: 0.010 trying p = 2011 1026901 Time: 0.000 trying p = 2017 27739 Time: 0.030 trying p = 2027 4228531 Time: 0.060 trying p = 2029 1335585 Time: 0.050 trying p = 2039 995005 Time: 0.040 trying p = 2053 4247881 Time: 0.060 trying p = 2063 863129 Time: 0.050 trying p = 2069 1442793 Time: 0.060 trying p = 2081 53555 Time: 0.490 trying p = 2083 265729 Time: 0.050 trying p = 2087 7381 Time: 0.040 trying p = 2089 289707 Time: 0.030 trying p = 2099 1462623 Time: 0.050 trying p = 2111 1129981 Time: 0.050 trying p = 2113 358017 Time: 0.050 trying p = 2129 380973 Time: 0.040 trying p = 2131 1486473 Time: 0.020 trying p = 2137 79035 Time: 0.050 trying p = 2141 1539813 Time: 0.060 trying p = 2143 4583701 Time: 0.030 trying p = 2153 1493007 Time: 0.060 trying p = 2161 4679251 Time: 0.040 trying p = 2179 419613 Time: 0.050 trying p = 2203 2231 Time: 0.250 trying p = 2207 4888501 Time: 0.030 trying p = 2213 632690 Time: 0.020 trying p = 2221 2233 Time: 0.260 trying p = 2237 1292689 Time: 0.030 trying p = 2239 449045 Time: 0.040 trying p = 2243 49166 Time: 0.320 trying p = 2251 5067859 Time: 0.030 trying p = 2267 5329111 Time: 0.050 trying p = 2269 987719 Time: 0.050 trying p = 2273 5252659 Time: 0.030 trying p = 2281 5146741 Time: 0.030 trying p = 2287 5117005 Time: 0.060 trying p = 2293 5300929 Time: 0.040 trying p = 2297 727615 Time: 0.070 trying p = 2309 5377441 Time: 0.030 trying p = 2311 432057 Time: 0.040 trying p = 2333 5405305 Time: 0.030 trying p = 2339 284405 Time: 0.050 trying p = 2341 1321249 Time: 0.030 trying p = 2347 1845867 Time: 0.040 trying p = 2351 5919409 Time: 0.040 trying p = 2357 5503711 Time: 0.040 trying p = 2371 1380445 Time: 0.040 trying p = 2377 5367769 Time: 0.020 trying p = 2381 5531899 Time: 0.030 trying p = 2383 5778091 Time: 0.040 trying p = 2389 2373 Time: 0.200 trying p = 2393 5805859 Time: 0.060 trying p = 2399 84676 Time: 0.030 trying p = 2411 1839027 Time: 0.020 trying p = 2417 33759 Time: 0.060 trying p = 2423 239041 Time: 0.040 trying p = 2437 221043 Time: 0.590 trying p = 2441 5933971 Time: 0.030 trying p = 2447 771242 Time: 0.040 trying p = 2459 1557379 Time: 0.040 trying p = 2467 2409 Time: 0.210 trying p = 2473 1550719 Time: 0.040 trying p = 2477 6464095 Time: 0.060 trying p = 2503 6242539 Time: 0.050 trying p = 2521 241953 Time: 0.630 trying p = 2531 693045 Time: 0.070 trying p = 2539 6682909 Time: 0.050 trying p = 2543 6289819 Time: 0.030 trying p = 2549 6755869 Time: 0.060 trying p = 2551 1282205 Time: 0.050 trying p = 2557 6698971 Time: 0.070 trying p = 2579 6525019 Time: 0.060 trying p = 2591 270870 Time: 0.040 trying p = 2593 2295915 Time: 0.050 trying p = 2609 6738301 Time: 0.050 trying p = 2617 2376165 Time: 0.040 trying p = 2621 2302113 Time: 0.040 trying p = 2633 7297651 Time: 0.070 trying p = 2647 7294681 Time: 0.040 trying p = 2657 6999871 Time: 0.040 trying p = 2659 7368499 Time: 0.050 trying p = 2663 7128295 Time: 0.040 trying p = 2671 257487 Time: 0.680 trying p = 2677 672545 Time: 0.040 trying p = 2683 1407149 Time: 0.070 trying p = 2687 7120861 Time: 0.070 trying p = 2689 7339489 Time: 0.050 trying p = 2693 677405 Time: 0.050 trying p = 2699 291475 Time: 0.030 trying p = 2707 7147321 Time: 0.050 trying p = 2711 1879141 Time: 0.050 trying p = 2713 7341895 Time: 0.040 trying p = 2719 7359649 Time: 0.040 trying p = 2729 1850959 Time: 0.040 trying p = 2731 909 Time: 0.220 trying p = 2741 7462069 Time: 0.030 trying p = 2749 644313 Time: 0.050 trying p = 2753 923318 Time: 0.040 trying p = 2767 7581481 Time: 0.050 trying p = 2777 7977649 Time: 0.050 trying p = 2789 1580975 Time: 0.060 trying p = 2791 2560953 Time: 0.030 trying p = 2797 7705051 Time: 0.030 trying p = 2801 7869781 Time: 0.050 trying p = 2803 374241 Time: 0.050 trying p = 2819 838129 Time: 0.050 trying p = 2833 2036149 Time: 0.040 trying p = 2837 507445 Time: 0.040 trying p = 2843 2090791 Time: 0.040 trying p = 2851 2681907 Time: 0.060 trying p = 2857 404681 Time: 0.040 trying p = 2861 125296 Time: 0.720 trying p = 2879 1148035 Time: 0.040 trying p = 2887 929291 Time: 0.030 trying p = 2897 2103799 Time: 0.050 trying p = 2903 718527 Time: 0.040 trying p = 2909 2112001 Time: 0.040 trying p = 2917 2109655 Time: 0.070 trying p = 2927 8543071 Time: 0.050 trying p = 2939 315867 Time: 0.060 trying p = 2953 67323 Time: 0.900 trying p = 2957 2925285 Time: 0.070 trying p = 2963 2813973 Time: 0.050 trying p = 2969 9125461 Time: 0.050 trying p = 2971 2273659 Time: 0.040 trying p = 2999 9224305 Time: 0.050 > ords := []; for p in P do print "trying p = ", p; time o := order(p); Append(~ords,o); end for; trying p = 3 Time: 0.010 trying p = 5 Time: 0.000 trying p = 7 Time: 0.010 trying p = 11 Time: 0.000 trying p = 13 Time: 0.010 trying p = 17 Time: 0.000 trying p = 19 Time: 0.010 trying p = 23 Time: 0.000 trying p = 29 Time: 0.010 trying p = 31 Time: 0.000 trying p = 37 Time: 0.010 trying p = 41 Time: 0.000 trying p = 43 Time: 0.010 trying p = 47 Time: 0.000 trying p = 53 Time: 0.010 trying p = 59 Time: 0.000 trying p = 61 Time: 0.010 trying p = 71 Time: 0.000 trying p = 73 Time: 0.020 trying p = 79 Time: 0.000 trying p = 83 Time: 0.010 trying p = 89 Time: 0.010 trying p = 97 Time: 0.010 trying p = 101 Time: 0.010 trying p = 103 Time: 0.000 trying p = 107 Time: 0.010 trying p = 109 Time: 0.010 trying p = 113 Time: 0.010 trying p = 127 Time: 0.010 trying p = 131 Time: 0.000 trying p = 137 Time: 0.020 trying p = 139 Time: 0.000 trying p = 149 Time: 0.010 trying p = 151 Time: 0.010 trying p = 157 Time: 0.020 trying p = 163 Time: 0.010 trying p = 167 Time: 0.020 trying p = 173 Time: 0.010 trying p = 179 Time: 0.010 trying p = 181 Time: 0.010 trying p = 191 Time: 0.010 trying p = 193 Time: 0.010 trying p = 197 Time: 0.010 trying p = 199 Time: 0.010 trying p = 211 Time: 0.010 trying p = 223 Time: 0.020 trying p = 227 Time: 0.010 trying p = 229 Time: 0.010 trying p = 233 Time: 0.020 trying p = 239 Time: 0.010 trying p = 241 Time: 0.010 trying p = 251 Time: 0.020 trying p = 257 Time: 0.000 trying p = 263 Time: 0.010 trying p = 269 Time: 0.000 trying p = 271 Time: 0.000 trying p = 277 Time: 0.010 trying p = 281 Time: 0.000 trying p = 283 Time: 0.010 trying p = 293 Time: 0.000 trying p = 307 Time: 0.010 trying p = 311 Time: 0.000 trying p = 313 Time: 0.010 trying p = 317 Time: 0.000 trying p = 331 Time: 0.010 trying p = 337 Time: 0.000 trying p = 347 Time: 0.010 trying p = 349 Time: 0.000 trying p = 353 Time: 0.010 trying p = 359 Time: 0.000 trying p = 367 Time: 0.010 trying p = 373 Time: 0.000 trying p = 379 Time: 0.010 trying p = 383 Time: 0.000 trying p = 389 Time: 0.010 trying p = 397 Time: 0.000 trying p = 401 Time: 0.010 trying p = 409 Time: 0.010 trying p = 419 Time: 0.000 trying p = 421 Time: 0.010 trying p = 431 Time: 0.000 trying p = 433 Time: 0.010 trying p = 439 Time: 0.000 trying p = 443 Time: 0.010 trying p = 449 Time: 0.000 trying p = 457 Time: 0.000 trying p = 461 Time: 0.010 trying p = 463 Time: 0.000 trying p = 467 Time: 0.000 trying p = 479 Time: 0.010 trying p = 487 Time: 0.000 trying p = 491 Time: 0.010 trying p = 499 Time: 0.010 trying p = 503 Time: 0.000 trying p = 509 Time: 0.010 trying p = 521 Time: 0.000 trying p = 523 Time: 0.010 trying p = 541 Time: 0.010 trying p = 547 Time: 0.000 trying p = 557 Time: 0.000 trying p = 563 Time: 0.010 trying p = 569 Time: 0.000 trying p = 571 Time: 0.010 trying p = 577 Time: 0.000 trying p = 587 Time: 0.010 trying p = 593 Time: 0.000 trying p = 599 Time: 0.010 trying p = 601 Time: 0.000 trying p = 607 Time: 0.010 trying p = 613 Time: 0.000 trying p = 617 Time: 0.010 trying p = 619 Time: 0.000 trying p = 631 Time: 0.010 trying p = 641 Time: 0.010 trying p = 643 Time: 0.000 trying p = 647 Time: 0.010 trying p = 653 Time: 0.000 trying p = 659 Time: 0.010 trying p = 661 Time: 0.000 trying p = 673 Time: 0.010 trying p = 677 Time: 