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#1 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts |
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S.S.W. announced extension to the 2+, 2-, 2LM tables.
First round is: ECM/nfs results are invited. Here are the NFS (useable) complexities: Code:
190 2 1455 + 233.5 0.81 /3/5 211 2 1311 + 263 0.8 /3 229 2 2622 L 263 0.87 /3 212 2 1317 - 264.2 0.8 /3 221 2 2634 L 264.2 0.83 /3 260 2 1317 + 264.2 0.98 /3 254 2 2658 M 266.6 0.95 /3 238 2 1332 + 267.2 0.89 /3 221 2 2682 M 269 0.82 /3 204 2 2694 L 270.2 0.75 /3 204 2 2694 M 270.2 0.75 /3 256 2 1347 - 270.2 0.94 /3 270 2 1347 + 270.2 0.99 /3 202 2 1353 - 271.5 0.74 /3 241 2 2706 M 271.5 0.88 /3 212 2 2718 M 272.7 0.77 /3 223 2 1359 - 272.7 0.81 /3 255 2 1359 + 272.7 0.93 /3 260 2 2718 L 272.7 0.95 /3 241 2 1368 + 274.5 0.87 /3 240 2 1371 - 275.1 0.87 /3 241 2 2742 L 275.1 0.87 /3 225 2 2754 L 276.3 0.81 /3 252 2 1377 - 276.3 0.91 /3 261 2 2766 M 277.5 0.94 /3 224 2 2778 M 278.7 0.8 /3 229 2 1389 + 278.7 0.82 /3 276 2 2778 L 278.7 0.99 /3 234 2 1392 + 279.3 0.83 /3 276 2 1401 - 281.1 0.98 /3 281 2 2802 L 281.1 0.99 /3 192 2 1404 + 281.7 0.68 /3 245 2 2826 L 283.5 0.86 /3 241 2 1416 + 284.1 0.84 /3 241 2 1419 - 284.7 0.84 /3 232 2 2862 M 287.1 0.8 /3 282 2 2862 L 287.1 0.98 /3 192 2 1437 - 288.3 0.66 /3 212 2 2874 M 288.3 0.73 /3 242 2 2886 L 289.5 0.83 /3 248 2 1443 - 289.5 0.85 /3 233 2 2922 L 293.1 0.79 /3 229 2 1467 - 294.3 0.77 /3 246 2 2946 L 295.5 0.83 /3 260 2 1473 + 295.5 0.87 /3 296 2 2946 M 295.5 1 /3 266 2 2958 M 296.7 0.89 /3 240 2 1488 + 298.5 0.8 /3 245 2 1497 - 300.3 0.81 /3 300 2 1497 + 300.3 0.99 /3 193 2 2630 M 316.6 0.6 /5 275 2 1315 - 316.6 0.86 /5 293 2 2630 L 316.6 0.92 /5 316 2 1315 + 316.6 0.99 /5 256 2 2650 M 319 0.8 /5 282 2 1325 - 319 0.88 /5 314 2 1325 + 319 0.98 /5 278 2 1345 - 323.8 0.85 /5 317 2 1345 + 323.8 0.97 /5 258 2 1355 + 326.2 0.79 /5 300 2 2710 M 326.2 0.91 /5 312 2 2710 L 326.2 0.95 /5 309 2 1360 + 327.4 0.94 /5 257 2 1375 + 331.1 0.77 /5 261 2 2750 L 331.1 0.78 /5 246 2 1385 - 333.5 0.73 /5 262 2 1385 + 333.5 0.78 /5 239 2 2618 M 337.7 0.7 /7 315 2 2810 L 338.3 0.93 /5 307 2 1316 + 339.5 0.9 /7 217 2 1415 - 340.7 0.63 /5 219 2 1415 + 340.7 0.64 /5 283 2 2830 L 340.7 0.83 /5 333 2 1420 + 341.9 0.97 /5 197 2 2870 M 345.5 0.57 /5 230 2 1435 + 345.5 0.66 /5 240 2 1445 + 347.9 0.68 /5 283 2 2702 L 348.5 0.81 /7 322 2 1351 - 348.5 0.92 /7 336 2 1351 + 348.5 0.96 /7 274 2 1460 + 351.5 0.77 /5 249 2 1465 + 352.7 0.7 /5 292 2 1465 - 352.7 0.82 /5 340 2 2930 M 352.7 0.96 /5 334 2 1372 + 353.9 0.94 /7 252 2 1475 + 355.1 0.7 /5 322 2 1475 - 355.1 0.9 /5 334 2 2950 M 355.1 0.94 /5 328 2 1379 + 355.7 0.92 /7 342 2 1379 - 355.7 0.96 /7 355 2 2758 L 355.7 0.99 /7 284 2 1480 + 356.3 0.79 /5 241 2 1393 + 359.3 0.67 /7 283 2 2786 L 359.3 0.78 /7 258 2 1495 + 359.9 0.71 /5 250 2 1331 - 364.2 0.68 /11 361 2 2662 M 364.2 0.99 /11 290 2 1313 + 364.8 0.79 /13 339 2 2626 M 364.8 0.92 /13 216 2 1421 + 366.6 0.58 /7 289 2 2842 M 366.6 0.78 /7 316 2 1421 - 366.6 0.86 /7 350 2 1339 - 372 0.94 /13 320 2 1456 + 375.6 0.85 /7 245 2 2926 M 377.4 0.64 /7 249 2 1463 - 377.4 0.65 /7 293 2 2926 L 377.4 0.77 /7 315 2 1477 - 381 0.82 /7 354 2 2954 L 381 0.92 /7 296 2 1397 + 382.2 0.77 /11 343 2 2794 L 382.2 0.89 /11 345 2 2794 M 382.2 0.9 /11 366 2 1484 + 382.8 0.95 /7 330 2 1408 + 385.2 0.85 /11 256 2 2782 M 386.4 0.66 /13 307 2 1391 + 