Factores primos de Gúgolplex + 10 con 67 dígitos

Alpertron
Teoría de números
Factores primos de Gúgolplex + 10 con 67 digitos

Esta es una lista de factores primos de 67 dígitos de gúgolplex + 10, es decir, 10^{10^100} + 10.

Estos números tienen la forma 1 + 2k ∏_i p_i^e_i, donde p_i es un factor primo de 10¹⁰⁰ − 1 y e_i es cero o uno.

La lista de factores primos de 10¹⁰⁰ − 1 es: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 y 168058 8011350901.

En esta lista se pueden ver los factores primos, sus descubridores y los valores de k.

1003828 9709999874 3017016983 6982983016 3017016983 6983986845 2727016859 (David Broadhurst, k=21)
1004412 4627795277 2381130973 2564554404 2944820304 2700393820 3971728407 (Phil Carmody, k=2207)
1005323 2242652675 2198833453 9140079376 1553752673 2282629765 1855339477 (Norm Dresner, k=12646)
1006834 7890830606 0000000000 0000000000 0000000000 0001006834 7890830607 (Phil Carmody, k=1261)
1010468 2227846069 4689334216 1373923253 9177995002 6273503686 7690101641 (Patrick Demichel, k=1879980)
1010757 2345389956 3424366654 6725994153 6696444537 5475705840 4128238299 (David Broadhurst, k=1)
1021391 9104645708 7766545819 7836916808 5635477665 4580956977 2576210647 (Patrick Demichel, k=47023)
1022244 1390119111 4306425622 8805583430 5606660743 9235191766 9516785699 (Patrick Demichel, k=103523)
1022952 8134701817 8721500388 1278499611 8721500388 1279522564 6856202207 (David Broadhurst, k=1)
1025322 6401270423 2008410993 2008410993 2008410993 2007385670 5607140571 (David Broadhurst, k=15)
1029804 7991262191 7953311552 9772833637 5696438271 1786687734 1978470371 (Patrick Demichel, k=1038845)
1031206 7378987278 1003924726 6911163707 4261656627 4192966348 2916936773 (Patrick Demichel, k=205042)
1031446 5814846990 4725587475 4284276194 4961186746 6899240714 1091608211 (David Broadhurst, k=55)
1035588 0711289032 6883192329 6574134958 6680263674 5962802286 7881983769 (Patrick Demichel, k=560548)
1036468 5983246375 4305540098 1021580998 3505761016 0456621365 3500092607 (Patrick Demichel, k=1957531)
1037962 0732492711 1733272496 2345510771 9509110543 7901741483 7473803729 (David Broadhurst, k=8)
1039013 8458957838 9362111079 8198727183 2590949048 3036985941 6533048077 (David Broadhurst, k=62)
1044688 4440941597 1106320184 7121063147 1314129245 0199244704 0055589727 (John Gamble, k=16591)
1050500 2943857020 5458434575 4541565424 5458434575 4542615924 8402291597 (David Broadhurst, k=2)
1051099 2498107963 5076035805 0191302715 3148135161 2077773356 6541961971 (Patrick Demichel, k=197265)
1069386 9188255924 6711705101 4518789138 1852006053 6805858595 9214998727 (Paul Leyland, k=34787)
1073700 3308827713 3727039965 3727039965 3727039965 3725966265 0418212253 (David Broadhurst, k=2)
1083184 0897616963 0610535327 2895231427 0717444850 1561738819 1055226819 (Phil Carmody, k=653)
1088730 2822758863 4464910302 7550294162 7747344649 1029186772 6593518611 (Phil Carmody, k=2035)
1090497 1064138169 0236035050 6872854345 2233305207 6760818827 9047408213 (Patrick Demichel, k=987826)
1090867 8372472811 3785023490 3656790880 7677932148 3935750095 2408338081 (John Gamble, k=15280)
1091824 5041095320 5138091395 7446466879 1690168725 8140480444 3798690699 (Phil Carmody, k=2221)
