Certificate for Preda Mihailescu's 50,005 bit prime



This file contains the certificate for the primality of Preda Mihailescu's 50,005

bit prime stored at



     https://t5k.org/lists/single_primes/50005bit.html



==========================================================

Certificate: prime with 84 bits

A125B1EAFC7A7B91524E1



Certificate: prime with 231 bits

9B86608AC4CD1F28AEBF4DE012BE94A5B8F67001C6E131B6200E338969



Certificate: prime with 676 bits

2432C81B29CF506471AD9D1DEC1BECC4E3C021FD35D56434B10DCFFE64C2EA4FE8A1618D739E20E7669E672E86EE2C77003E5B8B61D9426AFBA40399212F068D7EC03A3BE5F7C59E25034304744D593757ED9C7943



Certificate: prime with 1952 bits

4142E83929D1AC2572DAE37550BAEC1459E41FB19C35284BE162B7CEFF67864FB68DE2E03AAA6A36CD198C962D40A9F0DF406DB375E4EF46C9B7C9963309353E30F5DAE67DD3AD1BE6585F6B4802B96C2573175EDB5D2A8C7B763F00DABE02CEFB45835E72AFB6A92B65ED18F6EFD701B049A63E418E641C0D29B8513D5B97D



DBE482ED6DB932580B0B46BD0E25E9AB523494FCE6B22C63155162367F327BB0B447C974568F743716AA7E352C192D061324E05E731540BA662161AFB5165410C697DECCC2C7937154C6EC50587B6FE6CF70FB299221F1CED4B77CC10DADEE7EB437A1080F3D92B49A9A6D5A6A1B3FBD4DC6964615

Certificate: prime with 5755 bits

31ED981C09420F6AF034F5EBEF77C9C24F04F775BE0077B43010AE1F8FDD3AC8E262247446EAB94326F73F197F044E1B18595F8E98F71CEF972901B079ACEAB734286C07EA6541FD4851EBB69BE330EE4D8EAE8A761F0372ED1C613E46B2508CE20F26B4FCCD69DA35B75942348CB2220332DDE45F82CD139EAC32A1E6D3016



8DDB772AF706C8FBDD7AAA995163D52B89268C864BEC1E326168B415E952892D1EED5D18E51E6A4F833F4CDB2BBF70571C4E8C1781B986E87F6947D3DD9EA8028964EC64AFF70AEF0250162ADB255ECD5A3E4551AE5F227F292B4363A5790CAA1F5D79F78C24462A4125D71F45CAF438371FFAE0CFE980489167DD67D51DA54



2B30059E87279C2C411C2BCC9DC15424C3897534A4D34853FFE01643ADDBBD1FA156E8E1484E2E03DDDB6FB332D82F2C68BF701B73ADB3C034DFAFD45A0521C1777290BEEEC1AD09A2688D2FC357E42B884DACE236F08001E518CD1665862CADDEAB003ADECEDEEC9A5CC5DB190DD1310AC55ED34375731F183DC6A78851E5C



A2AB99E012F6758AF7F85339E4F75757EB5C4CBD5458129D33EA0A69FBAC8A192C4365F986325E585145FEBE5FA59646BD8869865AB0FCA6AA4FEEA2B9E394DA713DA8E919BA36E0E9F14D735C9C7C50F9EF4898B5D6B0D8048EC2B5CBB4EF2BA8C512D9D023076A36A58DC7D2D8262FCA!

9653DA75F2CBEC5584967F9F4C7B88CD

9BA4D6DDDB499C7D9CC7B9CB8E5116F4A537E4F4399D11ECC7ADDB12F55BA35A6C6CC987FD977E744B9E45E51CEFC1007F5EE72CD1B61D181D8A7CBBBF2D02DADD3D6BC94778FB8868AF79A16281D98F4BA3EA9953C5074FF1459F6D3BC34B4269AC2E0FBA98653EF680B1321D975A7DFB9D32203E5934D5D01A651BDC3FDF7



4F0B7D28F335569F915B3B6BDDCDEA4574A4EAAC83874A1C79E67D6E1A035198114A91CD496F69F9BBDE83618E8AC9D6FFCE36C5834470544779E06F9F6F6DCDBDC9877D0B41548386D61B95A6F0A52D41



Certificate: prime with 16837 bits

18A792089AEB186893F12CA690CE550D97AB0BF237F1488EF22264E5DD4401EC8BF06326FF86218E83408EB0CD76E019AC8D3533C6B52B3783B4643B3BB4DE5F9CE89027BE213ECB41DA50C68B6998A9151CF1A4758AA52B3B35DB77FFDE2060E8AD59B2E4161D28E39EA645CCE56CE06FD062E4D2546EA58DC6010344A9897



