Known 20-digit prime factors of Googolplex + 10

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Number Theory
Known 20-digit prime factors of Googolplex + 10

This is a list of known 20-digit prime factors of googolplex + 10, i.e., 10^{10^100} + 10.

These numbers have the form 1 + 2k ∏_i p_i^e_i, where p_i is a prime factor of 10¹⁰⁰ − 1 and e_i is zero or one.

The list of prime factors of 10¹⁰⁰ − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

1016893883 1019335571 (Patrick Demichel, k=215915)
1027909103 1023975053 (David Broadhurst, k=2)
1029303441 4591586179 (Patrick Demichel, k=1480671)
1031544921 3671830339 (David Broadhurst, k=31)
1049345044 0980479677 (David Broadhurst, k=2)
1061112244 8334248343 (Patrick Demichel, k=1540109)
1062017919 7119800263 (David Broadhurst, k=9)
1076069219 9887950409 (Patrick Demichel, k=2025476)
1079135916 8819853983 (David Broadhurst, k=1)
1089077278 5939393007 (David Broadhurst, k=1)
1089293757 0567495539 (Patrick Demichel, k=8089)
1091625997 4261909357 (Phil Carmody, k=178)
1108714104 6935566339 (David Broadhurst, k=1)
1115418492 9782490487 (David Broadhurst, k=1)
1129317460 6641884533 (Phil Carmody, k=4274)
1133992286 4793975343 (David Broadhurst, k=1)
1163057527 8822378691 (Patrick Demichel, k=131005)
1198777746 4164041797 (Phil Carmody, k=162)
1219923995 2391390077 (David Broadhurst, k=2)
1229096607 2044855933 (David Broadhurst, k=2)
1235007156 4400558291 (Patrick Demichel, k=528095)
1236816344 7991018207 (David Broadhurst, k=7)
1252091980 2753277807 (David Broadhurst, k=1)
1259395041 1192734167 (David Broadhurst, k=53)
1277775261 1671955841 (Phil Carmody, k=320)
1281791268 9965031893 (Phil Carmody, k=206)
1289229952 1529598237 (David Broadhurst, k=2)
1294337051 9833731209 (Patrick Demichel, k=6244)
1295456186 6106552721 (Patrick Demichel, k=1507240)
1302701923 5666995047 (David Broadhurst, k=1)
1304119506 0242924299 (Phil Carmody, k=1121)
1306326068 3520389893 (David Broadhurst, k=2)
+13192823012106528121 (David Broadhurst using ECM) (k=796379512984820)
1320568133 8406137183 (David Broadhurst, k=49)
1321725519 8004962887 (David Broadhurst, k=1)
1328354359 5952418449 (David Broadhurst, k=8)
1328937344 0737483321 (Phil Carmody, k=140)
1340343784 0058220091 (David Broadhurst, k=5)
1386803784 7839170623 (Phil Carmody, k=697)
1389893483 9975780971 (Patrick Demichel, k=307565)
1394575499 9792127277 (David Broadhurst, k=2)
1407424942 9004266213 (David Broadhurst, k=2)
1408313024 0647968259 (Phil Carmody, k=691)
1411934707 6470753133 (David Broadhurst, k=2)
1446374143 3615424317 (David Broadhurst, k=2)
1448565725 0285751619 (David Broadhurst, k=1)
1454811033 5841398293 (Phil Carmody, k=114)
1492442709 3173776681 (Phil Carmody, k=1460)
1500615006 1500615007 (David Broadhurst, k=61)
1504731382 0603717453 (David Broadhurst, k=2)
1506491838 6978356647 (David Broadhurst, k=1)
1509754402 7670512761 (Patrick Demichel, k=1272860)
1517479386 5375367499 (David Broadhurst, k=1)
1530773190 2696869087 (Norm Dresner, k=13411)
1538679586 2905764859 (Phil Carmody, k=1289)
1555648785 1027622503 (David Broadhurst, k=29)
1591154893 1742178441 (Phil Carmody, k=340)
1594225626 6655639477 (David Broadhurst, k=2)
1607082381 5128249241 (David Broadhurst, k=20)