1091859 0785712872 9498833053 1195287740 3672172881 0969308915 0943454247 (Phil Carmody, k=1061)
1103091 8526756494 3909961425 3829254331 3862875609 2809193622 7080116653 (Patrick Demichel, k=1188062)
1103838 7859832884 2288121388 6521382612 9451729315 3090430412 7301412619 (David Broadhurst, k=1)
1108989 5976028887 1292785195 1134257234 3841327580 5530220176 2351373209 (David Broadhurst, k=4)
1110837 5826015915 2513929519 4932637187 3370341527 3713606502 7121917049 (David Broadhurst, k=68)
1116985 8287392812 0000000000 0000000000 0000000000 0001116985 8287392813 (Patrick Demichel, k=1806154)
1118332 3937446179 2181286251 7296532008 2940217869 5635897830 8586780049 (David Broadhurst, k=56)
1122723 6788758706 3252454179 6743333442 2031408126 7856620311 8995237211 (Patrick Demichel, k=353885)
1130607 9235033129 8693005341 6013571920 0082666079 3595774390 2967888059 (Norm Dresner, k=11293)
1131903 5063038044 3971432442 6202632443 8265732769 4646702134 5139763167 (Patrick Demichel, k=7267)
1132716 5998365812 5921521810 5149726505 4985439719 2991098567 9145938619 (Phil Carmody, k=2511)
1138845 2972371463 6466039553 1725388077 0200053632 8761147325 6296625331 (Phil Carmody, k=455)
1143703 9929056826 3465541289 6534458710 3465541289 6535602414 3394598117 (Norm Dresner, k=13162)
1146581 3212070451 9714326881 0644828382 9130495410 0385525407 5396455371 (Phil Carmody, k=145)
1146606 6525914099 5878380175 0243309029 5556849692 8925446735 5286132379 (Norm Dresner, k=13891)
1150424 2572147914 7258066577 8864294114 9473004765 2711137622 5142771689 (Phil Carmody, k=188)
1152080 1203197244 1171523092 3501432575 1131391420 0324867329 1753618041 (Patrick Demichel, k=645220)
1154435 7124376702 0320236033 5707450693 7715620469 7699254203 5426676263 (David Broadhurst, k=29)
1156505 5256144003 0788896107 3338696904 1466186943 9871404940 4536736169 (David Broadhurst, k=4)
1157258 5556893787 2153918942 1602109332 5381617329 4744309134 4960678131 (Patrick Demichel, k=1677355)
1158474 4803368843 5126009596 9400410705 6313893184 3483591965 8570512463 (David Broadhurst, k=1)
1166976 2076519921 3754903287 6484343454 1819637947 4391342887 1472085527 (Phil Carmody, k=667)
1168091 8655487990 6813590292 6813590292 6813590292 6812422200 8158102303 (David Broadhurst, k=39)
1173526 9738034376 2048730530 8355323704 7409365358 7077935475 7691923889 (David Broadhurst, k=8)
1177926 5813223080 1873536570 9934187776 0047914264 5457585071 9666439463 (David Broadhurst, k=11)
1179948 7681023286 6712877723 6433993261 4920049038 3843171878 4609543681 (Phil Carmody, k=1280)
1184887 7290083366 0769148105 2018732579 2821407691 4809335299 5967844849 (David Broadhurst, k=8)
1193673 2309129043 0429658970 2730749361 6178090946 9302512714 8822556441 (Patrick Demichel, k=6820)
1196203 2372352166 1852295157 2570221886 0895922374 1079041595 1228970619 (Patrick Demichel, k=58391)
1196819 6475259635 1733397755 3872695636 7188599405 6905816010 8944985957 (David Broadhurst, k=2)
1196905 9684657153 4941558463 1735203636 1292985030 1500615131 8914737117 (Phil Carmody, k=222)
1197445 6601655440 1782178217 8217821782 1782178217 8219019227 8383833659 (Patrick Demichel, k=1693739)
1199752 1921071815 7396259799 5894313537 1760980394 9454595662 2160964933 (David Broadhurst, k=2)
