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 2022-06-15, 21:22 #1662 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 22×7×132 Posts Well, I am exploring some ideas, but I'll have to see if any work out. One thing going toward identification of these is that, although the term will be different for each sequence, values (comp = factor1 * factor2 * factor3) will all be identical.
2022-06-17, 16:13   #1663
RichD

Sep 2008
Kansas

3·1,213 Posts

Quote:
 Originally Posted by garambois I also noticed yesterday that the prime 181 was missing from the list of all bases < 200 that are primes. I don't know why we had forgotten 181 ? I will initialize it.
Oops, I seem to have missed this. I did some work on base 181. I will stop now.

2022-06-17, 17:07   #1664
garambois

"Garambois Jean-Luc"
Oct 2011
France

72×19 Posts

Quote:
 Originally Posted by RichD Oops, I seem to have missed this. I did some work on base 181. I will stop now.
OK, now I understand better why the work for some exponents was already done !
Thanks.

 2022-06-17, 17:45 #1665 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 22×7×132 Posts I have not solved the entire problem with merged duplication entirely, but I have come up with some results. I ran some work on all the primes from all the sequences from base 2 through base 200, that have the first digit of 1, against the entire set. In my attempt to cull those that appeared in merged sequences, I did find a couple triplets where a prime exists within merged sequences and outside of them. I suspect many more, but my scripts still need work in this area: Code: These two are merged: 1370602529,276,1,69 1370602529,84,7,158 This one is outside the merged sequences: 1370602529,38,21,5071 These two are merged: 1849563931,15472,9,1741 1849563931,70,15,1582 This one is outside the merged sequences: 1849563931,43,57,1 Here is the entire list (omitting the above triplets): Code: 1000066283,157,6,1611 1000066283,80,33,1128 1001655821,20,67,692 1001655821,73,28,1192 1005523957,46,38,48 1005523957,99,44,1332 1006120013,167,6,165 1006120013,7,16,719 1008355279,103,8,1220 1008355279,86,41,38 1010085299,37,6,2502 1010085299,46,65,653 1012433291,101,4,1556 1012433291,30,37,2112 1013226583,6,23,544 1013226583,61,18,3451 1014907567,13,50,1573 1014907567,21,20,329 1027180397,34,71,160 1027180397,51,81,24 1035744623,109,38,628 1035744623,6,47,1523 1038824309,5,48,1350 1038824309,62,57,517 1040789047,10,47,500 1040789047,61,70,232 1051654267,19,22,2102 1051654267,2,468,58 1057464631,119,44,195 1057464631,87,38,1726 1061367701,10,77,3358 1061367701,11,68,2558 10655948837,19,56,310 10655948837,33,36,599 1068398117,113,30,200 1068398117,19,88,141 1068829721,11,68,3819 1068829721,34,49,281 10689931771,30,23,782 10689931771,46,13,392 1070974591,107,40,1628 1070974591,5,136,3285 1071660347,15,34,1721 1071660347,41,28,169 1073335301,50,18,8 1073335301,93,20,20 10749423863,11,116,3078 10749423863,30,5,1531 1078474589,10,37,1132 1078474589,19,76,1235 1088336201,26,73,395 1088336201,54,33,155 1097038783,2,501,61 1097038783,67,83,11 109964639887,193,22,263 109964639887,40,19,182 1104735523,3,106,342 1104735523,7,158,510 1108463827,43,20,227 1108463827,6,53,577 1108476167,11,88,15 1108476167,23,44,3475 1114626413,19,52,2714 1114626413,30,25,267 1117906721,109,36,220 1117906721,11,50,711 1118156813,46,27,334 1118156813,70,19,161 1121641319,10,37,2588 1121641319,57,48,200 