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

Batalov · 2021-01-30, 02:41

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:

221	2	2634	L	264.2	0.83	/3
254	2	2658	M	266.6	0.95	/3
204	2	2694	L	270.2	0.75	/3
204	2	2694	M	270.2	0.75	/3
241	2	2706	M	271.5	0.88	/3
241	2	2742	L	275.1	0.87	/3
261	2	2766	M	277.5	0.94	/3
224	2	2778	M	278.7	0.8	/3
276	2	2778	L	278.7	0.99	/3
281	2	2802	L	281.1	0.99	/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
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
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
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
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	
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
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	
234	2	1361	+	409.6	0.57	
356	2	2722	M	409.6	0.86		
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	
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	
352	2	2858	L	430.1	0.9	
299	2	1432	+	431	0.69	
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	
350	2	2914	L	438.5	0.79	
416	2	1457	+	438.5	0.94	
371	2	2918	M	439.1	0.84		
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

Batalov · 2021-01-30, 06:38

I will run 2,1335+ c190.

VBCurtis · 2021-01-30, 17:19

I'll take 2,1455+ c190.

charybdis · 2021-01-30, 19:14

Taking 2,1431+ c184 and 2,2750M c185.

VBCurtis · 2021-01-31, 17:35

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.

Batalov · 2021-02-01, 17:13

Quote:

Originally Posted by Batalov

I will run 2,1335+ c190.

Done (SNFS, quartic). c190 = p81 * p109.

jyb · 2021-02-07, 06:34

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.

Batalov · 2021-02-07, 07:31

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.

jyb · 2021-02-07, 09:31

Quote:

Originally Posted by Batalov

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.

henryzz · 2021-02-07, 09:41

I think we are getting to the point where working out the crossover point between quartic and octic would be quite useful.

charybdis · 2021-02-07, 12:55

Quote:

Originally Posted by Batalov

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.

2021-01-31, 17:35	#5
VBCurtis "Curtis" Feb 2005 Riverside, CA 41·131 Posts	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

2021-02-07, 06:34	#7
jyb Aug 2005 Seattle, WA 5·367 Posts	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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2021-01-30, 06:38	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9901₁₀ Posts	I will run 2,1335+ c190.

2021-01-30, 17:19	#3
VBCurtis "Curtis" Feb 2005 Riverside, CA 5371₁₀ Posts	I'll take 2,1455+ c190.

2021-01-30, 19:14	#4
charybdis Apr 2020 797 Posts	Taking 2,1431+ c184 and 2,2750M c185.

2021-02-07, 07:31	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,901 Posts	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.

2021-02-07, 09:41	#10
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 2³·7·107 Posts	I think we are getting to the point where working out the crossover point between quartic and octic would be quite useful.