mersenneforum.org Subproject #11: 2^2 * 3 - Lose the '3'
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 2011-09-22, 10:47 #1 schickel     "Frank <^>" Dec 2004 CDP Janesville 2·1,061 Posts Subproject #11: 2^2 * 3 - Lose the '3' This is a project suggested by 10metreh. He hopes we can achieve some terminations with this project. The hope is that a sequence that currently has 2^2 * 3 as a guide will lose the 3, if the remaining composite factors "properly". I pulled a status on these sequences right before posting but, as always, check the status of a sequence in the DB before starting any significant work.... [Note: Due to the sheer number of sequences that are currently 2^2 * 3, this message has been split....] Sequences: Code: 894702 1071. sz 112 2^2 * 3 * 11 668922 1469. sz 112 2^2 * 3 * 5 800010 1351. sz 112 2^2 * 3 * 5 596808 1007. sz 112 2^2 * 3 * 5 867228 1034. sz 112 2^2 * 3^2 638680 833. sz 112 2^2 * 3^2 738240 1698. sz 112 2^2 * 3^2 * 17 844758 1712. sz 112 2^2 * 3^2 * 5 630024 2457. sz 112 2^2 * 3^2 * 7 * 89459 * 138072719 293136 989. sz 113 2^2 * 3 369978 1188. sz 113 2^2 * 3 642000 1705. sz 113 2^2 * 3 * 1669 526752 618. sz 113 2^2 * 3 * 17 244872 844. sz 113 2^2 * 3 * 2437094789966273 966180 1880. sz 113 2^2 * 3 * 29 832314 2263. sz 113 2^2 * 3 * 5 932070 1072. sz 113 2^2 * 3 * 5 872784 1104. sz 113 2^2 * 3 * 5 * 11 746880 538. sz 113 2^2 * 3 * 5 * 11 734088 1169. sz 113 2^2 * 3 * 5^2 823116 1414. sz 113 2^2 * 3 * 53 665478 757. sz 113 2^2 * 3 * 577 592506 1114. sz 113 2^2 * 3 * 79 836694 894. sz 113 2^2 * 3^2 * 29 992970 999. sz 113 2^2 * 3^2 * 37 681500 1255. sz 113 2^2 * 3^2 * 5 704850 1590. sz 113 2^2 * 3^2 * 71 227200 781. sz 113 2^2 * 3^3 682380 1726. sz 113 2^2 * 3^3 777762 1384. sz 113 2^2 * 3^3 493992 1754. sz 113 2^2 * 3^3 * 5 385176 1097. sz 113 2^2 * 3^3 * 5 968484 970. sz 114 2^2 * 3 962232 828. sz 114 2^2 * 3 933240 1082. sz 114 2^2 * 3 891702 1122. sz 114 2^2 * 3 769068 1128. sz 114 2^2 * 3 601824 2081. sz 114 2^2 * 3 533160 1064. sz 114 2^2 * 3 564870 772. sz 114 2^2 * 3 239778 1486. sz 114 2^2 * 3 358506 1062. sz 114 2^2 * 3 656616 2093. sz 114 2^2 * 3 * 1097 106080 873. sz 114 2^2 * 3 * 137 559548 1250. sz 114 2^2 * 3 * 17 * 75883 699588 1280. sz 114 2^2 * 3 * 181 517392 878. sz 114 2^2 * 3 * 1823 323964 1940. sz 114 2^2 * 3 * 19 377160 1123. sz 114 2^2 * 3 * 281 946728 1014. sz 114 2^2 * 3 * 29 515220 1546. sz 114 2^2 * 3 * 317 712824 899. sz 114 2^2 * 3 * 3313 596032 546. sz 114 2^2 * 3 * 467 * 3582899 202776 1403. sz 114 2^2 * 3 * 47 384606 2109. sz 114 2^2 * 3 * 5 803616 1068. sz 114 2^2 * 3 * 5 * 103 425052 1059. sz 114 2^2 * 3 * 5 * 11 865032 1739. sz 114 2^2 * 3 * 5 * 13 * 37 870072 1052. sz 114 2^2 * 3 * 5 * 173 * 203989 871470 904. sz 114 2^2 * 3 * 5 * 19 863370 494. sz 114 2^2 * 3 * 5 * 383 * 9293 * 48673 429072 1087. sz 114 2^2 * 3 * 5^2 * 11 357408 1233. sz 114 2^2 * 3 * 5^3 960900 1599. sz 114 2^2 * 3 * 53 450570 2498. sz 114 2^2 * 3 * 543734960947 380610 2199. sz 114 2^2 * 3 * 607 636024 965. sz 114 2^2 * 3 * 71 556920 1027. sz 114 2^2 * 3 * 727 666384 978. sz 114 2^2 * 3^2 573648 530. sz 114 2^2 * 3^2 993438 510. sz 114 2^2 * 3^2 * 11 * 13 652296 1544. sz 114 2^2 * 3^2 * 11 * 19 940224 1739. sz 114 2^2 * 3^2 * 479 967024 1144. sz 114 2^2 * 3^2 * 5 * 17 779892 779. sz 114 2^2 * 3^3 933870 685. sz 114 2^2 * 3^3 442344 1132. sz 114 2^2 * 3^3 856548 1112. sz 114 2^2 * 3^3 * 11 * 37 582144 1095. sz 114 2^2 * 3^3 * 37 922158 1305. sz 115 2^2 * 3 862866 646. sz 115 2^2 * 3 274272 985. sz 115 2^2 * 3 * 283 894066 1194. sz 115 2^2 * 3 * 31 * 24373 192360 963. sz 115 2^2 * 3 * 37 * 53^2 680544 1275. sz 115 2^2 * 3 * 373 788106 1476. sz 115 2^2 * 3 * 439 377688 2005. sz 115 2^2 * 3 * 5 641520 934. sz 115 2^2 * 3 * 5 * 617 915384 1102. sz 115 2^2 * 3 * 79 216390 920. sz 115 2^2 * 3^2 269208 1199. sz 115 2^2 * 3^4 * 43 303756 2519. sz 116 2^2 * 3 749832 680. sz 116 2^2 * 3 865164 1065. sz 116 2^2 * 3 844536 1279. sz 116 2^2 * 3 687336 1137. sz 116 2^2 * 3 487656 2478. sz 116 2^2 * 3 475668 907. sz 116 2^2 * 3 * 11 * 1637 126756 1184. sz 116 2^2 * 3 * 11 * 433 287304 1485. sz 116 2^2 * 3 * 127 214728 1292. sz 116 2^2 * 3 * 13 394680 2382. sz 116 2^2 * 3 * 149 * 8712059 941850 2111. sz 116 2^2 * 3 * 17 270504 1912. sz 116 2^2 * 3 * 173 466656 799. sz 116 2^2 * 3 * 19 * 89 983328 1614. sz 116 2^2 * 3 * 239 492688 2368. sz 116 2^2 * 3 * 2591 333300 1237. sz 116 2^2 * 3 * 38923 863640 1048. sz 116 2^2 * 3 * 3943 929880 1075. sz 116 2^2 * 3 * 41 215088 912. sz 116 2^2 * 3 * 4421 950280 1250. sz 116 2^2 * 3 * 5 624798 1728. sz 116 2^2 * 3 * 5 746564 871. sz 116 2^2 * 3 * 5 478440 978. sz 116 2^2 * 3 * 5 * 47 443370 1530. sz 116 2^2 * 3 * 5 * 97 * 197 448476 851. sz 116 2^2 * 3 * 5^2 * 25121 376992 672. sz 116 2^2 * 3 * 59 758322 2239. sz 116 2^2 * 3 * 59 * 271 840012 1918. sz 116 2^2 * 3 * 709 426072 2703. sz 116 2^2 * 3 * 73 * 1151 324072 1027. sz 116 2^2 * 3^2 664356 2924. sz 116 2^2 * 3^2 407736 586. sz 116 2^2 * 3^2 180108 751. sz 116 2^2 * 3^2 103782 851. sz 116 2^2 * 3^2 * 11 850164 2307. sz 116 2^2 * 3^2 * 11 * 1289 967680 2008. sz 116 2^2 * 3^2 * 1571 582750 1396. sz 116 2^2 * 3^2 * 17 * 19 346200 1908. sz 116 2^2 * 3^2 * 17 * 29 421428 951. sz 116 2^2 * 3^2 * 2617 143676 1430. sz 116 2^2 * 3^2 * 283 296904 902. sz 116 2^2 * 3^2 * 37 183042 758. sz 116 2^2 * 3^2 * 467 649944 1514. sz 116 2^2 * 3^2 * 5 674912 407. sz 116 2^2 * 3^2 * 5 561000 2208. sz 116 2^2 * 3^2 * 5 * 13 190620 1468. sz 116 2^2 * 3^2 * 5^3 * 3408058099731294299 918054 835. sz 116 2^2 * 3^2 * 61 778300 1004. sz 116 2^2 * 3^2 * 991 338250 2866. sz 116 2^2 * 3^3 171462 1162. sz 116 2^2 * 3^3 * 115133 652386 1993. sz 116 2^2 * 3^3 * 13 971280 1235. sz 116 2^2 * 3^4 760000 832. sz 116 2^2 * 3^4 * 151 722142 1099. sz 116 2^2 * 3^5 * 11 834312 1311. sz 117 2^2 * 3 338040 1463. sz 117 2^2 * 3 711800 1277. sz 117 2^2 * 3 * 1073491 346980 2708. sz 117 2^2 * 3 * 1087 834756 645. sz 117 2^2 * 3 * 11 * 13 * 41 273552 898. sz 117 2^2 * 3 * 19 * 37 * 269 652068 1160. sz 117 2^2 * 3 * 23 * 853 245274 1424. sz 117 2^2 * 3 * 23333 852264 1187. sz 117 2^2 * 3 * 281 435504 702. sz 117 2^2 * 3 * 29 * 443 118230 1680. sz 117 2^2 * 3 * 333271 228228 1231. sz 117 2^2 * 3 * 3347 125016 980. sz 117 2^2 * 3 * 35839 288144 1343. sz 117 2^2 * 3 * 37 * 1393326973 * 13825514861 710610 1215. sz 117 2^2 * 3 * 41 441450 1068. sz 117 2^2 * 3 * 5 Last complete status update: 2012-Jun-08 PS. Check below for some discussion about what it takes to lose the 3. Last fiddled with by schickel on 2012-07-21 at 06:31 Reason: Moving reserves to main reserve thread
 2011-09-22, 23:10 #2 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 10AB16 Posts [Old message at the bottom...] Code: 112350 2272. sz 117 2^2 * 3 * 5 * 11 * 71 594288 1962. sz 117 2^2 * 3 * 5 * 19 * 23 * 137 408408 576. sz 117 2^2 * 3 * 5 * 20297 997944 2058. sz 117 2^2 * 3 * 5 * 229 799512 421. sz 117 2^2 * 3 * 5 * 59 * 1409 516588 1126. sz 117 2^2 * 3 * 5 * 593 * 12176539883962932799 753372 1284. sz 117 2^2 * 3 * 61 313704 573. sz 117 2^2 * 3 * 853999 * 2705291 958056 647. sz 117 2^2 * 3^2 357792 1206. sz 117 2^2 * 3^2 * 111491 193320 986. sz 117 2^2 * 3^2 * 17 139056 2251. sz 117 2^2 * 3^2 * 44533 427704 1480. sz 117 2^2 * 3^2 * 5 559368 1873. sz 117 2^2 * 3^2 * 5 * 173 392340 1906. sz 117 2^2 * 3^2 * 5^4 477084 707. sz 117 2^2 * 3^3 * 19 574344 797. sz 117 2^2 * 3^3 * 5 * 103561 197310 1125. sz 117 2^2 * 3^3 * 5 * 2671 781302 2328. sz 117 2^2 * 3^3 * 5 * 9619 619800 1502. sz 117 2^2 * 3^4 * 5 353520 1009. sz 118 2^2 * 3 786720 977. sz 118 2^2 * 3 578760 1618. sz 118 2^2 * 3 * 101 * 110647 * 722321737 509832 1739. sz 118 2^2 * 3 * 31 * 42257 136192 622. sz 118 2^2 * 3 * 5 * 103 878752 1562. sz 118 2^2 * 3 * 5 * 7^2 893670 1174. sz 118 2^2 * 3 * 5146289 251580 1474. sz 118 2^2 * 3 * 67 233304 818. sz 118 2^2 * 3^2 927468 1292. sz 118 2^2 * 3^2 111426 1149. sz 