0.000 trying p = 683 Time: 0.000 trying p = 691 Time: 0.010 trying p = 701 Time: 0.000 trying p = 709 Time: 0.010 trying p = 719 Time: 0.000 trying p = 727 Time: 0.010 trying p = 733 Time: 0.000 trying p = 739 Time: 0.010 trying p = 743 Time: 0.000 trying p = 751 Time: 0.010 trying p = 757 Time: 0.000 trying p = 761 Time: 0.010 trying p = 769 Time: 0.000 trying p = 773 Time: 0.010 trying p = 787 Time: 0.010 trying p = 797 Time: 0.000 trying p = 809 Time: 0.010 trying p = 811 Time: 0.000 trying p = 821 Time: 0.010 trying p = 823 Time: 0.000 trying p = 827 Time: 0.010 trying p = 829 Time: 0.000 trying p = 839 Time: 0.010 trying p = 853 Time: 0.010 trying p = 857 Time: 0.000 trying p = 859 Time: 0.010 trying p = 863 Time: 0.000 trying p = 877 Time: 0.010 trying p = 881 Time: 0.000 trying p = 883 Time: 0.010 trying p = 887 Time: 0.000 trying p = 907 Time: 0.010 trying p = 911 Time: 0.000 trying p = 919 Time: 0.010 trying p = 929 Time: 0.000 trying p = 937 Time: 0.010 trying p = 941 Time: 0.000 trying p = 947 Time: 0.010 trying p = 953 Time: 0.010 trying p = 967 Time: 0.000 trying p = 971 Time: 0.000 trying p = 977 Time: 0.010 trying p = 983 Time: 0.000 trying p = 991 Time: 0.010 trying p = 997 Time: 0.000 trying p = 1009 Time: 0.010 trying p = 1013 Time: 0.010 trying p = 1019 Time: 0.000 trying p = 1021 Time: 0.010 trying p = 1031 Time: 0.010 trying p = 1033 Time: 0.000 trying p = 1039 Time: 0.000 trying p = 1049 Time: 0.000 trying p = 1051 Time: 0.010 trying p = 1061 Time: 0.000 trying p = 1063 Time: 0.010 trying p = 1069 Time: 0.010 trying p = 1087 Time: 0.000 trying p = 1091 Time: 0.000 trying p = 1093 Time: 0.010 trying p = 1097 Time: 0.010 trying p = 1103 Time: 0.000 trying p = 1109 Time: 0.010 trying p = 1117 Time: 0.000 trying p = 1123 Time: 0.010 trying p = 1129 Time: 0.010 trying p = 1151 Time: 0.000 trying p = 1153 Time: 0.010 trying p = 1163 Time: 0.000 trying p = 1171 Time: 0.010 trying p = 1181 Time: 0.010 trying p = 1187 Time: 0.000 trying p = 1193 Time: 0.010 trying p = 1201 Time: 0.000 trying p = 1213 Time: 0.010 trying p = 1217 Time: 0.010 trying p = 1223 Time: 0.000 trying p = 1229 Time: 0.010 trying p = 1231 Time: 0.000 trying p = 1237 Time: 0.010 trying p = 1249 Time: 0.010 trying p = 1259 Time: 0.010 trying p = 1277 Time: 0.000 trying p = 1279 Time: 0.010 trying p = 1283 Time: 0.000 trying p = 1289 Time: 0.010 trying p = 1291 Time: 0.010 trying p = 1297 Time: 0.000 trying p = 1301 Time: 0.010 trying p = 1303 Time: 0.010 trying p = 1307 Time: 0.000 trying p = 1319 Time: 0.010 trying p = 1321 Time: 0.010 trying p = 1327 Time: 0.000 trying p = 1361 Time: 0.010 trying p = 1367 Time: 0.010 trying p = 1373 Time: 0.000 trying p = 1381 Time: 0.010 trying p = 1399 Time: 0.010 trying p = 1409 Time: 0.000 trying p = 1423 Time: 0.010 trying p = 1427 Time: 0.010 trying p = 1429 Time: 0.000 trying p = 1433 Time: 0.010 trying p = 1439 Time: 0.000 trying p = 1447 Time: 0.010 trying p = 1451 Time: 0.010 trying p = 1453 Time: 0.000 trying p = 1459 Time: 0.000 trying p = 1471 Time: 0.000 trying p = 1481 Time: 0.010 trying p = 1483 Time: 0.000 trying p = 1487 Time: 0.010 trying p = 1489 Time: 0.010 trying p = 1493 Time: 0.000 trying p = 1499 Time: 0.000 trying p = 1511 Time: 0.010 trying p = 1523 Time: 0.000 trying p = 1531 Time: 0.010 trying p = 1543 Time: 0.000 trying p = 1549 Time: 0.000 trying p = 1553 Time: 0.010 trying p = 1559 Time: 0.000 trying p = 1567 Time: 0.010 trying p = 1571 Time: 0.000 trying p = 1579 Time: 0.000 trying p = 1583 Time: 0.010 trying p = 1597 Time: 0.000 trying p = 1601 Time: 0.010 trying p = 1607 Time: 0.000 trying p = 1609 Time: 0.010 trying p = 1613 Time: 0.000 trying p = 1619 Time: 0.010 trying p = 1621 Time: 0.000 trying p = 1627 Time: 0.010 trying p = 1637 Time: 0.000 trying p = 1657 Time: 0.010 trying p = 1663 Time: 0.000 trying p = 1667 Time: 0.000 trying p = 1669 Time: 0.010 trying p = 1693 Time: 0.000 trying p = 1697 Time: 0.010 trying p = 1699 Time: 0.010 trying p = 1709 Time: 0.000 trying p = 1721 Time: 0.010 trying p = 1723 Time: 0.010 trying p = 1733 Time: 0.000 trying p = 1741 Time: 0.010 trying p = 1747 Time: 0.000 trying p = 1753 Time: 0.010 trying p = 1759 Time: 0.000 trying p = 1777 Time: 0.010 trying p = 1783 Time: 0.000 trying p = 1787 Time: 0.010 trying p = 1789 Time: 0.000 trying p = 1801 Time: 0.010 trying p = 1811 Time: 0.000 trying p = 1823 Time: 0.010 trying p = 1831 Time: 0.000 trying p = 1847 Time: 0.010 trying p = 1861 Time: 0.000 trying p = 1867 Time: 0.010 trying p = 1871 Time: 0.000 trying p = 1873 Time: 0.010 trying p = 1877 Time: 0.000 trying p = 1879 Time: 0.010 trying p = 1889 Time: 0.000 trying p = 1901 Time: 0.010 trying p = 1907 Time: 0.000 trying p = 1913 Time: 0.010 trying p = 1931 Time: 0.000 trying p = 1933 Time: 0.010 trying p = 1949 Time: 0.000 trying p = 1951 Time: 0.010 trying p = 1973 Time: 0.000 trying p = 1979 Time: 0.000 trying p = 1987 Time: 0.010 trying p = 1993 Time: 0.010 trying p = 1997 Time: 0.000 trying p = 1999 Time: 0.010 trying p = 2003 Time: 0.000 trying p = 2011 Time: 0.010 trying p = 2017 Time: 0.000 trying p = 2027 Time: 0.000 trying p = 2029 Time: 0.010 trying p = 2039 Time: 0.010 trying p = 2053 Time: 0.000 trying p = 2063 Time: 0.010 trying p = 2069 Time: 0.000 trying p = 2081 Time: 0.010 trying p = 2083 Time: 0.000 trying p = 2087 Time: 0.010 trying p = 2089 Time: 0.010 trying p = 2099 Time: 0.000 trying p = 2111 Time: 0.010 trying p = 2113 Time: 0.010 trying p = 2129 Time: 0.000 trying p = 2131 Time: 0.010 trying p = 2137 Time: 0.000 trying p = 2141 Time: 0.010 trying p = 2143 Time: 0.000 trying p = 2153 Time: 0.010 trying p = 2161 Time: 0.000 trying p = 2179 Time: 0.010 trying p = 2203 Time: 0.000 trying p = 2207 Time: 0.010 trying p = 2213 Time: 0.000 trying p = 2221 Time: 0.010 trying p = 2237 Time: 0.000 trying p = 2239 Time: 0.010 trying p = 2243 Time: 0.000 trying p = 2251 Time: 0.010 trying p = 2267 Time: 0.000 trying p = 2269 Time: 0.010 trying p = 2273 Time: 0.000 trying p = 2281 Time: 0.010 trying p = 2287 Time: 0.000 trying p = 2293 Time: 0.010 trying p = 2297 Time: 0.000 trying p = 2309 Time: 0.010 trying p = 2311 Time: 0.000 trying p = 2333 Time: 0.010 trying p = 2339 Time: 0.000 trying p = 2341 Time: 0.010 trying p = 2347 Time: 0.000 trying p = 2351 Time: 0.010 trying p = 2357 Time: 0.000 trying p = 2371 Time: 0.010 trying p = 2377 Time: 0.000 trying p = 2381 Time: 0.010 trying p = 2383 Time: 0.000 trying p = 2389 Time: 0.010 trying p = 2393 Time: 0.000 trying p = 2399 Time: 0.000 trying p = 2411 Time: 0.010 trying p = 2417 Time: 0.000 trying p = 2423 Time: 0.010 trying p = 2437 Time: 0.000 trying p = 2441 Time: 0.010 trying p = 2447 Time: 0.000 trying p = 2459 Time: 0.010 trying p = 2467 Time: 0.000 trying p = 2473 Time: 0.010 trying p = 2477 Time: 0.000 trying p = 2503 Time: 0.010 trying p = 2521 Time: 0.000 trying p = 2531 Time: 0.010 trying p = 2539 Time: 0.000 trying p = 2543 Time: 0.010 trying p = 2549 Time: 0.000 trying p = 2551 Time: 0.000 trying p = 2557 Time: 0.010 trying p = 2579 Time: 0.000 trying p = 2591 Time: 0.010 trying p = 2593 Time: 0.010 trying p = 2609 Time: 0.000 trying p = 2617 Time: 0.000 trying p = 2621 Time: 0.000 trying p = 2633 Time: 0.010 trying p = 2647 Time: 0.000 trying p = 2657 Time: 0.000 trying p = 2659 Time: 0.010 trying p = 2663 Time: 0.000 trying p = 2671 Time: 0.010 trying p = 2677 Time: 0.010 trying p = 2683 Time: 0.000 trying p = 2687 Time: 0.010 trying p = 2689 Time: 0.000 trying p = 2693 Time: 0.010 trying p = 2699 Time: 0.000 trying p = 2707 Time: 0.010 trying p = 2711 Time: 0.000 trying p = 2713 Time: 0.010 trying p = 2719 Time: 0.010 trying p = 2729 Time: 0.000 trying p = 2731 Time: 0.010 trying p = 2741 Time: 0.000 trying p = 2749 Time: 0.010 trying p = 2753 Time: 0.000 trying p = 2767 Time: 0.000 trying