1127225591,41,74,127 1127225591,51,58,1063 1128708899,119,20,94 1128708899,26,79,122 1129552253,19,18,510 1129552253,2,341,25 1130529443,26,51,719 1130529443,57,28,2387 1134318569,151,4,144 1134318569,95,26,161 1134335339,17,92,2030 1134335339,73,34,367 1134461173,18,79,74 1134461173,6,35,1513 1134797117,42,9,252 1134797117,7,98,969 1138574441,44,69,1203 1138574441,99,32,2256 1142266651,11,116,2980 1142266651,85,12,4627 1144636907,14,45,396 1144636907,3,146,561 1145898077,10,133,462 1145898077,70,29,1651 1146191047,31,28,66 1146191047,5,72,721 1150135219,11,29,4 1150135219,35,28,209 1153942483,3,211,7 1153942483,44,53,2201 1157788561,22,87,76 1157788561,46,33,1095 1158926663,26,31,550 1158926663,79,12,2168 1167137717,69,20,703 1167137717,79,8,528 1170750769,55,26,1389 1170750769,83,8,282 1180516231,29,15,1366 1180516231,7,104,955 1187125579,55,32,364 1187125579,65,52,79 1193918981,35,10,1480 1193918981,59,4,831 1194671551,191,34,223 1194671551,5,170,627 1195389149,17,22,608 1195389149,61,20,86 1195502977,19,32,1315 1195502977,6,133,785 1198306349,76,25,2555 1198306349,79,24,398 1205900173,12,69,1027 1205900173,38,29,755 1207589143,24,15,466 1207589143,3,58,3357 1221597011,37,22,1144 1221597011,5,82,750 1221597011,6,73,2552 12227903759,20,69,893 12227903759,54,23,1030 1229334677,35,50,540 1229334677,38,27,33 1234453553,3,214,2283 1234453553,94,37,271 1234704811,113,20,179 1234704811,28,43,135 1239548699,5,136,117 1239548699,52,27,797 1257729269,19,46,123 1257729269,77,8,421 1259803487,44,47,175 1259803487,6,73,1724 1264657091,14,71,1359 1264657091,94,45,628 1267449919,26,97,832 1267449919,43,8,2363 1267528987,3,34,252 1267528987,66,9,1037 1270550651,45,24,625 1270550651,76,19,783 12742648307,21,54,2903 12742648307,28,17,151 1274602453,69,56,810 1274602453,97,26,401 12755626837,10,17,754 12755626837,17,6,3969 1277097533,11,18,593 1277097533,74,57,1418 1278222611,39,22,290 1278222611,61,46,368 1279946509,14,89,1255 1279946509,41,24,750 1288234043,26,39,3163 1288234043,70,53,29 1291308467,19,76,2878 1291308467,7,48,1115 1293967729,19,42,92 1293967729,82,41,626 1294170701,30,25,1418 1294170701,37,22,3218 1298562247,29,16,3065 1298562247,60,18,3 1307652473,15,98,15 1307652473,44,35,2513 1309129933,3,68,1069 1309129933,48,31,714 1309588837,101,20,115 1309588837,14,77,208 1317570083,12,71,172 1317570083,29,40,273 1326169571,15,4,853 1326169571,39,32,1557 13273901521,42,65,81 13273901521,75,10,4528 1329031787,17,46,1751 1329031787,58,69,733 1331215709,44,27,657 1331215709,58,9,931 1331502647,24,61,92 1331502647,79,26,398 1334284499,68,45,388 1334284499,82,3,1467 1334602861,197,49,32 1334602861,75,16,852 1339215721,15,36,307 1339215721,69,24,316 13441505989,15,20,908 13441505989,17,20,1044 1349251559,17,92,1245 1349251559,61,68,170 1350352741,11,20,1203 1350352741,22,15,1475 1364492747,29,10,1071 1364492747,66,19,1327 1371644347,38,55,1181 1371644347,77,6,88 1373075419,42,23,661 1373075419,62,27,49 1375618577,5,136,1315 1375618577,51,32,633 1385682629,17,70,199 1385682629,51,74,1313 1388392903,20,25,1069 1388392903,58,11,169 1388696473,22,31,1809 1388696473,99,20,1224 1399913257,45,39,42 1399913257,6,11,298 1400714869,107,22,1039 1400714869,22,13,3897 1417019537,11,36,1691 1417019537,46,31,279 142754777149,101,32,504 142754777149,52,39,640 1428485593,13,16,376 1428485593,74,57,1188 1442122849,10,35,2506 1442122849,19,20,1399 1443633649,105,48,58 1443633649,109,10,386 1447677043,151,24,34 