386.4 0.79 /13 276 2 1301 + 391.6 0.7 385 2 2602 L 391.6 0.98 392 2 2602 M 391.6 1 302 2 2606 L 392.2 0.77 327 2 1303 + 392.2 0.83 352 2 2606 M 392.2 0.89 260 2 1304 + 392.5 0.66 352 2 2614 L 393.4 0.89 361 2 2614 M 393.4 0.91 284 2 1417 - 393.7 0.72 /13 289 2 2834 M 393.7 0.73 /13 311 2 1417 + 393.7 0.78 /13 330 2 2834 L 393.7 0.83 /13 347 2 1441 + 394.3 0.88 /11 306 2 1312 + 394.9 0.77 307 2 1319 - 397 0.77 357 2 1319 + 397 0.89 387 2 1321 + 397.6 0.97 277 2 2654 L 399.4 0.72 396 2 1327 + 399.4 0.99 329 2 1328 + 399.7 0.82 360 2 2666 L 401.2 0.89 366 2 2666 M 401.2 0.91 293 2 2686 L 404.2 0.72 309 2 2686 M 404.2 0.76 312 2 1343 - 404.2 0.77 368 2 1343 + 404.2 0.91 383 2 1348 + 405.7 0.94 298 2 1349 + 406 0.73 322 2 2698 L 406 0.79 349 2 2698 M 406 0.85 367 2 1349 - 406 0.9 355 2 1469 + 408.1 0.86 /13 389 2 2938 L 408.1 0.95 /13 275 2 1357 + 408.4 0.67 307 2 2714 M 408.4 0.75 374 2 1357 - 408.4 0.91 378 2 2714 L 408.4 0.92 316 2 1496 + 409.3 0.77 /11 234 2 1361 + 409.6 0.57 356 2 2722 M 409.6 0.86 377 2 2722 L 409.6 0.92 336 2 1363 + 410.2 0.81 381 2 2726 M 410.2 0.92 348 2 2734 M 411.4 0.84 371 2 1367 + 411.4 0.9 375 2 1367 - 411.4 0.91 273 2 1369 + 412 0.66 378 2 2738 M 412 0.91 398 2 2738 L 412 0.96 368 2 2746 L 413.2 0.89 375 2 1373 + 413.2 0.9 378 2 2746 M 413.2 0.91 349 2 1376 + 414.1 0.84 291 2 1381 - 415.6 0.7 321 2 2762 L 415.6 0.77 325 2 1381 + 415.6 0.78 358 2 2762 M 415.6 0.86 363 2 1384 + 416.5 0.87 318 2 2774 L 417.4 0.76 321 2 2774 M 417.4 0.76 334 2 1387 + 417.4 0.8 390 2 1387 - 417.4 0.93 405 2 1396 + 420.1 0.96 389 2 2798 L 421 0.92 392 2 1399 + 421 0.93 285 2 1403 - 422.3 0.67 328 2 1403 + 422.3 0.77 380 2 2806 M 422.3 0.89 389 2 1409 + 424.1 0.91 420 2 2818 L 424.1 0.99 202 2 2822 M 424.7 0.5 396 2 2822 L 424.7 0.93 424 2 1412 + 425 0.99 392 2 1423 + 428.3 0.91 394 2 2846 L 428.3 0.91 412 2 1423 - 428.3 0.96 398 2 1424 + 428.6 0.92 356 2 2854 L 429.5 0.82 367 2 1427 + 429.5 0.85 400 2 2858 M 430.1 0.92 403 2 1429 - 430.1 0.93 413 2 2858 L 430.1 0.96 299 2 1432 + 431 0.69 360 2 2866 M 431.3 0.83 386 2 1433 - 431.3 0.89 418 2 2866 L 431.3 0.96 431 2 1433 + 431.3 0.99 401 2 1436 + 432.2 0.92 260 2 1439 + 433.1 0.6 360 2 2878 M 433.1 0.83 380 2 1439 - 433.1 0.87 401 2 1444 + 434.6 0.92 309 2 2894 M 435.5 0.7 360 2 1447 - 435.5 0.82 395 2 1448 + 435.8 0.9 384 2 2902 M 436.7 0.87 396 2 2902 L 436.7 0.9 407 2 1451 - 436.7 0.93 426 2 1451 + 436.7 0.97 409 2 2906 M 437.3 0.93 418 2 1453 - 437.3 0.95 311 2 2914 M 438.5 0.7 350 2 2914 L 438.5 0.79 416 2 1457 + 438.5 0.94 371 2 2918 M 439.1 0.84 426 2 2918 L 439.1 0.97 365 2 2942 M 442.7 0.82 423 2 1471 + 442.7 0.95 443 2 2942 L 442.7 1 236 2 1472 + 443 0.53 308 2 2962 L 445.7 0.69 311 2 1481 - 445.7 0.69 350 2 1481 + 445.7 0.8 375 2 2966 L 446.3 0.84 394 2 2966 M 446.3 0.88 405 2 1483 - 446.3 0.9 409 2 1483 + 446.3 0.91 340 2 1487 + 447.5 0.75 376 2 2974 L 447.5 0.84 328 2 2978 M 448.1 0.73 421 2 1489 + 448.1 0.93 444 2 2978 L 448.1 0.99 333 2 2986 L 449.3 0.74 400 2 1493 - 449.3 0.89 445 2 2986 M 449.3 0.99 354 2 1499 + 451.1 0.78 401 2 1499 - 451.1 0.88 406 2 2998 L 451.1 0.89 426 2 2998 M 451.1 0.94 Last fiddled with by Batalov on 2021-03-31 at 08:29 Reason: 2,2958L and 1393- done |
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#2 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts |
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I will run 2,1335+ c190.