1616363040 6944498659 (Patrick Demichel, k=1402273)
1645453009 7743249969 (David Broadhurst, k=8)
1648436474 3105231611 (Phil Carmody, k=185)
1655477577 9615930847 (David Broadhurst, k=61)
1669443923 1434948281 (Phil Carmody, k=1060)
1725832199 3955785647 (David Broadhurst, k=1)
1729947463 8327682219 (David Broadhurst, k=1)
1754644824 4085921161 (Phil Carmody, k=1820)
1763298281 0476169569 (David Broadhurst, k=16)
1764960128 1764960129 (Patrick Demichel, k=79424)
1788534420 3130283059 (David Broadhurst, k=43)
1795308654 2343176489 (David Broadhurst, k=4)
1805296591 1428472179 (David Broadhurst, k=21)
1821188893 0494588811 (Patrick Demichel, k=75335)
1865204646 5609909533 (Patrick Demichel, k=349574)
1878944457 7679739169 (Phil Carmody, k=4208)
1893694965 2297976049 (David Broadhurst, k=8)
1901931358 4906732263 (David Broadhurst, k=99)
1948156474 4729484499 (Phil Carmody, k=4231)
1954081830 5052663929 (Patrick Demichel, k=564964)
1957744500 9153366611 (David Broadhurst, k=5)
1963017381 2699929249 (Phil Carmody, k=336)
1964947442 0484313703 (Patrick Demichel, k=153331)
2014922318 6801402209 (David Broadhurst, k=16)
2100177322 1900521579 (David Broadhurst, k=71)
2105003824 5553195979 (Phil Carmody, k=449)
2109329402 9219420249 (Patrick Demichel, k=7724)
2114395477 1735543023 (Patrick Demichel, k=160007)
2126757227 6158534717 (David Broadhurst, k=26)
2151719515 3056908887 (David Broadhurst, k=7)
2162446364 8027921651 (David Broadhurst, k=25)
2171360933 6493452419 (David Broadhurst, k=1)
2182868319 7817131681 (Phil Carmody, k=18160)
2186160234 8872878769 (David Broadhurst, k=88)
2189696829 2538534973 (Phil Carmody, k=854)
2213541444 3087304441 (Patrick Demichel, k=1318180)
2239603304 8900640491 (David Broadhurst, k=5)
2268514275 4316524303 (David Broadhurst, k=19)
2286704931 4840666343 (David Broadhurst, k=1)
2312771124 1065291037 (David Broadhurst, k=2)
2323688063 0600329397 (Patrick Demichel, k=1132178)
2351180021 2608169573 (David Broadhurst, k=2)
2383142812 5000144133 (David Broadhurst, k=34)
2383907312 3744770321 (Phil Carmody, k=520)
2402655819 9214251259 (David Broadhurst, k=1)
2413568953 5376008943 (David Broadhurst, k=79)
2437251468 5771400413 (Phil Carmody, k=4106)
2468297747 1320627779 (David Broadhurst, k=1)
2469356362 3524316489 (Patrick Demichel, k=830156)
2495067548 2748702237 (Patrick Demichel, k=79358)
2511090902 4057374783 (David Broadhurst, k=1)
2514107762 5143348133 (David Broadhurst, k=2)
2531425819 5073895689 (Phil Carmody, k=316)
2586413616 6589478143 (David Broadhurst, k=7)
2603819410 9534512481 (David Broadhurst, k=80)
2632813924 6075673161 (Patrick Demichel, k=50820)
2638554102 2638554103 (David Broadhurst, k=9)
2672056593 0211461727 (David Broadhurst, k=1)
2765599076 8210583413 (Patrick Demichel, k=5814)
2777959594 9181196361 (David Broadhurst, k=20)
2807893245 3784161973 (David Broadhurst, k=2)
2808734103 4312916903 (David Broadhurst, k=91)
2830651368 2830651369 (David Broadhurst, k=68)
2853487142 8389150001 (Patrick Demichel, k=25000)
2887354549 8164462041 (John Gamble, k=17180)
2894836530 1144230397 (Phil Carmody, k=182)
2903466045 3756913693 (Patrick Demichel, k=1782474)
2924776995 2816651809 (Phil Carmody, k=208)