1447677043,28,31,1017 1453059701,35,10,2424 1453059701,57,38,792 1455497123,26,37,2577 1455497123,34,51,1425 1455649541,44,11,307 1455649541,86,15,304 1456319983,10,131,1394 1456319983,5,70,669 1458245561,60,63,96 1458245561,73,61,41 1458985963,3,190,1280 1458985963,59,24,523 1473659471,101,48,77 1473659471,15,34,1246 1476281803,127,42,939 1476281803,58,7,605 1494655627,10,123,334 1494655627,12,51,1186 1514980781,46,63,17 1514980781,99,12,887 1520335771,12,113,137 1520335771,19,105,80 1520459723,22,41,1246 1520459723,29,91,105 1539077593,41,52,232 1539077593,5,164,143 154198251007,17,76,702 154198251007,22,87,1336 1542335789,149,20,506 1542335789,79,10,228 1545539087,56,5,810 1545539087,94,13,2113 1573252489,31,86,120 1573252489,78,43,915 1575372067,10,121,1314 1575372067,35,32,1858 1576788293,54,61,1078 1576788293,55,30,800 1581829609,86,19,305 1581829609,97,40,2150 1592634581,35,10,58 1592634581,58,37,1275 1600807519,30,27,260 1600807519,6,89,821 1622062093,14,89,637 1622062093,46,58,43 1625043389,34,65,1601 1625043389,58,69,845 1639132051,2,422,11 1639132051,22,41,508 16409695231,38,21,2631 16409695231,6,7,253 1646665309,41,26,306 1646665309,99,12,334 1648370369,33,72,491 1648370369,70,62,7 1652665811,119,44,14 1652665811,26,73,1337 1661797037,22,41,396 1661797037,31,50,1756 1662398893,50,64,40 1662398893,68,31,1626 1668820973,12,97,23 1668820973,57,70,327 1671507989,70,29,341 1671507989,79,28,343 1672617637,15,114,298 1672617637,62,23,273 1691208683,55,12,1800 1691208683,93,6,1086 1691734123,109,8,205 1691734123,61,14,219 16955341633,12,23,488 16955341633,74,39,2353 1714204097,34,45,1669 1714204097,44,75,2169 1725886607,10,39,357 1725886607,15,98,1191 1728697067,14,17,563 1728697067,54,7,1236 1738718167,109,46,167 1738718167,23,18,1210 1743048779,10,77,1440 1743048779,3,110,956 1748701403,54,47,974 1748701403,76,11,2431 1751490079,3,152,892 1751490079,6,161,1959 1757771591,3,110,2457 1757771591,62,19,74 1758281221,62,11,1019 1758281221,7,18,472 1767263009,11,70,2398 1767263009,14,53,1440 1770121069,44,35,675 1770121069,57,8,2118 1782789427,33,24,636 1782789427,45,10,679 1786026601,101,22,403 1786026601,40,33,439 1789860791,29,36,654 1789860791,69,22,597 1800704767,127,8,121 1800704767,78,37,2122 1807530251,54,3,233 1807530251,96,11,583 1818419051,22,15,394 1818419051,3,70,1243 1821849553,67,38,1203 1821849553,83,6,1017 1823692711,20,27,1481 1823692711,86,5,1051 1848424423,14,29,365 1848424423,28,51,67 1888970921,17,34,428 1888970921,3,14,1694 1889889973,103,26,1378 1889889973,20,41,1 1897073869,12,37,336 1897073869,90,31,1881 1900569103,21,38,414 1900569103,5,74,2044 1909012393,2,195,46 1909012393,6,99,110 1909553381,167,20,429 1909553381,62,65,407 1912420217,101,36,1187 1912420217,7,132,2790 1930550801,30,3,1761 1930550801,53,58,215 1945784677,33,58,42 1945784677,75,26,582 1978558717,127,24,1546 1978558717,58,41,3703 19805197549,21,34,715 19805197549,28,71,128 1991389019,11,14,614 1991389019,6,33,373 1993048741,137,14,810 1993048741,35,56,526 19971331781,47,68,1399 19971331781,93,12,207 Of note, although I ran the primes against the entire set of bases, only 276 and 15472 appear in the results. And, they're only in the triplets above. I didn't notice any greater than 193 in the last listing. I also didn't notice any triplets that didn't involve merged sequences. There are some primes of greater than 10 digits in the listing.
2022-06-17, 19:55   #1666
garambois