1200479 2144975701 6469237131 9409310170 8338541218 6059370140 1219484211 (Patrick Demichel, k=73685)
1200928 0722087470 5154406851 2159212810 5107948455 9313677479 7996861451 (David Broadhurst, k=25)
1206631 7747580677 2995218612 7577154587 8914309155 9960136143 1648161543 (David Broadhurst, k=7)
1207974 8583239697 4151738962 1859309106 8977781790 0924093394 9622052087 (Patrick Demichel, k=402817)
1217652 0039820068 9285744215 8194213783 6995035507 4043193870 1440774903 (Paul Leyland, k=37349)
1218374 0191249560 8772493693 1972857920 0464514592 3653470054 6579350877 (Phil Carmody, k=238)
1224738 5098533572 6613980894 5902416650 0125184417 3113073678 6969793129 (Phil Carmody, k=364)
1229094 0355519027 4965345669 3929489095 6877696267 0023877531 5326958117 (David Broadhurst, k=38)
1230505 8376893490 4313352072 0822635068 1657930377 9305317240 8855974579 (Patrick Demichel, k=111463)
1233218 4975401744 9159082418 6393737002 0025457354 1646962699 8265530237 (Phil Carmody, k=2306)
1238392 7006921494 4308467768 1901023697 7090095168 7047280850 4448645859 (Patrick Demichel, k=7253)
1241910 4562445420 1009015031 8990984968 1009015031 8992226878 5571460453 (David Broadhurst, k=2)
1254294 4067702962 2910052650 8567959362 2544667715 4981087003 1945726197 (Patrick Demichel, k=629662)
1259680 5839366160 7199452865 3635381042 0486432070 5118708030 6462933041 (David Broadhurst, k=40)
1259849 4256165893 1485148514 8514851485 1485148514 8516111334 5741314409 (Norm Dresner, k=12596)
1261450 6019536294 0066494762 4583659850 1866363448 1947402089 0616478573 (David Broadhurst, k=2)
1262144 3201824166 0391339626 9017220187 0211729419 9369381016 8112807051 (John Gamble, k=14425)
1262672 0098250304 8554827546 4321380511 2468663348 4973358342 0172852183 (Patrick Demichel, k=162907)
1264640 6573845075 6057981712 8411572890 3293960698 6053606883 5054922571 (Patrick Demichel, k=2564495)
1268134 6597385011 4449500949 4590950772 1757776652 0532580370 4997367379 (Patrick Demichel, k=206211)
1269475 3144509513 2149082652 3695272082 7699757854 4627603841 0427403849 (Patrick Demichel, k=82868)
1274081 2636102767 9712258401 3392449267 7243082993 0906199842 2674289213 (Phil Carmody, k=1066)
1277646 9173006662 5898117509 5940918399 4545859465 1701282246 2618539281 (Patrick Demichel, k=94760)
1286899 2488094749 1768705915 6885800604 0621873027 5056237299 2038266811 (Phil Carmody, k=1285)
1289865 9978254184 3840362793 6159637206 3840362793 6160927072 3818616979 (David Broadhurst, k=49)
1297883 3327574741 0785171826 6311540029 6649474064 1938062626 4873783863 (Patrick Demichel, k=110749)
1304283 7321895552 9142385646 7230035049 1134417519 2328332359 0067502047 (David Broadhurst, k=11)
1306275 1004725266 4092077665 8895471411 3563747874 2046998041 7062340133 (David Broadhurst, k=2)
1312637 9081683946 4020170335 9096112347 4880351680 2153288282 8871759133 (Patrick Demichel, k=599314)
1317764 4960592691 7754138394 5006181755 9275767443 9029230614 0160206481 (Phil Carmody, k=3640)
1321938 1864714304 6857500107 7067226602 3313798671 7906471370 4208479201 (Patrick Demichel, k=100400)
1326564 1907053162 4255101916 2928793349 5866860262 0484137421 5074739611 (Phil Carmody, k=535)
1332263 8370477189 8046191072 8839951301 0297448987 8070099561 9707832957 (Patrick Demichel, k=20066)