p = 2777 Time: 0.010 trying p = 2789 Time: 0.000 trying p = 2791 Time: 0.010 trying p = 2797 Time: 0.000 trying p = 2801 Time: 0.010 trying p = 2803 Time: 0.000 trying p = 2819 Time: 0.010 trying p = 2833 Time: 0.010 trying p = 2837 Time: 0.000 trying p = 2843 Time: 0.000 trying p = 2851 Time: 0.010 trying p = 2857 Time: 0.010 trying p = 2861 Time: 0.000 trying p = 2879 Time: 0.010 trying p = 2887 Time: 0.000 trying p = 2897 Time: 0.010 trying p = 2903 Time: 0.000 trying p = 2909 Time: 0.010 trying p = 2917 Time: 0.000 trying p = 2927 Time: 0.010 trying p = 2939 Time: 0.000 trying p = 2953 Time: 0.010 trying p = 2957 Time: 0.000 trying p = 2963 Time: 0.010 trying p = 2969 Time: 0.000 trying p = 2971 Time: 0.000 trying p = 2999 Time: 0.010 > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361, 3153, 2309, 3077, 60259, 12991, 64231, 48169, 14761, 70969, 7821, 70339, 5861, 4579, 75349, 85669, 30543, 23059, 2013, 105289, 104371, 12938, 108289, 120979, 178, 123895, 189, 33571, 16245, 188, 162661, 38551, 179251, 52665, 14457, 8795, 202039, 161599, 190045, 66747, 210661, 187861, 231181, 6765, 25749, 207811, 53995, 224905, 75783, 525, 221761, 22173, 135, 8569, 68599, 94485, 347509, 26787, 78649, 323779, 315799, 313009, 97339, 44102, 86629, 109983, 126015, 19509, 109219, 139287, 79211, 428269, 113905, 53462, 15989, 399019, 17067, 459559, 453601, 171, 116839, 1866, 455605, 350, 365, 539209, 552931, 529579, 537109, 387, 199677, 603229, 210615, 628111, 44547, 235065, 141119, 683845, 165241, 662191, 171151, 237423, 250503, 234177, 12333, 252165, 820831, 165, 798391, 869545, 306237, 305223, 848161, 846355, 312747, 20795, 178505, 332427, 914569, 979855, 108161, 905251, 1006891, 1017901, 325527, 365163, 66315, 201905, 1097179, 1168381, 1076839, 1157941, 1143679, 282979, 270355, 1253179, 1209781, 76684, 1224949, 1268341, 256505, 113201, 96657, 437637, 197533, 1289371, 82021, 591, 606, 1442551, 1394479, 1473751, 482343, 357841, 1516561, 1472581, 308705, 89689, 2937, 171809, 1742155, 1662529, 1575919, 1624645, 84491, 410971, 1636669, 560985, 1678171, 54440, 624993, 156633, 437581, 1856371, 166199, 608757, 1974631, 1944745, 1911205, 2214139, 497629, 1937659, 427475, 73473, 546829, 135691, 2228869, 532069, 2149669, 2225659, 2212339, 2219695, 2281459, 44283, 572755, 2313361, 757515, 196473, 2434879, 622441, 2590429, 798753, 2599795, 507155, 70479, 162165, 2499481, 288905, 2678149, 27714, 644005, 2669059, 858615, 2707459, 886173, 2709601, 945843, 314149, 302495, 242727, 25113, 2989639, 176380, 2860261, 265485, 771481, 717229, 3119161, 395690, 70205, 161045, 1054707, 352831, 3314611, 3288781, 74099, 3474091, 3321505, 216589, 185261, 3550459, 3585331, 1194423, 135465, 742961, 1206687, 3442429, 3884821, 977071, 3706999, 227524, 3754531, 4046101, 4069255, 1845, 4019845, 4007695, 3730591, 3937459, 1026901, 27739, 4228531, 1335585, 995005, 4247881, 863129, 1442793, 53555, 265729, 7381, 289707, 1462623, 1129981, 358017, 380973, 1486473, 79035, 1539813, 4583701, 1493007, 4679251, 419613, 2231, 4888501, 632690, 2233, 1292689, 449045, 49166, 5067859, 5329111, 987719, 5252659, 5146741, 5117005, 5300929, 727615, 5377441, 432057, 5405305, 284405, 1321249, 1845867, 5919409, 5503711, 1380445, 5367769, 5531899, 5778091, 2373, 5805859, 84676, 1839027, 33759, 239041, 221043, 5933971, 771242, 1557379, 2409, 1550719, 6464095, 6242539, 241953, 693045, 6682909, 6289819, 6755869, 1282205, 6698971, 6525019, 270870, 2295915, 6738301, 2376165, 2302113, 7297651, 7294681, 6999871, 7368499, 7128295, 257487, 672545, 1407149, 7120861, 7339489, 677405, 291475, 7147321, 1879141, 7341895, 7359649, 1850959, 909, 7462069, 644313, 923318, 7581481, 7977649, 1580975, 2560953, 7705051, 7869781, 374241, 838129, 2036149, 507445, 2090791, 2681907, 404681, 125296, 1148035, 929291, 2103799, 718527, 2112001, 2109655, 8543071, 315867, 67323, 2925285, 2813973, 9125461, 2273659, 9224305 ] > Sort(Set(ords)); >> Sort(Set(ords)); ^ Runtime error in 'Sort': Argument 1 must be a variable reference (use ~) Argument types given: SetEnum[RngIntElt] > Set(Sort(ords)); { 9, 27, 29, 33, 39, 61, 63, 109, 123, 135, 139, 143, 153, 165, 171, 178, 188, 189, 295, 350, 365, 387, 421, 525, 591, 606, 839, 909, 1069, 1471, 1795, 1845, 1866, 1891, 2013, 2231, 2233, 2309, 2373, 2409, 2539, 2937, 3057, 3077, 3079, 3153, 3747, 4189, 4351, 4579, 5673, 5861, 6481, 6765, 6871, 6897, 7381, 7821, 8095, 8311, 8569, 8795, 8929, 9505, 11311, 12333, 12421, 12938, 12991, 14457, 14761, 15989, 16245, 17067, 19509, 20795, 20959, 22173, 23059, 25113, 25749, 26787, 27714, 27739, 28045, 30543, 32569, 33571, 33759, 34309, 37411, 38005, 38551, 42361, 42829, 44102, 44283, 44547, 48169, 49166, 52665, 53462, 53555, 53995, 54440, 60259, 64231, 66315, 66747, 67323, 68599, 70205, 70339, 70479, 70969, 73473, 74099, 75349, 75783, 76684, 78649, 79035, 79211, 82021, 84491, 84676, 85669, 86629, 89689, 94485, 96657, 97339, 104371, 105289, 108161, 108289, 109219, 109983, 113201, 113905, 116839, 120979, 123895, 125296, 126015, 135465, 135691, 139287, 141119, 156633, 161045, 161599, 162165, 162661, 165241, 166199, 171151, 171809, 176380, 178505, 179251, 185261, 187861, 190045, 196473, 197533, 199677, 201905, 202039, 207811, 210615, 210661, 216589, 221043, 221761, 224905, 227524, 231181, 234177, 235065, 237423, 239041, 241953, 242727, 250503, 252165, 256505, 257487, 265485, 265729, 270355, 270870, 282979, 284405, 288905, 289707, 291475, 302495, 305223, 306237, 308705, 312747, 313009, 314149, 315799, 315867, 323779, 325527, 332427, 347509, 352831, 357841, 358017, 365163, 374241, 380973, 395690, 399019, 404681, 410971, 419613, 427475, 428269, 432057, 437581, 437637, 449045, 453601, 455605, 459559, 482343, 497629, 507155, 507445, 529579, 532069, 537109, 539209, 546829, 552931, 560985, 572755, 603229, 608757, 622441, 624993, 628111, 632690, 644005, 644313, 662191, 672545, 677405, 683845, 693045, 717229, 718527, 727615, 742961, 757515, 771242, 771481, 798391, 798753, 820831, 838129, 846355, 848161, 858615, 863129, 869545, 886173, 905251, 914569, 923318, 929291, 945843, 977071, 979855, 987719, 995005, 1006891, 1017901, 1026901, 1054707, 1076839, 1097179, 1129981, 1143679, 1148035, 1157941, 1168381, 1194423, 1206687, 1209781, 1224949, 1253179, 1268341, 1282205, 1289371, 1292689, 1321249, 1335585, 1380445, 1394479, 1407149, 1442551, 1442793, 1462623, 1472581, 1473751, 1486473, 1493007, 1516561, 1539813, 1550719, 1557379, 1575919, 1580975, 1624645, 1636669, 1662529, 1678171, 1742155, 1839027, 1845867, 1850959, 1856371, 1879141, 1911205, 1937659, 1944745, 1974631, 2036149, 2090791, 2103799, 2109655, 2112001, 2149669, 2212339, 2214139, 2219695, 2225659, 2228869, 2273659, 2281459, 2295915, 2302113, 2313361, 2376165, 2434879, 2499481, 2560953, 2590429, 2599795, 2669059, 2678149, 2681907, 2707459, 2709601, 2813973, 2860261, 2925285, 2989639, 3119161, 3288781, 3314611, 3321505, 3442429, 3474091, 3550459, 3585331, 3706999, 3730591, 3754531, 3884821, 3937459, 4007695, 4019845, 4046101, 4069255, 4228531, 4247881, 4583701, 4679251, 4888501, 5067859, 5117005, 5146741, 5252659, 5300929, 5329111, 5367769, 5377441, 5405305, 5503711, 5531899, 5778091, 5805859, 5919409, 5933971, 6242539, 6289819, 6464095, 6525019, 6682909, 6698971, 6738301, 6755869, 6999871, 7120861, 7128295, 7147321, 7294681, 7297651, 7339489, 7341895, 7359649, 7368499, 7462069, 7581481, 7705051, 7869781, 7977649, 8543071, 9125461, 9224305 } > P := [p : p in [3001..5000] | IsPrime(p) and p ne 2 and p ne 67]; > for p in P do print "trying p = ", p; time o := order(p); Append(~ords,o); end for; trying p = 3001 Time: 0.000 trying p = 3011 Time: 0.070 trying p = 3019 Time: 0.070 trying p = 3023 Time: 0.050 trying p = 3037 Time: 0.200 trying p = 3041 Time: 0.060 trying p = 3049 Time: 0.040 trying p = 3061 Time: 0.040 trying p = 3067 Time: 0.060 