Why a(17115) = 3377464733 is the last term ------------------------------------------ The candidates for a(17115+1) are enumerated together with their factorizations, or, if prime, with their position where they were obtained earlier (there are three such cases). The factorizations were calculated by using Dario Alpertron's Elliptic Curve Method applet: http://www.alpertron.com.ar/ECM.HTM ---------| 337746473_ ---------- 3377464731 = 3 * 3 * 375273859 3377464737 = 3 * 107 * 10521697 3377464739 = 11 * 23 * 269 * 49627 (omitting last digit = 0|2|3|4|5|6|8) --------|- 33774647_3 ---------- 3377464703 = a(17107) -- prime 3377464713 = 3 * 3 * 7 * 43 * 1246757 3377464723 = a(17108) -- prime 3377464743 = 3 * 1125821581 3377464753 = 13 * 259804981 3377464763 = 22993 * 146891 3377464773 = 3 * 4721 * 238471 3377464783 = 7 * 11 * 17 * 2580187 3377464793 = 73 * 46266641 -------|-- 3377464_33 ---------- 3377464033 = 29 * 293 * 397489 3377464133 = 47 * 71860939 3377464233 = 3 * 11 * 13 * 23 * 342299 3377464333 = 197 * 17144489 3377464433 = 7 * 482494919 3377464533 = 3 * 3 * 3 * 3 * 3 * 71 * 195761 3377464633 = 673 * 5018521 3377464833 = 3 * 19 * 59253769 3377464933 = a(17114) -- prime ------|--- 337746_733 ---------- 3377460733 = 89 * 127 * 131 * 2281 3377461733 = 8443 * 400031 3377462733 = 3 * 3 * 375273637 3377463733 = 7 * 31 * 15564349 3377465733 = 3 * 41 * 27459071 3377466733 = 19 * 383 * 464129 3377467733 = 107 * 31565119 3377468733 = 3 * 379 * 2970509 3377469733 = 11 * 11 * 11 * 2537543 -----|---- 33774_4733 ---------- 3377404733 = 37 * 91281209 3377414733 = 3 * 7 * 11 * 29 * 227 * 2221 3377424733 = 41 * 59 * 1396207 3377434733 = 293 * 2393 * 4817 3377444733 = 3 * 3 * 13 * 3559 * 8111 3377454733 = 47 * 53 * 1355863 3377474733 = 3 * 1801 * 625111 3377484733 = 7 * 482497819 3377494733 = 31 * 103 * 1057781 ----|----- 3377_64733 ---------- 3377064733 = 7 * 1487 * 324437 3377164733 = 17 * 613 * 324073 3377264733 = 3 * 3 * 3 * 193 * 739 * 877 3377364733 = 263 * 283 * 45377 3377564733 = 3 * 83 * 13564517 3377664733 = 61 * 733 * 75541 3377764733 = 7 * 67 * 7202057 3377864733 = 3 * 7669 * 146819 3377964733 = 11 * 13 * 13 * 1817087 ---|------ 337_464733 ---------- 3370464733 = 8461 * 398353 3371464733 = 7 * 13 * 239 * 155017 3372464733 = 3 * 11 * 79 * 1293619 3373464733 = 31 * 5839 * 18637 3374464733 = 19 * 177603407 3375464733 = 3 * 3 * 17 * 22061861 3376464733 = 103 * 32781211 3378464733 = 3 * 7 * 23 * 6994751 3379464733 = 6397 * 528289 --|------- 33_7464733 ---------- 3307464733 = 17 * 5741 * 33889 3317464733 = 11 * 19 * 19 * 37 * 67 * 337 3327464733 = 3 * 11863 * 93497 3337464733 = 5113 * 652741 3347464733 = 167 * 20044699 3357464733 = 3 * 3 * 7 * 53293091 3367464733 = 1783 * 1888651 3387464733 = 3 * 173 * 509 * 12823 3397464733 = 13 * 261343441 -|-------- 3_77464733 ---------- 3077464733 = 7 * 439637819 3177464733 = 3 * 3 * 3 * 117683879 3277464733 = 8689 * 377197 3477464733 = 3 * 17 * 29 * 41 * 57347 3577464733 = 353 * 929 * 10909 3677464733 = 23 * 159889771 3777464733 = 3 * 7 * 7 * 25697039 3877464733 = 367 * 10565299 3977464733 = 11 * 983 * 367841 |--------- _377464733 ---------- 1377464733 = 3 * 3 * 23 * 127 * 151 * 347 2377464733 = 7 * 339637819 4377464733 = 3 * 89 * 16394999 5377464733 = 9029 * 595577 6377464733 = 29 * 47 * 47 * 113 * 881 7377464733 = 3 * 2459154911 8377464733 = 11 * 761587703 9377464733 = 7 * 13 * 13 * 73 * 108587 |---------- _3377464733 ----------- 13377464733 = 3 * 43 * 103701277 23377464733 = 7 * 7 * 477091117 33377464733 = 61 * 2063 * 265231 43377464733 = 3 * 14459154911 53377464733 = 47 * 179 * 6344641 63377464733 = 11 * 2081 * 2768663 73377464733 = 3 * 3 * 3 * 2717683879 83377464733 = 17 * 683 * 7180903 93377464733 = 7 * 19 * 23 * 29 * 89 * 11827 -- Apr 20 2011, Reinhard Zumkeller -- reinhard.zumkeller@gmail.com