1333127 3636031579 0990853242 9009146757 0990853242 9010479884 4626884823 (David Broadhurst, k=1)
1333812 9349486290 0280463370 0280463370 0280463370 0279129557 0930977081 (Phil Carmody, k=1180)
1343921 1053500586 9806103249 7770852327 9924931330 8976453238 2374782933 (David Broadhurst, k=2)
1348076 1508389140 8061256963 5389798130 4729444566 0081874619 0104023077 (Phil Carmody, k=986)
1349961 9756872335 3653133168 8165931313 0048371853 7520276763 7950335567 (David Broadhurst, k=1)
1359370 2838330924 9311297918 8491036391 4840655399 7897619563 1806347459 (Phil Carmody, k=181)
1366054 1283839781 3599321568 0079684581 5697824807 3117620448 5182632383 (Patrick Demichel, k=2326049)
1374914 8500617507 1287652780 8712347219 1287652780 8713722133 9788270289 (David Broadhurst, k=8)
1375352 7080544280 7022255616 3574218557 1982102768 7198557010 9970221211 (Patrick Demichel, k=822185)
1385976 6895101194 8883652070 8293554354 5891251531 1964117820 8605551489 (David Broadhurst, k=64)
1387123 7590551995 3818110713 5365503708 2590834450 5745808617 4786793291 (David Broadhurst, k=95)
1392102 1915288105 3311658876 1703437457 5351533116 5886224932 1830465411 (Patrick Demichel, k=91295)
1394371 1950496812 4047355925 0189303505 1915798563 9782065612 2590980437 (Phil Carmody, k=1162)
1398628 0220397642 4429244292 4429244292 4429244292 4427845664 4208846651 (Phil Carmody, k=275)
1399684 9629680988 7067217067 8175804575 8819344630 8811503043 7455940527 (David Broadhurst, k=7)
1400814 9933489285 3630476777 5865205490 5953732630 2347030924 1474816133 (Patrick Demichel, k=1884766)
1406231 9656107892 2298375224 3413879932 4570404308 7822498362 7290360397 (Patrick Demichel, k=56026)
1408956 2204157930 8933232955 7989362143 4068674829 4362357701 5836635211 (David Broadhurst, k=5)
1411250 7381412039 4257380759 1448680704 0587391907 0460424561 5754697693 (Patrick Demichel, k=109262)
1413309 0956126627 2489188571 2082384800 1879724891 8855707514 7523892171 (Patrick Demichel, k=62395)
1414268 3070276933 4588004108 3417782452 0973368474 8667865611 9130589659 (Patrick Demichel, k=41311)
1415099 3410023594 3667456348 3574964393 0683436674 5633420650 3029283241 (Phil Carmody, k=380)
1422559 4167994382 2772277227 7227722772 2772277227 7229145331 6940271611 (David Broadhurst, k=5)
1425362 6203887698 3384041975 7806352732 7527468270 6012098684 8733939139 (Patrick Demichel, k=162629)
1432534 5988051143 5048222489 2148544014 1226049517 7749645979 9610536597 (David Broadhurst, k=2)
1438345 6934319982 1038797490 7104909649 3362822360 7457021561 0321128407 (Patrick Demichel, k=356627)
1439517 0333671643 7855546410 8876607392 3326869600 8186873470 1189871493 (Patrick Demichel, k=275182)
1439618 1256742257 2869353742 7130646257 2869353742 7132085875 4126096001 (Patrick Demichel, k=8000)
1447733 4567685834 7286742174 0302894626 2151875815 2832275843 8262790583 (David Broadhurst, k=7)
1449341 1776387789 7762187753 5857574652 5350172597 9276304210 6191260689 (David Broadhurst, k=8)
1449475 4113096647 1129492704 2810347980 4639688705 0728122421 1088856957 (David Broadhurst, k=2)
1450619 8271825183 7759502135 5640418812 6089370294 4573940865 4635861813 (David Broadhurst, k=34)