trying p = 3079 Time: 0.030 trying p = 3083 Time: 0.020 trying p = 3089 Time: 0.030 trying p = 3109 Time: 0.060 trying p = 3119 Time: 0.050 trying p = 3121 Time: 0.040 trying p = 3137 Time: 0.050 trying p = 3163 Time: 0.030 trying p = 3167 Time: 0.040 trying p = 3169 Time: 0.060 trying p = 3181 Time: 0.060 trying p = 3187 Time: 0.060 trying p = 3191 Time: 0.060 trying p = 3203 Time: 0.050 trying p = 3209 Time: 0.050 trying p = 3217 Time: 0.730 trying p = 3221 Time: 0.040 trying p = 3229 Time: 0.040 trying p = 3251 Time: 0.030 trying p = 3253 Time: 0.060 trying p = 3257 Time: 0.040 trying p = 3259 Time: 0.230 trying p = 3271 Time: 0.080 trying p = 3299 Time: 0.030 trying p = 3301 Time: 0.050 trying p = 3307 Time: 0.040 trying p = 3313 Time: 0.050 trying p = 3319 Time: 0.040 trying p = 3323 Time: 0.080 trying p = 3329 Time: 0.050 trying p = 3331 Time: 0.050 trying p = 3343 Time: 0.060 trying p = 3347 Time: 0.050 trying p = 3359 Time: 0.070 trying p = 3361 Time: 0.050 trying p = 3371 Time: 0.040 trying p = 3373 Time: 0.050 trying p = 3389 Time: 0.040 trying p = 3391 Time: 0.070 trying p = 3407 Time: 0.040 trying p = 3413 Time: 0.050 trying p = 3433 Time: 0.070 trying p = 3449 Time: 0.050 trying p = 3457 Time: 0.050 trying p = 3461 Time: 0.050 trying p = 3463 Time: 0.070 trying p = 3467 Time: 0.040 trying p = 3469 Time: 0.040 trying p = 3491 Time: 0.070 trying p = 3499 Time: 0.050 trying p = 3511 Time: 0.060 trying p = 3517 Time: 0.260 trying p = 3527 Time: 0.070 trying p = 3529 Time: 0.050 trying p = 3533 Time: 0.060 trying p = 3539 Time: 0.040 trying p = 3541 Time: 0.080 trying p = 3547 Time: 0.050 trying p = 3557 Time: 0.050 trying p = 3559 Time: 0.030 trying p = 3571 Time: 0.060 trying p = 3581 Time: 0.050 trying p = 3583 Time: 0.040 trying p = 3593 Time: 0.040 trying p = 3607 Time: 0.050 trying p = 3613 Time: 0.040 trying p = 3617 Time: 0.880 trying p = 3623 Time: 0.070 trying p = 3631 Time: 0.050 trying p = 3637 Time: 0.070 trying p = 3643 Time: 0.050 trying p = 3659 Time: 0.070 trying p = 3671 Time: 0.080 trying p = 3673 Time: 0.060 trying p = 3677 Time: 0.050 trying p = 3691 Time: 0.050 trying p = 3697 Time: 0.070 trying p = 3701 Time: 0.050 trying p = 3709 Time: 0.060 trying p = 3719 Time: 0.050 trying p = 3727 Time: 0.040 trying p = 3733 Time: 0.060 trying p = 3739 Time: 0.040 trying p = 3761 Time: 0.060 trying p = 3767 Time: 0.080 trying p = 3769 Time: 0.070 trying p = 3779 Time: 0.040 trying p = 3793 Time: 0.060 trying p = 3797 Time: 0.040 trying p = 3803 Time: 0.040 trying p = 3821 Time: 0.070 trying p = 3823 Time: 0.060 trying p = 3833 Time: 0.080 trying p = 3847 Time: 0.080 trying p = 3851 Time: 0.050 trying p = 3853 Time: 0.070 trying p = 3863 Time: 0.070 trying p = 3877 Time: 0.050 trying p = 3881 Time: 0.060 trying p = 3889 Time: 0.100 trying p = 3907 Time: 0.050 trying p = 3911 Time: 0.050 trying p = 3917 Time: 0.060 trying p = 3919 Time: 0.300 trying p = 3923 Time: 0.040 trying p = 3929 Time: 0.060 trying p = 3931 Time: 0.060 trying p = 3943 Time: 0.040 trying p = 3947 Time: 0.050 trying p = 3967 Time: 0.070 trying p = 3989 Time: 0.080 trying p = 4001 Time: 0.010 trying p = 4003 Time: 0.080 trying p = 4007 Time: 0.040 trying p = 4013 Time: 0.050 trying p = 4019 Time: 0.590 trying p = 4021 Time: 0.060 trying p = 4027 Time: 0.080 trying p = 4049 Time: 0.070 trying p = 4051 Time: 0.040 trying p = 4057 Time: 0.290 trying p = 4073 Time: 0.050 trying p = 4079 Time: 0.030 trying p = 4091 Time: 0.060 trying p = 4093 Time: 0.060 trying p = 4099 Time: 0.050 trying p = 4111 Time: 0.080 trying p = 4127 Time: 0.060 trying p = 4129 Time: 0.050 trying p = 4133 Time: 0.060 trying p = 4139 Time: 0.040 trying p = 4153 Time: 0.300 trying p = 4157 Time: 0.850 trying p = 4159 Time: 0.080 trying p = 4177 Time: 1.180 trying p = 4201 Time: 0.290 trying p = 4211 Time: 0.110 trying p = 4217 Time: 0.040 trying p = 4219 Time: 0.070 trying p = 4229 Time: 0.070 trying p = 4231 Time: 0.050 trying p = 4241 Time: 0.050 trying p = 4243 Time: 0.050 trying p = 4253 Time: 0.040 trying p = 4259 Time: 0.080 trying p = 4261 Time: 0.040 trying p = 4271 Time: 0.070 trying p = 4273 Time: 0.050 trying p = 4283 Time: 0.060 trying p = 4289 Time: 0.050 trying p = 4297 Time: 0.050 trying p = 4327 Time: 0.060 trying p = 4337 Time: 0.070 trying p = 4339 Time: 0.060 trying p = 4349 Time: 0.060 trying p = 4357 Time: 0.050 trying p = 4363 Time: 0.080 trying p = 4373 Time: 0.050 trying p = 4391 Time: 0.060 trying p = 4397 Time: 0.070 trying p = 4409 Time: 0.070 trying p = 4421 Time: 0.080 trying p = 4423 Time: 0.050 trying p = 4441 Time: 0.040 trying p = 4447 Time: 0.090 trying p = 4451 Time: 0.090 trying p = 4457 Time: 0.050 trying p = 4463 Time: 0.070 trying p = 4481 Time: 0.060 trying p = 4483 Time: 0.070 trying p = 4493 Time: 0.050 trying p = 4507 Time: 0.050 trying p = 4513 Time: 0.340 trying p = 4517 Time: 0.100 trying p = 4519 Time: 0.080 trying p = 4523 Time: 0.070 trying p = 4547 Time: 0.350 trying p = 4549 Time: 0.060 trying p = 4561 Time: 0.050 trying p = 4567 Time: 0.100 trying p = 4583 Time: 0.070 trying p = 4591 Time: 0.060 trying p = 4597 Time: 0.070 trying p = 4603 Time: 0.060 trying p = 4621 Time: 0.080 trying p = 4637 Time: 0.060 trying p = 4639 Time: 0.330 trying p = 4643 Time: 0.040 trying p = 4649 Time: 0.050 trying p = 4651 Time: 0.060 trying p = 4657 Time: 0.070 trying p = 4663 Time: 0.060 trying p = 4673 Time: 0.060 trying p = 4679 Time: 0.060 trying p = 4691 Time: 0.080 trying p = 4703 Time: 0.080 trying p = 4721 Time: 0.070 trying p = 4723 Time: 0.060 trying p = 4729 Time: 0.070 trying p = 4733 Time: 0.090 trying p = 4751 Time: 0.070 trying p = 4759 Time: 0.050 trying p = 4783 Time: 0.070 trying p = 4787 Time: 0.040 trying p = 4789 Time: 0.050 trying p = 4793 Time: 0.030 trying p = 4799 Time: 0.070 trying p = 4801 Time: 0.240 trying p = 4813 Time: 0.060 trying p = 4817 Time: 0.080 trying p = 4831 Time: 0.070 trying p = 4861 Time: 0.060 trying p = 4871 Time: 0.040 trying p = 4877 Time: 0.040 trying p = 4889 Time: 0.080 trying p = 4903 Time: 0.070 trying p = 4909 Time: 0.060 trying p = 4919 Time: 0.080 trying p = 4931 Time: 0.070 trying p = 4933 Time: 0.070 trying p = 4937 Time: 0.060 trying p = 4943 Time: 0.050 trying p = 4951 Time: 0.060 trying p = 4957 Time: 1.280 trying p = 4967 Time: 2.400 trying p = 4969 Time: 0.050 trying p = 4973 Time: 0.030 trying p = 4987 Time: 0.050 trying p = 4993 Time: 0.060 trying p = 4999 Time: 0.050 > Set(Sort(ords)); { 9, 27, 29, 33, 39, 61, 63, 109, 123, 135, 139, 143, 153, 165, 171, 178, 188, 189, 295, 350, 365, 387, 421, 525, 591, 606, 839, 909, 999, 1069, 1195, 1471, 1795, 1845, 1866, 1891, 2013, 2030, 2231, 2233, 2263, 2309, 2373, 2409, 2539, 2937, 3057, 3077, 3079, 3153, 3253, 3414, 3603, 3747, 3925, 4069, 4189, 4287, 4351, 4467, 4579, 4609, 5673, 5861, 6481, 6765, 6871, 6897, 7381, 7821, 8095, 8311, 8569, 8795, 8929, 9505, 11311, 12333, 12421, 12938, 12991, 14457, 14761, 15989, 16245, 17067, 19509, 20795, 20959, 22173, 23059, 25113, 25749, 26787, 27714, 27739, 28045, 30543, 32569, 33571, 33759, 34309, 37411, 38005, 38551, 42361, 42829, 43185, 44102, 44283, 44547, 48169, 48609, 49166, 52665, 53462, 53555, 53995, 54440, 60259, 64231, 66315, 66597, 66747, 67323, 68599, 70205, 70339, 70479, 70969, 73473, 74099, 75349, 75783, 76684, 78649, 79035, 79211, 80034, 82021, 84491, 84676, 85669, 86629, 89689, 94485, 96657, 97339, 104371, 105289, 108161, 108289, 109219, 109983, 113201, 113905, 116839, 120979, 123895, 125296, 126015, 135465, 135691, 139287, 140424, 141119, 156633, 159717, 161045, 161599, 162165, 162661, 165241, 166199, 171151, 171809, 176380, 178505, 179251, 185261, 187861, 190045, 196473, 197533, 199677, 201103, 201905, 202039, 207811, 210615, 210661, 216589, 221043, 221761, 224905, 227524, 229263, 231181, 234177, 235065, 235697, 