2935424474 8589194597 (Phil Carmody, k=2622)
2951092005 9813135637 (Patrick Demichel, k=3019786)
2952707379 2966655379 (David Broadhurst, k=1)
2954636327 0378697007 (David Broadhurst, k=41)
2970943022 1620915527 (David Broadhurst, k=31)
3005899717 1022215287 (David Broadhurst, k=1)
3011121763 8009728419 (Patrick Demichel, k=46391)
3012301230 1230123013 (David Broadhurst, k=2)
3014859963 0369806819 (Patrick Demichel, k=386459)
3028729793 6971270207 (Patrick Demichel, k=25197)
3029688023 9948456179 (Phil Carmody, k=473)
3031296565 4367077419 (Phil Carmody, k=263)
3038443319 2474324819 (David Broadhurst, k=1)
3080308030 8030803081 (Phil Carmody, k=140)
3087697740 1637594503 (David Broadhurst, k=17)
3099552058 0246599847 (David Broadhurst, k=7)
3102161892 2854752223 (Patrick Demichel, k=2091209)
3162234945 3214808173 (David Broadhurst, k=2)
3165219266 7938930939 (David Broadhurst, k=89)
3165991816 3238410807 (David Broadhurst, k=31)
3232924147 4977967053 (Patrick Demichel, k=958282)
3240014952 7905587413 (Phil Carmody, k=3062)
3244635086 3560852957 (David Broadhurst, k=2)
3263793910 8857418211 (David Broadhurst, k=35)
3281329026 7639542253 (Phil Carmody, k=174)
3352805587 9943520859 (John Gamble, k=15031)
3410558744 2531773407 (Phil Carmody, k=133)
3420175509 3055871641 (Patrick Demichel, k=26140)
3444867419 7138711247 (Phil Carmody, k=277)
3453645466 2433363957 (David Broadhurst, k=2)
3458986244 9624244383 (David Broadhurst, k=1)
3464527654 3651889047 (David Broadhurst, k=1)
3504892573 6159851493 (David Broadhurst, k=2)
3524123412 5811612823 (David Broadhurst, k=49)
3525459064 0640011477 (Phil Carmody, k=342)
3528230225 8705498811 (Phil Carmody, k=2155)
3565865580 3906009139 (Patrick Demichel, k=27941)
3576323197 5448067047 (David Broadhurst, k=57)
3634745451 8972720419 (David Broadhurst, k=1)
3668135288 3425534087 (Phil Carmody, k=4107)
3670051481 4793387699 (Patrick Demichel, k=2474031)
3770706354 4266064693 (David Broadhurst, k=2)
3774903526 7196097333 (David Broadhurst, k=2)
3839186728 5384911131 (Norm Dresner, k=10885)
3850124893 6163541637 (Phil Carmody, k=106)
3861555941 8091188451 (Phil Carmody, k=475)
3869763408 1761292903 (Phil Carmody, k=167)
3884923530 3884923531 (Norm Dresner, k=10085)
3889838898 3889838899 (Phil Carmody, k=2161)
3897486361 0993724077 (David Broadhurst, k=26)
3914727003 1590361489 (Patrick Demichel, k=9736)
3934942228 1098084933 (David Broadhurst, k=14)
3942640950 1666919579 (Phil Carmody, k=1099)
3968757764 5354896379 (Patrick Demichel, k=237233)
3993023894 4489834943 (Patrick Demichel, k=903407)
3993203489 9759958979 (David Broadhurst, k=1)
4022225788 5312594517 (David Broadhurst, k=2)
4050231517 2098805367 (Paul Leyland, k=31321)
4097782326 4097782327 (Patrick Demichel, k=247361)
4116933925 2652233767 (David Broadhurst, k=13)
4145666815 4982176053 (Patrick Demichel, k=459754)
4162107874 7525182847 (Patrick Demichel, k=1371523)
4176868756 9853678743 (Patrick Demichel, k=21959)
4185824759 3329989847 (Phil Carmody, k=601)
4220101617 6853487647 (David Broadhurst, k=7)
4241443394 1469166167 (David Broadhurst, k=1)
4243448457 5433608423 (David Broadhurst, k=1)
4334837892 0175939223 (David Broadhurst, k=1)
4354881069 1471677197 (Phil Carmody, k=1238)