1455480 2895369704 2852187193 1169048818 0432690673 2662079317 7683645779 (David Broadhurst, k=49)
1457150 8167529373 2017393492 7402172250 7930293422 9042271768 4662829327 (Patrick Demichel, k=563237)
1468479 6636180817 4720438417 1133707104 5917589878 8196455762 6217936019 (David Broadhurst, k=1)
1470998 7827205799 2340261538 0369467506 9320357638 9031049466 1110187053 (Patrick Demichel, k=60874)
1473601 5745095647 7863451309 1082156917 0444273591 5995029663 3919024321 (Phil Carmody, k=160)
1475236 8657833658 1024434869 4196471915 8366523597 2070499602 6242288859 (David Broadhurst, k=13)
1477464 4075533437 6648131850 3859347226 5013050903 3136543896 9120863339 (Patrick Demichel, k=48743)
1480339 9476114436 7564345251 2435654748 7564345251 2437135088 7040459689 (Patrick Demichel, k=815596)
1484160 7907416076 3857542260 0061527306 2240264677 2705729558 2278926491 (Patrick Demichel, k=26215)
1493496 7465673880 5621530162 2756842602 0819692578 9378370435 3158170681 (Patrick Demichel, k=5660)
1494801 2936669764 0397969994 0849950241 2496311375 1053463223 8855338917 (Phil Carmody, k=166)
1497207 1806230050 5812609478 7067481401 5073235036 3175669899 7686723091 (David Broadhurst, k=5)
1499124 6911952796 6247861449 9713996908 1387303681 0469469895 0013199491 (Phil Carmody, k=19005)
1501613 4661260221 4383636169 6228379992 3320944270 9866818873 8832359081 (David Broadhurst, k=60)
1506086 6964853856 4591988740 6544809144 9010757548 3038464090 7792927259 (Patrick Demichel, k=97883)
1516260 8559722176 7043862840 1470643044 0453495276 3798723283 3260907197 (David Broadhurst, k=2)
1525582 1869209295 4565946072 8789553605 8156401129 9384177197 4760489663 (Phil Carmody, k=2401)
1542061 5869943849 8202576203 6041929504 8517982025 7618818357 7080541331 (David Broadhurst, k=5)
1552917 8408912069 5906343828 9568989826 2062097887 4619105940 9112900731 (Patrick Demichel, k=1922785)
1557111 5178770936 6088915664 0282308818 7911576461 7088809379 8547839899 (David Broadhurst, k=1)
1558609 4518774236 7501924423 6988849440 2967224501 9007346203 8558526651 (David Broadhurst, k=25)
1560574 8176156889 5893069062 9758433733 9122091201 6068083623 0655401663 (Phil Carmody, k=437)
1561145 0801861779 6461372180 5244816900 9498481316 7373432337 2101089167 (David Broadhurst, k=1)
1566678 8950327001 1222887771 1222887771 1222887771 1221321092 2272560771 (Phil Carmody, k=4615)
1570941 1377104112 3775527294 5970755540 0657405882 7628287172 7921922383 (David Broadhurst, k=1)
1572828 4886011227 5340436959 5340436959 5340436959 5338864131 0454425733 (David Broadhurst, k=2)
1576497 8764548540 6276309874 8338153330 7804448311 3314581874 6334949063 (David Broadhurst, k=7)
1593069 9357965087 1291522740 9215952306 4313426062 6376084746 9577857331 (David Broadhurst, k=5)
1594133 6425685449 5778803405 9234803608 6557326216 6468852935 5532934251 (Patrick Demichel, k=1291625)
1599174 7953953780 9516698475 9328666228 8500752297 4017547849 4014115527 (Patrick Demichel, k=76351)
1602743 8237440743 7211184691 3913073025 9800854111 1223784123 2339333289 (Phil Carmody, k=156)
1605229 3390239206 4974165035 4999624099 0925297393 1736792418 4254517699 (Patrick Demichel, k=1375581)
1605338 5595796633 3907828846 4574059974 0281100505 8309546612 3996728757 (Patrick Demichel, k=181666)