118 2^2 * 3^2 * 11 * 13 * 6779 316960 1131. sz 118 2^2 * 3^2 * 29 * 467 768612 1943. sz 118 2^2 * 3^2 * 383 * 1933 547200 1441. sz 118 2^2 * 3^2 * 39317 708930 1343. sz 118 2^2 * 3^2 * 39461 * 7660223 474580 2321. sz 118 2^2 * 3^2 * 5 * 2377 799200 918. sz 118 2^2 * 3^2 * 5 * 71 * 1949 914760 2157. sz 118 2^2 * 3^2 * 5039 116040 1362. sz 118 2^2 * 3^3 * 19 * 29^2 * 53 * 1287989 922752 803. sz 118 2^2 * 3^3 * 5 * 13 * 47 753522 1597. sz 118 2^2 * 3^3 * 5 * 23 * 1223 531024 2662. sz 118 2^2 * 3^4 * 23 293496 857. sz 118 2^2 * 3^4 * 5 873528 561. sz 119 2^2 * 3 * 103 766560 1681. sz 119 2^2 * 3 * 11 * 17 * 47 * 331 787620 636. sz 119 2^2 * 3 * 19^2 * 71 * 2333 935008 1907. sz 119 2^2 * 3 * 2514737 533904 946. sz 119 2^2 * 3 * 41 * 769 394200 1372. sz 119 2^2 * 3 * 5^2 * 19 269688 2920. sz 119 2^2 * 3^2 * 13 * 71 838602 983. sz 120 2^2 * 3 643530 911. sz 120 2^2 * 3 * 1064685151 479136 2773. sz 120 2^2 * 3 * 11 558120 3407. sz 120 2^2 * 3 * 23 * 79 467016 4034. sz 120 2^2 * 3 * 281 557490 1239. sz 120 2^2 * 3 * 5 252588 1589. sz 120 2^2 * 3 * 5 * 103 * 2693 * 4856055876957941 308610 2389. sz 120 2^2 * 3 * 5 * 11 * 467 853740 551. sz 120 2^2 * 3 * 5 * 43 657816 1422. sz 120 2^2 * 3 * 653 277956 731. sz 120 2^2 * 3 * 7 * 13 * 643 * 6733 875520 1643. sz 120 2^2 * 3 * 7 * 71 * 257 * 997 * 6337 404868 1149. sz 120 2^2 * 3 * 800221 400158 1737. sz 120 2^2 * 3 * 911124659 623190 1551. sz 120 2^2 * 3^2 * 19 * 67 402780 439. sz 121 2^2 * 3 267102 654. sz 121 2^2 * 3 * 137 972720 1390. sz 121 2^2 * 3 * 1877 * 122029 * 504485371877 337008 592. sz 121 2^2 * 3 * 19 * 43 350994 959. sz 121 2^2 * 3 * 39610189 334548 809. sz 121 2^2 * 3 * 5 * 157 344136 889. sz 121 2^2 * 3^2 693812 1094. sz 121 2^2 * 3^2 * 19 * 77291 378642 1295. sz 121 2^2 * 3^2 * 5 227160 1294. sz 121 2^2 * 3^2 * 661 342216 1646. sz 121 2^2 * 3^5 * 2687 894456 441. sz 122 2^2 * 3 * 11 515064 1728. sz 122 2^2 * 3 * 11357029 201048 695. sz 122 2^2 * 3 * 13 * 412967 236840 722. sz 122 2^2 * 3 * 19 315780 405. sz 122 2^2 * 3 * 47 * 16573 438462 419. sz 122 2^2 * 3 * 5 230520 414. sz 122 2^2 * 3 * 5 * 29 716130 1911. sz 122 2^2 * 3 * 8200463933 448224 729. sz 122 2^2 * 3^2 497928 3332. sz 122 2^2 * 3^2 79584 1451. sz 122 2^2 * 3^2 * 11 * 23 981960 512. sz 122 2^2 * 3^2 * 12497 * 843811 662850 3663. sz 122 2^2 * 3^2 * 13 175602 561. sz 122 2^2 * 3^3 * 41 * 313 * 3187 * 6353 * 11117 * 201511 122508 1838. sz 122 2^2 * 3^3 * 5009 911484 401. sz 123 2^2 * 3 * 10037 178002 2070. sz 123 2^2 * 3^3 * 5 61116 1655. sz 124 2^2 * 3 767520 4433. sz 124 2^2 * 3 * 11 * 151 827880 1228. sz 124 2^2 * 3^2 985080 410. sz 125 2^2 * 3 494808 