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#3 |
"Curtis"
Feb 2005
Riverside, CA
112018 Posts |
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I'll take 2,1455+ c190.
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#4 |
Apr 2020
E616 Posts |
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Taking 2,1431+ c184 and 2,2750M c185.
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#5 |
"Curtis"
Feb 2005
Riverside, CA
3·1,579 Posts |
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Starting ECM on 2,1437-, a GNFS-193.
Edit: cownoise suggests the SNFS-sextic is about the same difficulty at 289 digits, so I'll test-sieve after poly select. Last fiddled with by VBCurtis on 2021-01-31 at 17:37 |
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#6 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts |
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Done (SNFS, quartic). c190 = p81 * p109.
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#7 |
Aug 2005
Seattle, WA
1,699 Posts |
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Since the table above is sorted by SNFS difficulty, it may be worthwhile* pointing out that for some of the numbers shown, the given difficulty is only achievable with a polynomial of impractical degree. E.g. 2,2626M can have a difficulty of 364.8, but only with a degree-12 polynomial. A polynomial with a degree that would work with current tools would have SNFS difficulty 395.3. There are 8 such numbers in the table, all Aurifeuillians.
*Or perhaps not. The difficulty alone makes these impractical for NFS at the moment, at any degree. Last fiddled with by jyb on 2021-02-07 at 06:36 |
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#8 |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
24AD16 Posts |
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Indeed I have listed useable complexities (many of them with a quartic or quintic), and not listed the Phi()-based "any degree allowed" complexity.
There are some numbers there where exponent is divisble by 35 (so, yes, you could come down to deg 12 poly, but you can't use it). The Aurifeuillians are tough for even divisible by 3 or 5 expos (obligatory quartics), but e.g. 2,1311+ is an easy sextic. |
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#9 | |
Aug 2005
Seattle, WA
6A316 Posts |
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And of course if an Aureifeuillian has an exponent divisible by 3 and 5, then it would be an obligatory octic, though it appears the first of these which aren't already factored are 2,3030L and 2,3030M. Ed Hall is currently sieving the Homogeneous Cunningham 10+3,930M, an octic of difficulty 250. It will be interesting to compare his results to quartics of a similar difficulty. |
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#10 |
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
10110111000012 Posts |
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I think we are getting to the point where working out the crossover point between quartic and octic would be quite useful.
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#11 | |
Apr 2020
2·5·23 Posts |
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For the non-Aurifeuillians, the exponents divisible by 17 are probably fastest with an octic that makes use of the algebraic factor. |
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