235962, 237423, 239041, 241953, 242727, 250503, 252165, 256505, 257487, 265485, 265729, 270355, 270870, 282979, 284405, 288905, 289707, 291475, 296419, 302495, 305223, 306237, 308705, 312747, 313009, 314149, 315799, 315867, 317787, 323779, 325527, 332427, 347509, 352831, 357841, 358017, 365163, 374241, 374410, 378385, 380973, 395690, 399019, 404681, 410971, 412863, 419613, 423437, 427475, 428269, 432057, 437581, 437637, 449045, 451445, 453601, 455605, 459559, 461709, 474837, 482343, 497629, 501828, 507155, 507445, 514311, 529579, 532069, 537109, 539209, 546829, 552931, 560985, 569154, 572755, 579671, 588047, 601339, 603229, 608757, 622441, 624993, 628111, 632690, 644005, 644313, 662191, 672545, 677405, 683845, 693045, 717229, 718527, 727615, 730159, 742961, 746491, 757515, 771242, 771481, 788869, 798391, 798753, 820831, 823495, 838129, 841017, 846355, 848161, 858615, 863129, 869545, 886173, 905251, 905547, 914569, 923318, 929291, 934077, 945843, 977071, 979855, 986865, 987719, 995005, 1006891, 1017901, 1019495, 1023294, 1026901, 1028191, 1054707, 1076839, 1097179, 1097535, 1129981, 1130291, 1143679, 1148035, 1155057, 1157941, 1158483, 1168381, 1194423, 1206687, 1209781, 1224949, 1253179, 1268341, 1275177, 1282205, 1289371, 1292689, 1321249, 1335585, 1380445, 1394479, 1396118, 1407149, 1442551, 1442793, 1462623, 1472581, 1473751, 1486473, 1493007, 1516561, 1539813, 1540113, 1544385, 1550719, 1557379, 1575919, 1580975, 1592133, 1624645, 1636669, 1659911, 1662529, 1678171, 1695159, 1742155, 1783199, 1836735, 1839027, 1845867, 1850959, 1856371, 1867323, 1879141, 1895409, 1911205, 1937659, 1944745, 1948178, 1974631, 1990137, 2036149, 2090791, 2103799, 2109655, 2112001, 2149669, 2212339, 2214139, 2219695, 2225659, 2228869, 2240501, 2269355, 2273659, 2281459, 2295915, 2302113, 2313361, 2376165, 2428861, 2434879, 2491955, 2499481, 2529539, 2560953, 2582369, 2590429, 2599795, 2619481, 2648305, 2669059, 2678149, 2681907, 2707459, 2709601, 2729309, 2752201, 2763805, 2808410, 2813973, 2860261, 2925285, 2989639, 3023318, 3043815, 3077359, 3080981, 3088931, 3102439, 3119161, 3153571, 3288781, 3314611, 3321505, 3323265, 3361711, 3442429, 3442729, 3474091, 3482385, 3489393, 3502137, 3550459, 3585331, 3599705, 3602913, 3632431, 3706999, 3719525, 3730591, 3754531, 3884821, 3937459, 4007695, 4019845, 4046101, 4069255, 4216711, 4226981, 4228531, 4247881, 4299301, 4305477, 4337835, 4348473, 4382461, 4420495, 4421373, 4422289, 4490403, 4497897, 4502839, 4583701, 4586793, 4616337, 4679251, 4736283, 4771939, 4809169, 4884055, 4888501, 4979491, 5017195, 5067859, 5103061, 5117005, 5135883, 5146741, 5252659, 5269039, 5276605, 5300929, 5301355, 5329111, 5362647, 5367769, 5377441, 5398501, 5405305, 5421001, 5503711, 5531899, 5560953, 5609731, 5660659, 5688327, 5778091, 5805859, 5877649, 5908083, 5919409, 5933971, 6242539, 6246589, 6289819, 6459211, 6464095, 6525019, 6682909, 6698971, 6738301, 6755869, 6999871, 7020165, 7091715, 7100643, 7120861, 7128295, 7147321, 7183815, 7231587, 7258737, 7294681, 7297651, 7339489, 7341895, 7359649, 7368499, 7424553, 7462069, 7506957, 7581481, 7705051, 7760733, 7869781, 7977649, 7979523, 8019987, 8276703, 8364885, 8543071, 9125461, 9191899, 9204751, 9224305, 9277381, 9338011, 9488569, 9501445, 9857395, 9863461, 9903505, 10093009, 10187419, 10284769, 10613959, 10625395, 10730371, 11138545, 11309269, 11494939, 11502271, 11630959, 11634841, 11935405, 11936419, 12026419, 12071599, 12286219, 12316309, 12379831, 12489151, 12606049, 12647911, 12668329, 12845011, 12981529, 13140445, 13296109, 13384471, 13579399, 13905421, 13946479, 14158321, 14370061, 14379259, 14533795, 14733031, 14837695, 15265045, 15313951, 15346705, 15417301, 15455161, 15515641, 15634009, 15702949, 16023289, 16172431, 16230841, 16317499, 16363069, 17361889, 17627251, 17694091, 18004531, 18165655, 18206569, 18264871, 18378289, 18599089, 18675301, 18746929, 18821221, 19010179, 19425841, 19686649, 19771645, 19993861, 20335309, 20575291, 20788759, 21177799, 21284101, 21594589, 22053601, 22636759, 22696405, 22794649, 22855519, 23269171, 23410531, 23439211, 23488411, 23895121, 24244651, 24576655, 25038211 } > #Set([o : o in ords | o le 200]); 18 > P := [p : p in [5001..6000] | IsPrime(p) and p ne 2 and p ne 67]; > for p in P do print "trying p = ", p; time o := order(p); Append(~ords,o); end for; trying p = 5003 Time: 0.000 trying p = 5009 Time: 0.060 trying p = 5011 Time: 0.090 trying p = 5021 Time: 0.060 trying p = 5023 Time: 0.330 trying p = 5039 Time: 0.050 trying p = 5051 Time: 0.050 trying p = 5059 Time: 0.320 trying p = 5077 Time: 0.060 trying p = 5081 Time: 0.070 trying p = 5087 Time: 0.060 trying p = 5099 Time: 0.060 trying p = 5101 Time: 0.060 trying p = 5107 Time: 0.050 trying p = 5113 Time: 0.080 trying p = 5119 Time: 0.050 trying p = 5147 Time: 0.040 trying p = 5153 Time: 0.060 trying p = 5167 Time: 0.070 trying p = 5171 Time: 0.040 trying p = 5179 Time: 0.050 trying p = 5189 Time: 0.090 trying p = 5197 Time: 0.070 trying p = 5209 Time: 0.060 trying p = 5227 Time: 0.080 trying p = 5231 Time: 0.080 trying p = 5233 Time: 0.110 trying p = 5237 Time: 0.060 trying p = 5261 Time: 0.040 trying p = 5273 Time: 0.060 trying p = 5279 Time: 0.050 trying p = 5281 Time: 0.080 trying p = 5297 Time: 0.050 trying p = 5303 Time: 0.040 trying p = 5309 Time: 0.060 trying p = 5323 Time: 0.060 trying p = 5333 Time: 0.050 trying p = 5347 Time: 0.050 trying p = 5351 Time: 0.050 trying p = 5381 Time: 0.050 trying p = 5387 Time: 0.040 trying p = 5393 Time: 0.050 trying p = 5399 Time: 0.070 trying p = 5407 Time: 0.070 trying p = 5413 Time: 0.070 trying p = 5417 Time: 0.050 trying p = 5419 Time: 0.080 trying p = 5431 Time: 0.080 trying p = 5437 Time: 0.050 trying p = 5441 Time: 0.080 trying p = 5443 Time: 0.070 trying p = 5449 Time: 0.070 trying p = 5471 Time: 0.080 trying p = 5477 Time: 0.080 trying p = 5479 Time: 0.050 trying p = 5483 Time: 0.090 trying p = 5501 Time: 0.080 trying p = 5503 Time: 1.100 trying p = 5507 Time: 0.060 trying p = 5519 Time: 0.080 trying p = 5521 Time: 0.080 trying p = 5527 Time: 0.050 trying p = 5531 Time: 0.070 trying p = 5557 Time: 0.060 trying p = 5563 Time: 0.060 trying p = 5569 Time: 0.080 trying p = 5573 Time: 0.060 trying p = 5581 Time: 0.050 trying p = 5591 Time: 0.060 trying p = 5623 Time: 0.070 trying p = 5639 Time: 0.040 trying p = 5641 Time: 0.060 trying p = 5647 Time: 0.060 trying p = 5651 Time: 0.050 trying p = 5653 Time: 0.100 trying p = 5657 Time: 0.050 trying p = 5659 Time: 0.070 trying p = 5669 Time: 0.070 trying p = 5683 Time: 0.060 trying p = 5689 Time: 0.080 trying p = 5693 Time: 0.050 trying p = 5701 Time: 0.030 trying p = 5711 Time: 0.060 trying p = 5717 Time: 0.060 trying p = 5737 Time: 0.070 trying p = 5741 Time: 0.040 trying p = 5743 Time: 0.080 trying p = 5749 Time: 0.050 trying p = 5779 Time: 0.080 trying p = 5783 Time: 0.050 trying p = 5791 Time: 0.850 trying p = 5801 Time: 0.050 trying p = 5807 Time: 0.060 trying p = 5813 Time: 0.090 trying p = 5821 Time: 0.050 trying p = 5827 Time: 0.060 trying p = 5839 Time: 0.050 trying p = 5843 Time: 0.080 trying p = 5849 Time: 0.060 trying p = 5851 Time: 0.060 trying p = 5857 Time: 0.080 trying p = 5861 Time: 0.080 trying p = 5867 Time: 0.070 trying p = 5869 Time: 0.060 trying p = 5879 Time: 0.060 trying p = 5881 Time: 0.060 trying p = 5897 Time: 0.060 trying p = 5903 Time: 0.060 trying p = 5923 Time: 0.060 trying p = 5927 Time: 0.070 trying p = 5939 Time: 0.070 trying p = 5953 Time: 0.090 trying p = 5981 Time: 0.080 trying p = 5987 Time: 0.070 > #Set([o : o in ords | o le 200]); 18 > Set(Sort(ords)); { 9, 27, 29, 33, 39, 61, 63, 109, 123, 135, 139, 143, 153, 165, 171, 178, 188, 189, 295, 350, 365, 387, 421, 525, 591, 606, 839, 909, 999, 1069, 1195, 1471, 1795, 1845, 1866, 1891, 2013, 2030, 2231, 2233, 2263, 2309, 2373, 