716. sz 125 2^2 * 3 919386 1065. sz 125 2^2 * 3 * 11 469812 3179. sz 125 2^2 * 3 * 1231 904188 2830. sz 125 2^2 * 3 * 17 * 107 * 9109 363126 1579. sz 125 2^2 * 3 * 19 938250 1967. sz 125 2^2 * 3 * 5 * 1013 * 30941 122688 1477. sz 125 2^2 * 3 * 5 * 181 * 300721 523044 1529. sz 125 2^2 * 3 * 5 * 58481 * 41557478047 462168 928. sz 125 2^2 * 3 * 5 * 59 795912 2455. sz 125 2^2 * 3 * 5 * 7 * 19^2 * 89 * 397 761516 1447. sz 125 2^2 * 3 * 5^2 * 11 * 673 996252 1758. sz 125 2^2 * 3 * 578861 336990 1354. sz 125 2^2 * 3^2 * 11 * 31019 980784 1188. sz 125 2^2 * 3^2 * 149 * 8218961 159846 857. sz 125 2^2 * 3^2 * 17 * 53 * 271 * 3529 170748 1565. sz 125 2^2 * 3^2 * 5 * 7 * 41 * 43 * 317 * 373 836244 1762. sz 125 2^2 * 3^2 * 7 * 31 * 2905087 * 3354133 116688 1237. sz 125 2^2 * 3^3 917790 2507. sz 125 2^2 * 3^3 * 5 * 7 * 342521 530640 3465. sz 126 2^2 * 3 * 149670900061 228150 881. sz 126 2^2 * 3^2 * 5 * 175753 509928 4524. sz 127 2^2 * 3 168912 2014. sz 127 2^2 * 3 * 47 * 2311 837480 1466. sz 127 2^2 * 3 * 47 * 6113 * 431567 511440 719. sz 127 2^2 * 3 * 5 * 89 161064 1786. sz 128 2^2 * 3 * 17 * 577 158814 3458. sz 130 2^2 * 3 * 17 * 3529 794184 1820. sz 130 2^2 * 3 * 5360837011597 129336 1923. sz 130 2^2 * 3^2 * 29 * 7949 102360 430. sz 130 2^2 * 3^3 * 109 * 131 * 194463079493 181650 1951. sz 131 2^2 * 3 259704 4605. sz 132 2^2 * 3 * 16607 * 22532987 381510 916. sz 132 2^2 * 3^2 * 5 * 683 * 737766131 643760 1373. sz 134 2^2 * 3 * 29^2 * 251 805686 472. sz 134 2^2 * 3 * 41 854418 404. sz 134 2^2 * 3 * 67 * 251 * 2809691 223692 1359. sz 135 2^2 * 3^2 * 491 715776 1941. sz 136 2^2 * 3 * 11 * 13 * 19 20076 3403. sz 136 2^2 * 3 * 50828150957 38880 1139. sz 138 2^2 * 3 425280 665. sz 138 2^2 * 3 * 61 * 787 * 82781 84054 1099. sz 139 2^2 * 3 * 5 128136 499. sz 139 2^2 * 3 * 5 * 118860961 52374 2535. sz 139 2^2 * 3^3 * 5 56928 1003. sz 140 2^2 * 3 * 17 * 766169 611156 5703. sz 144 2^2 * 3^2 * 167 * 6047 * 7451 998088 1304. sz 145 2^2 * 3^2 39060 1123. sz 147 2^2 * 3 * 17 * 29 940050 1624. sz 152 2^2 * 3^3 * 1163 890460 898. sz 156 2^2 * 3 * 53 * 103 Last complete update: 2012-Jun-08 Reserving 199710. Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info. Last fiddled with by schickel on 2012-07-21 at 06:35 Reason: Moving reservations to main thread...
2011-09-23, 02:30   #3
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 Originally Posted by Mini-Geek Reserving 199710. Are we deleting once reserved, or adding a reservation tag? For now, I'll add a reservation tag, as it's easier to delete than to recover the info.
That'll work for now. We'll have to see how the project goes....