"Garambois Jean-Luc"
Oct 2011
France

72×19 Posts

Quote:
 Originally Posted by EdH I have not solved the entire problem with merged duplication entirely, but I have come up with some results. I ran some work on all the primes from all the sequences from base 2 through base 200, that have the first digit of 1, against the entire set. In my attempt to cull those that appeared in merged sequences, I did find a couple triplets where a prime exists within merged sequences and outside of them. I suspect many more, but my scripts still need work in this area: ... ... Here is the entire list (omitting the above triplets): Code: 1000066283,157,6,1611 ... 1221597011,37,22,1144 1221597011,5,82,750 1221597011,6,73,2552 ... Of note, although I ran the primes against the entire set of bases, only 276 and 15472 appear in the results. And, they're only in the triplets above. I didn't notice any greater than 193 in the last listing. I also didn't notice any triplets that didn't involve merged sequences. There are some primes of greater than 10 digits in the listing.
I did some quick checking.
I'll take a more detailed look over the next weekend.

It looks like there are also some 11-digit pairs as you already report.
This leads me to think that 12-digit pairs must be very rare, with the reduced number of sequences we have to do this research.
As for triplets, apart from the cases of mergers that you mention above, they must be very rare too.

Otherwise, I also note a triplet that does not involve a merged sequence for the prime 1221597011 (see above), but for the 37^22 sequence, at index 1144, the term is :
14995180448395695667673983126 = 2 - 3533 - 2122159701159877677281911
And so, 1221597011 is not a factor, but the part of writing a factor.

Thanks a lot Edwin !

2022-06-17, 20:52   #1667
EdH

"Ed Hall"
Dec 2009

10010011111002 Posts

Quote:
 Originally Posted by garambois . . .Otherwise, I also note a triplet that does not involve a merged sequence for the prime 1221597011 (see above), but for the 37^22 sequence, at index 1144, the term is : 14995180448395695667673983126 = 2 - 3533 - 2122159701159877677281911 And so, 1221597011 is not a factor, but the part of writing a factor. Thanks a lot Edwin !
I weeded out a bunch of those triplets, but I guess I missed one. . . That's the trouble with manually doing this. I still need to do better with programming/scripts. Thanks for keeping me in line.

 2022-06-18, 00:10 #1668 RichD     Sep 2008 Kansas 3·1,213 Posts I'll start initializing prime bases 223, 227 & 229.
2022-06-18, 01:05   #1669
gd_barnes

May 2007
Kansas; USA

3×47×79 Posts

Quote:
 Originally Posted by garambois For example, I also noticed yesterday that the prime 181 was missing from the list of all bases < 200 that are primes. I don't know why we had forgotten 181 ? I will initialize it.

I am currently in the process of initializing just the same-parity exponents on bases 179 and 181 to add some interesting bases for the easier sequences effort. I started yesterday and it did not appear that those had been worked on because the elves were having to work to terminate the smaller same-parity exponents when I pulled them up.

I am currently up to exponent 55 on both bases. I have a batch job set up to initialize all of them up to a starting sequence of 160 digits...exponent 71. For now, the job stops any base that has a hard cofactor (fully ECM'd) of >= 102 digits. I will then run back through and run any remaining exponents until they hit a cofactor of >= 110 digits.

Hopefully this is OK.

Last fiddled with by gd_barnes on 2022-06-18 at 01:17

2022-06-18, 01:28   #1670
RichD

Sep 2008
Kansas

363910 Posts

Quote:
 Originally Posted by gd_barnes I am currently in the process of initializing just the same-parity exponents on bases 179 and 181 to add some interesting bases for the easier sequences effort. I started yesterday and it did not appear that those had been worked on because the elves were having to work to terminate the smaller same-parity exponents when I pulled them up. I am currently up to exponent 55 on both bases. I have a batch job set up to initialize all of them up to a starting sequence of 160 digits...exponent 71. For now, the job stops any base that has a hard cofactor (fully ECM'd) of >= 102 digits. I will then run back through and run any remaining exponents until they hit a cofactor of >= 110 digits. Hopefully this is OK.
Both bases are currently assigned according to the reservation table.
Attached Files
 ini.pdf (15.4 KB, 14 views)

2022-06-18, 07:50   #1671
garambois

"Garambois Jean-Luc"
Oct 2011
France

72·19 Posts

Quote:
 Originally Posted by gd_barnes I had also missed this. I am currently in the process of initializing just the same-parity exponents on bases 179 and 181 to add some interesting bases for the easier sequences effort. I started yesterday and it did not appear that those had been worked on because the elves were having to work to terminate the smaller same-parity exponents when I pulled them up. I am currently up to exponent 55 on both bases. I have a batch job set up to initialize all of them up to a starting sequence of 160 digits...exponent 71. For now, the job stops any base that has a hard cofactor (fully ECM'd) of >= 102 digits. I will then run back through and run any remaining exponents until they hit a cofactor of >= 110 digits. Hopefully this is OK.

Attention, I am calculating myself the sequences of bases 179 and 181, as RichD says.
It's just that I hadn't reported the results to FactorDB yet.
I am afraid that we have done the same calculations twice.
Please look at the last line of the table under the heading "Navigation" on the main project page : bases 179 and 181 were reserved for me.
Should I stop my calculations on these two bases if you have also done them ?
Have you also done calculations for the exponents of parity opposite to the base ?

2022-06-18, 07:58   #1672
garambois

"Garambois Jean-Luc"
Oct 2011
France

72·19 Posts

Quote:
 Originally Posted by RichD I'll start initializing prime bases 223, 227 & 229.
OK, many thanks !
It will extend my area of analysis a bit this summer if we integrated bases that are exhaustively prime numbers further than 200.

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