2409, 2501, 2539, 2937, 3057, 3077, 3079, 3153, 3253, 3414, 3603, 3747, 3925, 4069, 4189, 4287, 4351, 4467, 4579, 4609, 4971, 5673, 5861, 6481, 6765, 6871, 6897, 7381, 7821, 8095, 8311, 8569, 8795, 8929, 9505, 11311, 12333, 12421, 12938, 12991, 14457, 14761, 15989, 16245, 17067, 19509, 20795, 20959, 22173, 23059, 25113, 25749, 26787, 27714, 27739, 28045, 30543, 32569, 33571, 33759, 34309, 37411, 38005, 38551, 42361, 42829, 43185, 44102, 44283, 44547, 48169, 48609, 49166, 52665, 53462, 53555, 53995, 54440, 60259, 64231, 66315, 66597, 66747, 67323, 68599, 70205, 70339, 70479, 70969, 73473, 74099, 75349, 75783, 76684, 77499, 78649, 79035, 79211, 80034, 82021, 84491, 84676, 85035, 85669, 86629, 89689, 94485, 96657, 97339, 104371, 105289, 108161, 108289, 109219, 109983, 113201, 113905, 116839, 120979, 123895, 125296, 126015, 135465, 135691, 139287, 140424, 141119, 153961, 156633, 159717, 161045, 161599, 162165, 162661, 165241, 166199, 171151, 171809, 176380, 178505, 179251, 185261, 187861, 190045, 196473, 197533, 199677, 201103, 201905, 202039, 207811, 210615, 210661, 216589, 221043, 221761, 224905, 227524, 229263, 231181, 234177, 235065, 235697, 235962, 237423, 239041, 241953, 242727, 250503, 252165, 256505, 257487, 265485, 265729, 270355, 270870, 282979, 284405, 285150, 288905, 289707, 291475, 296419, 302495, 305223, 306237, 308705, 312747, 313009, 314149, 315799, 315867, 317787, 323779, 325527, 332427, 332804, 347509, 352831, 357841, 358017, 365163, 374241, 374410, 378385, 380973, 395690, 399019, 404681, 410971, 412863, 419613, 423437, 427475, 428269, 432057, 435182, 437581, 437637, 449045, 451445, 453601, 455605, 459559, 461709, 474837, 482343, 497629, 501828, 507155, 507445, 514311, 529579, 532069, 537109, 539209, 546829, 552931, 560985, 569154, 572755, 579671, 588047, 601339, 603229, 608757, 622441, 624993, 628111, 632690, 644005, 644313, 662191, 672545, 677405, 683845, 693045, 717229, 718527, 727615, 730159, 742961, 746491, 757515, 771242, 771481, 788869, 798391, 798753, 820831, 823495, 838129, 841017, 846355, 848161, 858615, 863129, 869545, 886173, 905251, 905547, 914569, 922243, 923318, 929291, 934077, 945843, 977071, 979855, 986865, 987719, 995005, 1006891, 1017901, 1019495, 1023294, 1026901, 1028191, 1054707, 1058907, 1076839, 1097179, 1097535, 1101666, 1129981, 1130291, 1143679, 1148035, 1155057, 1157941, 1158483, 1168381, 1194423, 1206687, 1209781, 1224949, 1251813, 1253179, 1266474, 1268341, 1275177, 1282205, 1289371, 1292689, 1294707, 1321249, 1335585, 1362251, 1380445, 1394479, 1396118, 1396830, 1402611, 1407149, 1442551, 1442793, 1462623, 1472581, 1473751, 1486473, 1493007, 1516561, 1531805, 1539813, 1540113, 1544385, 1550719, 1557379, 1575919, 1580975, 1592133, 1624645, 1636669, 1659911, 1662529, 1678171, 1695159, 1742155, 1783199, 1832235, 1836735, 1839027, 1845867, 1850959, 1856371, 1863825, 1867323, 1868147, 1879141, 1879665, 1895409, 1911205, 1937659, 1944745, 1948178, 1974631, 1990137, 2036149, 2042223, 2090791, 2103799, 2109655, 2112001, 2128785, 2149669, 2168245, 2212339, 2214139, 2219695, 2225659, 2228869, 2240501, 2269355, 2273307, 2273659, 2281459, 2295915, 2302113, 2313361, 2320557, 2376165, 2428861, 2434879, 2491955, 2499481, 2527993, 2529539, 2560953, 2582369, 2590429, 2599795, 2619481, 2648305, 2669059, 2678149, 2679539, 2681907, 2707459, 2709601, 2729309, 2752201, 2763805, 2776317, 2808410, 2813973, 2860261, 2889933, 2925285, 2989639, 3023318, 3043815, 3077359, 3080981, 3088931, 3102439, 3119161, 3153571, 3197498, 3288781, 3314611, 3321505, 3323265, 3361711, 3420289, 3442429, 3442729, 3474091, 3482385, 3489393, 3492981, 3502137, 3550459, 3585331, 3599705, 3602913, 3632431, 3706999, 3719525, 3730591, 3754531, 3870845, 3884821, 3937459, 4007695, 4019845, 4046101, 4069255, 4216711, 4226981, 4228531, 4247881, 4299301, 4305477, 4320110, 4337835, 4348473, 4382461, 4420495, 4421373, 4422289, 4490403, 4497897, 4502839, 4583701, 4586793, 4616337, 4679251, 4735465, 4736283, 4771939, 4809169, 4884055, 4888501, 4979491, 5017195, 5067859, 5103061, 5117005, 5135883, 5146741, 5156195, 5252659, 5269039, 5276605, 5300929, 5301355, 5304275, 5329111, 5329775, 5362647, 5367769, 5377441, 5398501, 5405305, 5421001, 5434025, 5503711, 5531899, 5560953, 5609731, 5660659, 5688327, 5778091, 5805859, 5877649, 5908083, 5919409, 5933971, 6142931, 6242539, 6246589, 6289819, 6383101, 6400649, 6459211, 6464095, 6514955, 6525019, 6571381, 6580429, 6682909, 6698971, 6738301, 6755869, 6874879, 6913919, 6999871, 7020165, 7056991, 7091715, 7100643, 7120861, 7128295, 7147321, 7183815, 7211105, 7231587, 7241461, 7258737, 7294681, 7297651, 7339489, 7341895, 7359649, 7368499, 7424553, 7462069, 7506957, 7581481, 7705051, 7760733, 7869781, 7977649, 7979523, 7986031, 7988191, 8019987, 8144911, 8246757, 8276703, 8364885, 8543071, 8793529, 8981689, 9068523, 9125461, 9191899, 9204751, 9224305, 9277381, 9338011, 9488569, 9501445, 9756183, 9857395, 9863461, 9895413, 9902967, 9903505, 10093009, 10123467, 10187419, 10284769, 10613959, 10625395, 10730371, 11138545, 11309269, 11366583, 11494939, 11502271, 11630959, 11634841, 11689653, 11935405, 11936419, 12026419, 12071599, 12072093, 12286219, 12316309, 12379831, 12489151, 12606049, 12647911, 12668329, 12845011, 12981529, 13140445, 13296109, 13384471, 13579399, 13905421, 13946479, 14158321, 14370061, 14379259, 14533795, 14733031, 14837695, 15265045, 15313951, 15346705, 15417301, 15455161, 15515641, 15634009, 15702949, 16023289, 16172431, 16230841, 16317499, 16363069, 17361889, 17627251, 17694091, 18004531, 18165655, 18206569, 18264871, 18378289, 18599089, 18675301, 18746929, 18821221, 19010179, 19425841, 19686649, 19771645, 19993861, 20335309, 20575291, 20788759, 21177799, 21284101, 21594589, 22053601, 22636759, 22696405, 22794649, 22855519, 23269171, 23410531, 23439211, 23488411, 23895121, 24244651, 24576655, 24841729, 25038211, 25647799, 25649149, 25795921, 25859779, 25940431, 26099461, 26465359, 26981779, 26990689, 27309631, 27695821, 27719905, 27744655, 28108999, 28545229, 28755745, 28809955, 29023795, 29190409, 29456395, 29994649, 30057145, 30514489, 30651121, 30716545, 30872791, 30945349, 31002379, 31082689, 31639645, 31797601, 31872511, 31874671, 32280319, 32330551, 32521711, 32876551, 32890009, 32928901, 33286219, 33761941, 33777139, 34158589, 34523449, 34584631, 34768129, 36046609 } > ords; [ 29, 9, 61, 139, 295, 109, 123, 421, 1069, 33, 1471, 1891, 1795, 3079, 63, 27, 4189, 4351, 39, 6871, 8311, 8095, 839, 11311, 3747, 3057, 12421, 9505, 5673, 135, 6897, 143, 20959, 153, 2539, 28045, 6481, 37411, 8929, 34309, 38005, 32569, 42829, 42361, 3153, 2309, 3077, 60259, 12991, 64231, 48169, 14761, 70969, 7821, 70339, 5861, 4579, 75349, 85669, 30543, 23059, 2013, 105289, 104371, 12938, 108289, 120979, 178, 123895, 189, 33571, 16245, 188, 162661, 38551, 179251, 52665, 14457, 8795, 202039, 161599, 190045, 66747, 210661, 187861, 231181, 6765, 25749, 207811, 53995, 224905, 75783, 525, 221761, 22173, 135, 8569, 68599, 94485, 347509, 26787, 78649, 323779, 315799, 313009, 97339, 44102, 86629, 109983, 126015, 19509, 109219, 139287, 79211, 428269, 113905, 53462, 15989, 399019, 17067, 459559, 453601, 171, 116839, 1866, 455605, 350, 365, 539209, 552931, 529579, 537109, 387, 199677, 603229, 210615, 628111, 44547, 235065, 141119, 683845, 165241, 662191, 171151, 237423, 250503, 234177, 12333, 252165, 820831, 165, 798391, 869545, 306237, 305223, 848161, 846355, 312747, 20795, 178505, 332427, 914569, 979855, 108161, 905251, 1006891, 1017901, 325527, 365163, 66315, 201905, 1097179, 1168381, 1076839, 1157941, 1143679, 282979, 270355, 1253179, 1209781, 76684, 1224949, 1268341, 256505, 113201, 96657, 437637, 197533, 1289371, 82021, 591, 606, 1442551, 1394479, 1473751, 482343, 357841, 1516561, 1472581, 308705, 89689, 2937, 171809, 1742155, 1662529, 1575919, 