1606054 3458028542 0000000000 0000000000 0000000000 0001606054 3458028543 (David Broadhurst, k=69)
1606387 8249555210 6639845254 0556199163 7282072507 5796152509 9050326543 (Patrick Demichel, k=6377)
1607391 1569956306 6316736567 9643896366 5957674322 7440049605 5755946299 (Phil Carmody, k=113)
1614942 3395223458 5907927153 1502517859 3516477261 0895518264 6572529889 (Phil Carmody, k=3248)
1619870 5707461240 4586696457 9716260278 2663385526 5080613365 9183096289 (Patrick Demichel, k=1081264)
1622663 7280458527 2480087411 8783407774 8308742982 6921383352 1678842743 (Patrick Demichel, k=1629019)
1631680 7383282744 7566044488 4333852865 8124343881 7625079879 1081166721 (Patrick Demichel, k=21440)
1638012 4429948123 1148497631 1811759298 0319806307 0270133205 3533368939 (Phil Carmody, k=203)
1638664 1170834209 9537207567 6805075316 6411093926 8171482584 0227390979 (Phil Carmody, k=131)
1639532 9648733558 5100057180 1691510347 8253914853 0865709405 5901849757 (David Broadhurst, k=2)
1656850 0723882066 9424121695 0380296993 8428105758 7828839346 9576733653 (Patrick Demichel, k=1153774)
1657205 3009938358 2152438793 5498119465 8925621524 3877697775 8936650899 (David Broadhurst, k=1)
1663639 3032524205 8554612139 7874983575 0689407363 5831202459 5722923691 (Patrick Demichel, k=95905)
1671676 4423283474 3108668072 2155328262 7241035288 0568679177 8182054493 (David Broadhurst, k=2)
1674786 2617517055 8631003062 6817087088 6554925752 2615350356 7206886343 (Patrick Demichel, k=1442351)
1676106 9811712030 1258832581 8741167418 1258832581 8742843525 1070544613 (David Broadhurst, k=14)
1680960 6150582124 1625957415 6095217301 4515459553 9181689412 1291201851 (Phil Carmody, k=1225)
1683092 2871122102 4100653482 6099794141 1780041006 5346577905 6542995699 (David Broadhurst, k=1)
1686325 5324851780 6818371295 3181628704 6818371295 3183315030 2143223077 (Phil Carmody, k=3758)
1688210 2136439044 7157860692 3094115672 3890928421 3929080848 6296322047 (Patrick Demichel, k=385677)
1689681 2748107867 6022389299 7584364436 9476400861 3430278194 2420686499 (Phil Carmody, k=1311)
1692556 2301703936 0004350658 3936792820 0171256262 9630448357 8265903063 (Patrick Demichel, k=57709)
1699982 1636803059 2683039290 8729769022 1162871693 5921611244 1313383837 (Patrick Demichel, k=318042)
1722847 3548869214 0451871063 5591605622 8778095427 8013723977 7922509477 (Patrick Demichel, k=836666)
1731524 8763105423 9774937736 4820992447 7078476779 0938761975 2796208583 (Patrick Demichel, k=595417)
1741754 8634514578 3146855787 5698956905 4823143660 1233568568 1479668931 (Patrick Demichel, k=240385)
1743693 7090355492 3260844245 5200412638 7248132310 6106467408 7886515291 (David Broadhurst, k=5)
1744975 5536090189 3164992746 0665725544 8104511223 2967432251 4500653659 (David Broadhurst, k=1)
1745208 0436107455 0113705107 7418628149 0680257930 4851463419 6626203103 (Patrick Demichel, k=138241)
1747450 4810335843 3874148676 3293718592 3821447832 3956794577 6139811463 (Patrick Demichel, k=594579)
1748056 1788503784 5644620693 5755670000 2438693896 4059641373 0311122197 (David Broadhurst, k=2)
1750250 6541194735 0324779890 2019874894 1715296515 9583627258 5607820727 (Phil Carmody, k=757)
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