 2011-09-23, 10:34 #4 RobertS     Aug 2009 somewhere 197 Posts Reserving 321660
2011-09-23, 11:25   #5
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10AB16 Posts

Quote:
 Originally Posted by schickel PS. Clifford has mentioned the required form for a factorization to result in losing the 3, but I'm haven't been able to find that email yet....
On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.

2011-09-23, 15:40   #6
10metreh

Nov 2008

44228 Posts

Quote:
 Originally Posted by Mini-Geek On this sort of subject: My driver has become 2^2 * 3^3. Is this significantly worse to get out of than 2^2 * 3? I'm wondering if that's why only 2^2 * 3^1 is listed.
I think it has the same conditions; it isn't included because we don't the top post to become huge.

2011-09-23, 21:46   #7
schickel

"Frank <^>"
Dec 2004
CDP Janesville

212210 Posts

Quote:
 Originally Posted by 10metreh I think it has the same conditions; it isn't included because we don't the top post to become huge.
A quick count shows that there are >600 sequences with some combination of 2^2 * 3, either alone or with other factors, but without a 7.

This is the highest power of 3 right now:
Code:
940224  1734. sz 113 2^2 * 3^9
For those following along at home, I'll post an updated status file on everything open later this afternoon.....

 2011-09-23, 23:02 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×33×132 Posts I'll take 611156 (i4327), 960096 (i2655) and 378756 (i2911).
 2011-09-24, 02:59 #9 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 10AB16 Posts Escape from 2^2*3 to 2^2 successful at 118 digits! http://factordb.com/sequences.php?se=1&aq=199710 It's now on a slow downward-ish slide, hopefully it will become the downdriver!
 2011-09-24, 03:32 #10 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·33·132 Posts Don't forget - 3 comes and goes... See for example 611156.
2011-09-24, 03:40   #11
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 Originally Posted by schickel For those following along at home, I'll post an updated status file on everything open later this afternoon.....
As promised, here is a current status file for everything.....I left it sorted by sequence this time.

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