1624645, 84491, 410971, 1636669, 560985, 1678171, 54440, 624993, 156633, 437581, 1856371, 166199, 608757, 1974631, 1944745, 1911205, 2214139, 497629, 1937659, 427475, 73473, 546829, 135691, 2228869, 532069, 2149669, 2225659, 2212339, 2219695, 2281459, 44283, 572755, 2313361, 757515, 196473, 2434879, 622441, 2590429, 798753, 2599795, 507155, 70479, 162165, 2499481, 288905, 2678149, 27714, 644005, 2669059, 858615, 2707459, 886173, 2709601, 945843, 314149, 302495, 242727, 25113, 2989639, 176380, 2860261, 265485, 771481, 717229, 3119161, 395690, 70205, 161045, 1054707, 352831, 3314611, 3288781, 74099, 3474091, 3321505, 216589, 185261, 3550459, 3585331, 1194423, 135465, 742961, 1206687, 3442429, 3884821, 977071, 3706999, 227524, 3754531, 4046101, 4069255, 1845, 4019845, 4007695, 3730591, 3937459, 1026901, 27739, 4228531, 1335585, 995005, 4247881, 863129, 1442793, 53555, 265729, 7381, 289707, 1462623, 1129981, 358017, 380973, 1486473, 79035, 1539813, 4583701, 1493007, 4679251, 419613, 2231, 4888501, 632690, 2233, 1292689, 449045, 49166, 5067859, 5329111, 987719, 5252659, 5146741, 5117005, 5300929, 727615, 5377441, 432057, 5405305, 284405, 1321249, 1845867, 5919409, 5503711, 1380445, 5367769, 5531899, 5778091, 2373, 5805859, 84676, 1839027, 33759, 239041, 221043, 5933971, 771242, 1557379, 2409, 1550719, 6464095, 6242539, 241953, 693045, 6682909, 6289819, 6755869, 1282205, 6698971, 6525019, 270870, 2295915, 6738301, 2376165, 2302113, 7297651, 7294681, 6999871, 7368499, 7128295, 257487, 672545, 1407149, 7120861, 7339489, 677405, 291475, 7147321, 1879141, 7341895, 7359649, 1850959, 909, 7462069, 644313, 923318, 7581481, 7977649, 1580975, 2560953, 7705051, 7869781, 374241, 838129, 2036149, 507445, 2090791, 2681907, 404681, 125296, 1148035, 929291, 2103799, 718527, 2112001, 2109655, 8543071, 315867, 67323, 2925285, 2813973, 9125461, 2273659, 9224305, 9191899, 9501445, 3043815, 1019495, 999, 9277381, 9204751, 1028191, 9488569, 9338011, 3414, 601339, 9903505, 9863461, 2428861, 10284769, 9857395, 588047, 3482385, 3323265, 3489393, 378385, 2648305, 2619481, 43185, 10093009, 841017, 10187419, 3502137, 10730371, 3253, 317787, 10613959, 296419, 10625395, 2763805, 66597, 514311, 1396118, 3602913, 2240501, 934077, 11502271, 2269355, 11309269, 730159, 2752201, 11630959, 11634841, 11138545, 12316309, 579671, 11494939, 746491, 11936419, 12026419, 11935405, 12668329, 3102439, 12071599, 3603, 12286219, 3077359, 12606049, 12489151, 201103, 13140445, 3153571, 2491955, 12379831, 12647911, 474837, 12981529, 4305477, 12845011, 140424, 4337835, 4348473, 13946479, 13296109, 13579399, 4736283, 1155057, 569154, 3361711, 4497897, 3442729, 14370061, 13905421, 2729309, 4490403, 4421373, 13384471, 14158321, 4616337, 1158483, 4586793, 374410, 14379259, 14733031, 14533795, 235697, 986865, 3088931, 423437, 788869, 3632431, 1275177, 14837695, 3080981, 1948178, 15313951, 3925, 15702949, 5135883, 15634009, 1695159, 15265045, 15346705, 16172431, 15455161, 1783199, 15515641, 16230841, 48609, 15417301, 5560953, 16363069, 16023289, 2030, 461709, 5362647, 16317499, 4299301, 5688327, 17694091, 1097535, 4382461, 4216711, 1895409, 4069, 80034, 4502839, 235962, 4287, 18004531, 17361889, 18165655, 5908083, 18206569, 18378289, 18599089, 4422289, 1659911, 18264871, 18675301, 4420495, 17627251, 1540113, 3599705, 1592133, 18746929, 1544385, 4809169, 4884055, 18821221, 19686649, 19010179, 3719525, 19425841, 19993861, 4979491, 4771939, 20335309, 19771645, 20575291, 823495, 451445, 412863, 5103061, 5017195, 2263, 4226981, 20788759, 21177799, 4467, 7020165, 5276605, 7183815, 7091715, 5269039, 7100643, 159717, 7258737, 1836735, 4609, 21594589, 5301355, 7231587, 21284101, 5421001, 5398501, 5609731, 22053601, 2808410, 1130291, 5660659, 1867323, 7424553, 22794649, 22696405, 7760733, 22855519, 7506957, 22636759, 2529539, 1195, 5877649, 23488411, 23410531, 23439211, 23269171, 2582369, 24576655, 8019987, 3023318, 23895121, 1023294, 905547, 25038211, 8276703, 24244651, 229263, 501828, 1990137, 7979523, 8364885, 6459211, 6246589, 8246757, 25795921, 25859779, 24841729, 2501, 3197498, 25940431, 4971, 6383101, 5156195, 2128785, 6571381, 25649149, 5304275, 6580429, 25647799, 922243, 26981779, 26465359, 26099461, 1101666, 332804, 1832235, 9068523, 26990689, 1863825, 5329775, 5434025, 27309631, 27695821, 2273307, 29023795, 1362251, 27719905, 7241461, 27744655, 6874879, 28108999, 2320557, 28545229, 1879665, 7056991, 28755745, 1402611, 28809955, 29190409, 2679539, 9756183, 9902967, 30057145, 9895413, 29456395, 30651121, 30716545, 29994649, 6142931, 31082689, 77499, 1531805, 3420289, 31797601, 2042223, 30514489, 1266474, 435182, 30872791, 31872511, 10123467, 7986031, 8144911, 31002379, 85035, 7988191, 31874671, 4735465, 31639645, 30945349, 1868147, 32876551, 32890009, 32928901, 3492981, 6514955, 2776317, 32521711, 32280319, 6400649, 32330551, 2168245, 2527993, 285150, 33761941, 1396830, 34158589, 1251813, 2889933, 33777139, 11366583, 8793529, 1294707, 1058907, 153961, 34584631, 34768129, 34523449, 33286219, 6913919, 4320110, 7211105, 8981689, 3870845, 11689653, 36046609, 12072093 ] > P := [p : p in [2..2000] | IsPrime(p) and p ne 2 and p ne 67]; > function order(p) CC := ChangeRing(C,GF(p)); J := Jacobian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; > ordord := []; for p in P do print "trying p = ", p; time o := order(p); Append(~ordord,o); end for; trying p = 3 order( p: 3 ) >> ian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; ^ Runtime error in '!': Illegal coercion LHS: CrvHyp RHS: PtEll > order(7); order( p: 7 ) >> ian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; ^ Runtime error in '!': Illegal coercion LHS: CrvHyp RHS: PtEll > J; >> J; ^ User error: Identifier 'J' has not been declared or assigned > Q; (0 : 0 : 1) > C; Hyperelliptic Curve defined by y^2 = x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 - 2*x + 1 over Rational Field > function order(p) CC := ChangeRing(C,GF(p)); J := Jacobian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; > order(19); order( p: 19 ) >> ian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; ^ Runtime error in '!': Illegal coercion LHS: CrvHyp RHS: PtEll > CC := ChangeRing(C,GF(19)); > CC; Hyperelliptic Curve defined by y^2 = x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 + 17*x + 1 over GF(19) > CC!Q; >> CC!Q; ^ Runtime error in '!': Illegal coercion LHS: CrvHyp RHS: PtEll > Q; (0 : 0 : 1) > C; Hyperelliptic Curve defined by y^2 = x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 - 2*x + 1 over Rational Field > Q := C![0,0]; >> Q := C![0,0]; ^ Runtime error in '!': Point is not on curve > Q := C![0,-1]; > CC!Q; (0 : 18 : 1) > function order(p) CC := ChangeRing(C,GF(p)); J := Jacobian(CC); return [Order(J![CC!Q,CC!origin]), #J]; end function; > ordord := []; for p in P do print "trying p = ", p; time o := order(p); Append(~ordord,o); end for; trying p = 3 Time: 0.010 trying p = 5 Time: 0.000 trying p = 7 Time: 0.010 trying p = 11 Time: 0.000 trying p = 13 Time: 0.010 trying p = 17 Time: 0.010 trying p = 19 Time: 0.000 trying p = 23 Time: 0.010 trying p = 29 Time: 0.000 trying p = 31 Time: 0.010 trying p = 37 Time: 0.000 trying p = 41 Time: 0.010 trying p = 43 Time: 0.010 trying p = 47 Time: 0.000 trying p = 53 Time: 0.010 trying p = 59 Time: 0.000 trying p = 61 Time: 0.010 trying p = 71 Time: 0.010 trying p = 73 Time: 0.000 trying p = 79 Time: 0.010 trying p = 83 Time: 0.010 trying p = 89 Time: 0.000 trying p = 97 Time: 0.010 trying p = 101 Time: 0.010 trying p = 103 Time: 0.000 trying p = 107 Time: 0.010 trying p = 109 Time: 0.010 trying p = 113 Time: 0.000 trying p = 127 Time: 0.010 trying p = 131 Time: 0.010 trying p = 137 Time: 0.010 trying p = 139 Time: 0.010 trying p = 149 Time: 0.010 trying p = 151 Time: 0.000 trying p = 157 Time: 0.020 