4420654291 7317083887 (Patrick Demichel, k=595733)
4427315975 4115506139 (David Broadhurst, k=1)
4436844671 5563155329 (Phil Carmody, k=2496)
4437972436 6994432797 (Paul Leyland, k=31082)
4446406721 4245828579 (Patrick Demichel, k=1682759)
4564299013 1426400613 (Norm Dresner, k=10222)
4574226008 4574226009 (David Broadhurst, k=4)
4582974782 0872807049 (David Broadhurst, k=4)
4598222849 3583595333 (David Broadhurst, k=14)
4629806153 0372380411 (Phil Carmody, k=145)
4675314633 3987620077 (David Broadhurst, k=62)
4715056248 1701680647 (Patrick Demichel, k=443967)
4743352417 9822212259 (David Broadhurst, k=1)
4749227545 3432590637 (David Broadhurst, k=2)
4780600782 5827702811 (David Broadhurst, k=5)
4799705613 0351809539 (Patrick Demichel, k=28043)
4813746416 1188165521 (David Broadhurst, k=40)
4855475022 4855475023 (Norm Dresner, k=11897)
4875794788 5920496019 (Phil Carmody, k=2063)
4922739021 5732795887 (Patrick Demichel, k=22257)
4928124875 7482754539 (Patrick Demichel, k=47329)
4933128945 1430507419 (David Broadhurst, k=1)
4936595494 2641255557 (David Broadhurst, k=2)
4966867792 9784715859 (Patrick Demichel, k=64771)
4975578270 7973891693 (Phil Carmody, k=18226)
4979293651 2017668531 (David Broadhurst, k=5)
4999690197 6152031619 (David Broadhurst, k=23)
5033471993 8697565317 (Norm Dresner, k=10258)
5058719911 1366849167 (David Broadhurst, k=1)
5144886003 4855113997 (David Broadhurst, k=2)
5249456857 2148917127 (David Broadhurst, k=1)
5250882443 8710357169 (Phil Carmody, k=1448)
5321507760 5321507761 (Phil Carmody, k=120)
5338190520 5338190521 (Patrick Demichel, k=1094340)
5363027799 6940570333 (David Broadhurst, k=34)
5449561007 8914907543 (David Broadhurst, k=89)
5599581680 6170736023 (Patrick Demichel, k=56779)
5640478379 8929167317 (David Broadhurst, k=26)
5679403924 1614059727 (Patrick Demichel, k=46517)
5694817169 5821452539 (David Broadhurst, k=1)
5845679457 9730376303 (Patrick Demichel, k=2757011)
6063561544 9540508081 (David Broadhurst, k=40)
6077942346 3570176179 (Phil Carmody, k=1133)
6094481803 3905518197 (David Broadhurst, k=2)
6190889105 5048486529 (David Broadhurst, k=64)
6225107458 6402398247 (David Broadhurst, k=1)
6258369252 1833708769 (David Broadhurst, k=16)
6297019136 3423249767 (Phil Carmody, k=357)
6343665207 8306252521 (David Broadhurst, k=20)
6366181453 6193913733 (Patrick Demichel, k=325402)
6372857265 2511931583 (David Broadhurst, k=1)
6418102469 4979947613 (Phil Carmody, k=494)
6471548023 5247008331 (Phil Carmody, k=435)
6473514651 3120881293 (Patrick Demichel, k=83882)
6476740346 3328407131 (David Broadhurst, k=5)
6488750311 8258287611 (Phil Carmody, k=195)
6512245060 7263445287 (Patrick Demichel, k=23161)
6553012079 5415007601 (Patrick Demichel, k=20600)
6556538292 6556538293 (David Broadhurst, k=2)
6561803412 6561803413 (John Gamble, k=17034)
6591373716 2631555539 (David Broadhurst, k=19)
6637680213 0909344317 (Phil Carmody, k=3942)
6763947668 2307579411 (David Broadhurst, k=5)
6858560963 7206479687 (David Broadhurst, k=1)
6879327536 2721483773 (David Broadhurst, k=34)
6895877526 8621477647 (David Broadhurst, k=1)
6962402433 8004338143 (David Broadhurst, k=69)
6967797141 5452227059 (Phil Carmody, k=1939)
