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Old 2021-01-30, 02:41   #1
Batalov
 
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Mar 2008
Phi(4,2^7658614+1)/2

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Plus Extension to the Base 2 tables from 1300 to 1500, LM to 3000

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	
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 2021-04-19 at 20:39 Reason: 2,1481+ is done
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Old 2021-01-30, 06:38   #2
Batalov
 
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I will run 2,1335+ c190.
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Old 2021-01-30, 17:19   #3
VBCurtis
 
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I'll take 2,1455+ c190.
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Old 2021-01-30, 19:14   #4
charybdis
 
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Taking 2,1431+ c184 and 2,2750M c185.
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Old 2021-01-31, 17:35   #5
VBCurtis
 
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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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Old 2021-02-01, 17:13   #6
Batalov
 
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Quote:
Originally Posted by Batalov View Post
I will run 2,1335+ c190.
Done (SNFS, quartic). c190 = p81 * p109.
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Old 2021-02-07, 06:34   #7
jyb
 
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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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Old 2021-02-07, 07:31   #8
Batalov
 
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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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Old 2021-02-07, 09:31   #9
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Quote:
Originally Posted by Batalov View Post
The Aurifeuillians are tough for even divisible by 3 or 5 expos (obligatory quartics)
Some of the difficulties in this table have probably passed the point where an octic is better than a quartic. So while either one is probably beyond easy reach at difficulty 319 (2,2650M), the quartic is perhaps more beyond reach than the natural octic. And even more so for e.g. 2,2950M, at difficulty 355.1.

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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Old 2021-02-07, 09:41   #10
henryzz
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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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Old 2021-02-07, 12:55   #11
charybdis
 
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Quote:
Originally Posted by Batalov View Post
The Aurifeuillians are tough for even divisible by 3 or 5 expos (obligatory quartics)
...though those divisible by 9 still have sextics.

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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