trying p = 163 Time: 0.020 trying p = 167 Time: 0.010 trying p = 173 Time: 0.010 trying p = 179 Time: 0.020 trying p = 181 Time: 0.010 trying p = 191 Time: 0.010 trying p = 193 Time: 0.000 trying p = 197 Time: 0.010 trying p = 199 Time: 0.020 trying p = 211 Time: 0.010 trying p = 223 Time: 0.010 trying p = 227 Time: 0.010 trying p = 229 Time: 0.010 trying p = 233 Time: 0.020 trying p = 239 Time: 0.010 trying p = 241 Time: 0.010 trying p = 251 Time: 0.010 trying p = 257 Time: 0.010 trying p = 263 Time: 0.010 trying p = 269 Time: 0.000 trying p = 271 Time: 0.010 trying p = 277 Time: 0.010 trying p = 281 Time: 0.010 trying p = 283 Time: 0.000 trying p = 293 Time: 0.000 trying p = 307 Time: 0.010 trying p = 311 Time: 0.000 trying p = 313 Time: 0.010 trying p = 317 Time: 0.000 trying p = 331 Time: 0.010 trying p = 337 Time: 0.010 trying p = 347 Time: 0.000 trying p = 349 Time: 0.010 trying p = 353 Time: 0.010 trying p = 359 Time: 0.010 trying p = 367 Time: 0.010 trying p = 373 Time: 0.000 trying p = 379 Time: 0.010 trying p = 383 Time: 0.010 trying p = 389 Time: 0.010 trying p = 397 Time: 0.000 trying p = 401 Time: 0.010 trying p = 409 Time: 0.010 trying p = 419 Time: 0.010 trying p = 421 Time: 0.010 trying p = 431 Time: 0.000 trying p = 433 Time: 0.010 trying p = 439 Time: 0.010 trying p = 443 Time: 0.010 trying p = 449 Time: 0.000 trying p = 457 Time: 0.010 trying p = 461 Time: 0.010 trying p = 463 Time: 0.000 trying p = 467 Time: 0.010 trying p = 479 Time: 0.000 trying p = 487 Time: 0.010 trying p = 491 Time: 0.000 trying p = 499 Time: 0.010 trying p = 503 Time: 0.010 trying p = 509 Time: 0.010 trying p = 521 Time: 0.000 trying p = 523 Time: 0.010 trying p = 541 Time: 0.010 trying p = 547 Time: 0.010 trying p = 557 Time: 0.000 trying p = 563 Time: 0.000 trying p = 569 Time: 0.010 trying p = 571 Time: 0.010 trying p = 577 Time: 0.000 trying p = 587 Time: 0.010 trying p = 593 Time: 0.010 trying p = 599 Time: 0.000 trying p = 601 Time: 0.010 trying p = 607 Time: 0.010 trying p = 613 Time: 0.010 trying p = 617 Time: 0.000 trying p = 619 Time: 0.010 trying p = 631 Time: 0.010 trying p = 641 Time: 0.010 trying p = 643 Time: 0.000 trying p = 647 Time: 0.010 trying p = 653 Time: 0.010 trying p = 659 Time: 0.010 trying p = 661 Time: 0.000 trying p = 673 Time: 0.000 trying p = 677 Time: 0.010 trying p = 683 Time: 0.010 trying p = 691 Time: 0.000 trying p = 701 Time: 0.010 trying p = 709 Time: 0.000 trying p = 719 Time: 0.000 trying p = 727 Time: 0.020 trying p = 733 Time: 0.000 trying p = 739 Time: 0.000 trying p = 743 Time: 0.010 trying p = 751 Time: 0.010 trying p = 757 Time: 0.000 trying p = 761 Time: 0.010 trying p = 769 Time: 0.010 trying p = 773 Time: 0.000 trying p = 787 Time: 0.000 trying p = 797 Time: 0.010 trying p = 809 Time: 0.010 trying p = 811 Time: 0.010 trying p = 821 Time: 0.010 trying p = 823 Time: 0.000 trying p = 827 Time: 0.010 trying p = 829 Time: 0.010 trying p = 839 Time: 0.010 trying p = 853 Time: 0.000 trying p = 857 Time: 0.010 trying p = 859 Time: 0.010 trying p = 863 Time: 0.000 trying p = 877 Time: 0.000 trying p = 881 Time: 0.010 trying p = 883 Time: 0.000 trying p = 887 Time: 0.010 trying p = 907 Time: 0.000 trying p = 911 Time: 0.010 trying p = 919 Time: 0.010 trying p = 929 Time: 0.000 trying p = 937 Time: 0.010 trying p = 941 Time: 0.010 trying p = 947 Time: 0.000 trying p = 953 Time: 0.000 trying p = 967 Time: 0.010 trying p = 971 Time: 0.000 trying p = 977 Time: 0.010 trying p = 983 Time: 0.010 trying p = 991 Time: 0.000 trying p = 997 Time: 0.010 trying p = 1009 Time: 0.000 trying p = 1013 Time: 0.010 trying p = 1019 Time: 0.010 trying p = 1021 Time: 0.010 trying p = 1031 Time: 0.000 trying p = 1033 Time: 0.010 trying p = 1039 Time: 0.000 trying p = 1049 Time: 0.000 trying p = 1051 Time: 0.010 trying p = 1061 Time: 0.010 trying p = 1063 Time: 0.000 trying p = 1069 Time: 0.010 trying p = 1087 Time: 0.010 trying p = 1091 Time: 0.010 trying p = 1093 Time: 0.000 trying p = 1097 Time: 0.010 trying p = 1103 Time: 0.010 trying p = 1109 Time: 0.000 trying p = 1117 Time: 0.010 trying p = 1123 Time: 0.010 trying p = 1129 Time: 0.010 trying p = 1151 Time: 0.000 trying p = 1153 Time: 0.010 trying p = 1163 Time: 0.010 trying p = 1171 Time: 0.000 trying p = 1181 Time: 0.010 trying p = 1187 Time: 0.000 trying p = 1193 Time: 0.000 trying p = 1201 Time: 0.010 trying p = 1213 Time: 0.010 trying p = 1217 Time: 0.000 trying p = 1223 Time: 0.000 trying p = 1229 Time: 0.000 trying p = 1231 Time: 0.010 trying p = 1237 Time: 0.010 trying p = 1249 Time: 0.010 trying p = 1259 Time: 0.000 trying p = 1277 Time: 0.010 trying p = 1279 Time: 0.010 trying p = 1283 Time: 0.000 trying p = 1289 Time: 0.010 trying p = 1291 Time: 0.010 trying p = 1297 Time: 0.010 trying p = 1301 Time: 0.000 trying p = 1303 Time: 0.010 trying p = 1307 Time: 0.010 trying p = 1319 Time: 0.010 trying p = 1321 Time: 0.010 trying p = 1327 Time: 0.000 trying p = 1361 Time: 0.010 trying p = 1367 Time: 0.010 trying p = 1373 Time: 0.010 trying p = 1381 Time: 0.010 trying p = 1399 Time: 0.000 trying p = 1409 Time: 0.020 trying p = 1423 Time: 0.000 trying p = 1427 Time: 0.010 trying p = 1429 Time: 0.010 trying p = 1433 Time: 0.000 trying p = 1439 Time: 0.000 trying p = 1447 Time: 0.010 trying p = 1451 Time: 0.010 trying p = 1453 Time: 0.000 trying p = 1459 Time: 0.010 trying p = 1471 Time: 0.010 trying p = 1481 Time: 0.000 trying p = 1483 Time: 0.010 trying p = 1487 Time: 0.000 trying p = 1489 Time: 0.000 trying p = 1493 Time: 0.010 trying p = 1499 Time: 0.010 trying p = 1511 Time: 0.010 trying p = 1523 Time: 0.010 trying p = 1531 Time: 0.000 trying p = 1543 Time: 0.010 trying p = 1549 Time: 0.010 trying p = 1553 Time: 0.010 trying p = 1559 Time: 0.000 trying p = 1567 Time: 0.010 trying p = 1571 Time: 0.010 trying p = 1579 Time: 0.000 trying p = 1583 Time: 0.010 trying p = 1597 Time: 0.010 trying p = 1601 Time: 0.010 trying p = 1607 Time: 0.000 trying p = 1609 Time: 0.010 trying p = 1613 Time: 0.010 trying p = 1619 Time: 0.010 trying p = 1621 Time: 0.000 trying p = 1627 Time: 0.000 trying p = 1637 Time: 0.000 trying p = 1657 Time: 0.010 trying p = 1663 Time: 0.010 trying p = 1667 Time: 0.000 trying p = 1669 Time: 0.010 trying p = 1693 Time: 0.010 trying p = 1697 Time: 0.000 trying p = 1699 Time: 0.010 trying p = 1709 Time: 0.000 trying p = 1721 Time: 0.010 trying p = 1723 Time: 0.000 trying p = 1733 Time: 0.010 trying p = 1741 Time: 0.000 trying p = 1747 Time: 0.010 trying p = 1753 Time: 0.000 trying p = 1759 Time: 0.010 trying p = 1777 Time: 0.010 trying p = 1783 Time: 0.010 trying p = 1787 Time: 0.010 trying p = 1789 Time: 0.000 trying p = 1801 Time: 0.000 trying p = 1811 Time: 0.010 trying p = 1823 Time: 0.010 trying p = 1831 Time: 0.000 trying p = 1847 Time: 0.010 trying p = 1861 Time: 0.010 trying p = 1867 Time: 0.010 trying p = 1871 Time: 0.000 trying p = 1873 Time: 0.010 trying p = 1877 Time: 0.010 trying p = 1879 Time: 0.010 trying p = 1889 Time: 0.000 trying p = 1901 Time: 0.010 trying p = 1907 Time: 0.010 trying p = 1913 Time: 0.010 trying p = 1931 Time: 0.000 trying p = 1933 Time: 0.010 trying p = 1949 Time: 0.000 trying p = 1951 Time: 0.000 trying p = 1973 Time: 0.000 trying p = 1979 Time: 0.010 trying p = 1987 Time: 0.010 trying p = 1993 Time: 0.010 trying p = 1997 Time: 0.000 trying p = 1999 Time: 0.000 > ordord; [ [ 29, 29 ], [ 9, 81 ], [ 61, 61 ], [ 139, 139 ], [ 295, 295 ], [ 109, 436 ], [ 123, 369 ], [ 421, 421 ], [ 1069, 1069 ], [ 33, 1089 ], [ 1471, 1471 ], [ 1891, 1891 ], [ 1795, 1795 ], [ 3079, 3079 ], [ 63, 3969 ], [ 27, 2916 ], [ 4189, 4189 ], [ 4351, 4351 ], [ 39, 6084 ], [ 6871, 6871 ], [ 8311, 8311 ], [ 8095, 8095 ], [ 839, 9229 ], [ 11311, 11311 ], [ 3747, 11241 ], [ 3057, 9171 ], [ 12421, 12421 ], [ 9505, 9505 ], [ 5673, 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