C3297C9885B97D88577F262B0D0150096636452AA0BDBFB10B51566DDD2A8DA6E7A5F5068507721DC3579F9A02AA8E65D7DBD367C83D947FDD8A96F8CD22E68AF05D7E1E2F4B6991154F81379965566C3306BD3A0DC9FF2C2A786967A83161F51A9DC1FD235C58306B7336E451FA84D049F3CE165A29E3BC944A2CF1F0003D6



F03BCD539F943E8F5E715B4FEB30D1EE5FBB967835E01B42B09C68464A7A10174C028548613B6589BA0C21AEDA9DDA9C8ACB83815223D38288B2339622B8CB4771174F0DB1D83D34534ADF0DA3C65B67650B896A407DEC0A5F4D2D075DA25F8EDB03ACE7943B67F6C746208BF47DD4F1451DA81C54E6B7141DDC720C43A43E8



831E89C9DA814F6E39D8A499C0A62EF20DB638FD0182FBDB3C3FB34CB233BC6C741E228DD9BD5B325E3134E11AFA2D1F0F45F60CF9B1E1E5C02F54AE20342BDA70BA073E3AE6D42E43A5A570D87A713D37FC99E9F211AAA2B8DC56F2A2B24EDB3EBA2FADA7749C636E56446A91672A9176!

BA3CBA05B970E6634988D28999D3310C

99194D7348F007C458C7E3A04BFAA55ECB8C0299589A9A7D9307938AC5831647957741FCA5493C788E87DFFF118ABA4BDC5D769043655C2B706058C229FF13C760F65C938A0327AA236A8817FA03C3A97815BA12537A01DA65FF7E2ED18F429F7A5FA5BF029BFD62DCA9D7609CDC6723984F052757607B30109A8A445CE4A1B



18F3B17A09CAF86B6F49CF775267CDB1F517C244A7D2C4ACC1AE754ED7C0F7473D9C71ED89D9EED8902AC94DAF0ADB20BF4A19E82F69E10FB1D2A3FEA6017160F2FD16A3C2F7A2FD97D57FE882735AD041C424ABDCDA0879345FA54684485F6E6E5834965B31A9294296B4C1B1CCBB63446044F5F40FAB5459FA7870F58AA1D



51F9CF08792E4D3895FF234A7161E177203FD6C8F4F93DBD589BA68919E8DB169683AC086EE2EFA0EE99088B5F61DCAF94585106D76CD1405DD1AB0CA0E9A09EF0E0AC8B92667C59F054A0D387A6F46C81ADC21977434CCD004BAF6B3E0539D0835F9922D346A7E127603F7B548350CF0A5729A3FE8023CE3A76F2C4EA3B4E1



7D16537EC8AA148DA2588E7B35C31450720D7A836309C2EBC97BE8E2BCF1BACF16FD0C69FFAE12827AFE53323A9B9774FBE0928607AD79719B35D0F15794B89BF8B9047109E2F04519CB7F1290DE90F4F0A87C553751728D7E9F7F717A306B1A9B1FA5AC54B98DCF07E80EEBD1704686

9D218AB0CB33B7F55D8E55AE139BC6EE58BA5CA8C0FD5F36D4222B762682C949C83AE36A37EEE5BF9FA04A9E5812C82C20DFB42147E382886173D4695A98002B7A537E78D15005B32F0C58F0845B6910EC4E17A48CAE928ADB2E1504D9CC5D1C919956AC2E08F993B1ADF91D3CAE77F17AF92C5FAB7BB11E960EFCF85CE1626



5D5E0ABB6FD4901A73511BE000BC458D9E65CEA7226A11ABB40DBF42341473372D835FBFE499F2ECF50C22810034DBE5CDF3007212D53F28F27F14034690A36284B5BFACCAFA5388D7544E085F541DC6ED80CACDEDA3C6E1251AF8427D11D7D379B83BA47C52786B4CF607E03E6B507CAC0DEDF317C7B86B61E6BBAD37E4504



619E167D0C1BFF9E23FF5333D1DF17070BD4187870155652BACB8FF02445449DF608E21F82E5B8D281AE2537402D86B2DFC0770503B851992766E786120176ABEE33A9E52651880848AB913C15CF3D7E82F5098010C5C0946E48C2416856D6E231800F5B4BE240EA0169F77A550D5958D223F2782DA7B48323460A8DDA52278



220EE25F2439FA19A54F01CBD2A4F99CDCC8996DE1F30A74AA6609F67ACA903AB110D3E1E476C476EB5BE020F1BD0610EE7DE5B1D1352078696811C70AE5718CDB87257895A6212EDCF43544754B75C602ACD89A60350D6E53B86C005B8EF92A7B0B31E8A9B30138F57D719D286EB006DE!