6990112922 9665512703 (Phil Carmody, k=497)
6996937704 8829693289 (David Broadhurst, k=28)
7010631081 9494833973 (Patrick Demichel, k=9886)
7020189246 1893047329 (Phil Carmody, k=688)
7038741543 3515386249 (David Broadhurst, k=28)
7113625818 3997485293 (Patrick Demichel, k=1495786)
7198216927 0012783321 (Patrick Demichel, k=368620)
7337347191 4352167339 (Patrick Demichel, k=9673)
7413367745 7587772487 (Patrick Demichel, k=42567)
7433766623 7444282157 (David Broadhurst, k=2)
7445808145 6057517797 (Phil Carmody, k=1102)
7459353417 7200184087 (David Broadhurst, k=1)
7471697410 7841055717 (Patrick Demichel, k=75762)
7480526350 9219461877 (Phil Carmody, k=266)
7643426519 9130413059 (David Broadhurst, k=1)
7647658376 3141649517 (Patrick Demichel, k=328562)
7788117574 3604035171 (Patrick Demichel, k=8495)
7855819088 8920361813 (Phil Carmody, k=4734)
7916580641 3058742939 (David Broadhurst, k=43)
7944877343 5588012531 (David Broadhurst, k=5)
7983414161 0293496059 (Patrick Demichel, k=7131)
8016169779 0634385179 (David Broadhurst, k=1)
8052513193 2804988441 (Norm Dresner, k=11740)
8056463054 5493672447 (Phil Carmody, k=2713)
8178112602 8829019223 (David Broadhurst, k=1)
8215344389 0942618503 (David Broadhurst, k=7)
8248507418 9594160481 (Patrick Demichel, k=27280)
8266031025 0899438567 (Patrick Demichel, k=8273)
8347571156 0156161693 (Phil Carmody, k=262)
8366601101 7422911339 (Patrick Demichel, k=942401)
8371869775 1990424757 (David Broadhurst, k=2)
8390366513 4469604887 (David Broadhurst, k=7)
8499964227 1500035773 (David Broadhurst, k=14)
8522941717 4522727133 (Patrick Demichel, k=7514)
8680216484 5991259023 (David Broadhurst, k=1)
8682616938 3536937619 (David Broadhurst, k=1)
8734304526 8734304527 (David Broadhurst, k=1)
8809507640 8809507641 (David Broadhurst, k=20)
8839298356 4392949641 (Phil Carmody, k=340)
8866978074 4173388693 (David Broadhurst, k=2)
8882276259 8636741047 (David Broadhurst, k=1)
8899568125 6592310289 (David Broadhurst, k=8)
8901418921 9736494699 (Phil Carmody, k=2501)
8926561467 0722664263 (David Broadhurst, k=1)
9034536112 0559445169 (Patrick Demichel, k=6616)
9177919771 6336159459 (Phil Carmody, k=611)
9205063724 9403083527 (David Broadhurst, k=1)
9206426637 4218407611 (Patrick Demichel, k=1709285)
9288931566 3567778891 (David Broadhurst, k=5)
9300507319 0699492681 (Phil Carmody, k=260)
9302991895 5466844539 (David Broadhurst, k=41)
9349315770 9407253613 (Patrick Demichel, k=5462)
9352463969 5576694413 (David Broadhurst, k=2)
9438482117 9651608783 (Patrick Demichel, k=409499)
9601804972 0492894081 (Phil Carmody, k=960)
9634895404 9002586117 (David Broadhurst, k=2)
9671301796 3277627693 (Patrick Demichel, k=682186)
9675228810 5151083089 (Patrick Demichel, k=2317688)
9695856057 2166671659 (Phil Carmody, k=1421)
9786768876 2263470373 (David Broadhurst, k=14)
9812051575 3187740649 (Patrick Demichel, k=732644)
9927184513 8459068209 (Patrick Demichel, k=2222696)
9990771372 0748054573 (Phil Carmody, k=422)

Phil Carmody is organizing a distributed computing project in order to find more factors of Googolplex + 10. If you like these pages I would appreciate that you donate some idle cycles of your computer. You will be cited as the discoverer of the factors you find.