9F5DA6186E8A9B78E29C43D3F1BC08F5

3279904BB867CD496AB9C00D21E664C2F763F435DD2EC96677187BEC857754D04309FBEEADBB05DD3E3FE62B9FED3181B3DDB665BD3D1C3A7AD80A9001E253A4D12FF8FDAF584042FB4CAFED093881B914C24ADFD7EAE1DDCD5853B3D6FDA441D3635364E4C5E81642E31C4AE0E96BF792B90833647D8A8179B5FCE298C4CA7



1D26DFBC56C50E541B6874529ADCC262A8A3156BACAAF5300D1B9DBAA61C4232A9FC4757763F22643F2C8AB4DDAB45E18A2D927DDDA39D35D573D21498B5F90F1AB896AA31F186B73FF3547485A93CB0E01EE8B239C1CF18DE4CBB09DD3313F37F4556F242B8295137F817D43CC545D7CE1055F423C551EF12F3746C34CF76E



3A57BD23730FF604C83DB6CF8C10B4BEFF975D098B71F475E945839EC253F299F3362721855A99F24C37014FBB165202A277728744F5D8D2B31D4D5017C7126CD87B82524BD4DD4DDCF22A9B7BDAB69DD59B23B613D458033825E5931A3D71AB1602AC780C1EEA8AA486E03E6F045DDA44FC112B312D56F497F010F1E73BE5B



DCB9315B68DAF5DA68CDA143868382EF5DFABD3294A72DAE2484DFC1A590D6BC1954947DBDFF5FDA947B5119EB83D34DF13941E968003B2694F2B441F09A309C0B80197907A5A36E1573BC8A47BD903E057B7B3736C868412A0F44302AE6345EA12FDA2782EDCAC19C25960E2271C48CE8!

A030FDD39378E8E9B435B453B3F3ECD8



1765B6BDAA8A295B6E461632D42440D4743FFAA35AA488DDF92DF1E7DDDF36C27FDD4D5E3E6F8E38E27DB22EB87B68CCA8C263E242E7C6D44C3F0F13E02D424855515F4FFAAF6D1617A2391C9



Certificate: prime with 50000 bits

16210BD81E34A137E00E656CAD05E102A8243F6250C599F31656662EEA215AD3EC9D3B161E6FA9EFDBF8F5C74AE70708BA0846D06E5DCFC6F293EAAF34DE6E913CFAD59B9B5DEF8292CE344179CA1DF8260AFA345651381496BE9A7764A82631DADED4C72C9991D89DFBA2A57D0774F392BF0CCD688830C2558732E9045F638



FC2D09BA1222FBF43218849090886E6621287348DFECD4D7EF7D90B3CE54FE4CE48A9EE02FBF9169C9E092613E6D0CC1F4357C236379B18D6341C81024A250481FFC8606AB690FD6F46E46369EEC834BE64707EBE0361AB44FCACB6D87C35BD15F13FC74388CBB9D502CAD236D9C0383042BD964C3AB0BC7DF053D3FEB895A0



56EB7E27C188EEA28C80174D2670685F52AFCAC2D38ACDE6CACE23061468A4DB172D0D2B1D267AAF592478C35FB372480AE8EADC30C72445425F516A31D3620A5FB90681A66C000ECAD55CE1A3788578CE835591C120901E9897309508ABFE6C375A653843534F574F352D4509512E44DD7CFD6D8C86EE76F2EC230543E901E



E4FD85896142C8317E23C7622CFF25CE20AD8175952B7A920B667AF4A65FD5BDBA959413FFF81CAD2E51176A194F2C297A5280F77F82F0B0CB0F2237BB7739598A3F0FCB40A01219F1FEA2886E937D765CE6A385B07C21D5A9AB01B0FF72A2360046B5EDF944283FAA0876D17883865636!

6DA4D6575D40F6396FB930C0F7FB033C

B73C9AAC9410174C5F231C853B6F1154D30DA3357CCFF975D889497D7EE4D373CF9D3AE8269D2F48F5568868471665216FBE2AD5E9F4498984695B385BEBD7F9C43DAE0AC99978174A58F71930DA82992894B417DBFB23F2DCB9A4B0D8B2AD663E43210CBCE46A08FB16C83370765F14A27FD658FFE686D7664AF82302F8D1C



8358111B7CE402706CC4E81E4CA0979E932601FC3D5A3F233FC15713670F3AD5E1EA0CD6647E3CC8A4DF2F7EC2DACEF540D2A394161BDA999EEBDE9126586DDFE3567DCBBEC25138F51FD7119E716163E40B99FB7205DB8D426AB1CA16D5D9CA8663BEEE671D19EC60072953D988BE8C0E8274B13E0C081A8610FA81E4D6E3C



40CC7912E3FB0D956FC4A57C19AF8E56044DCE513669E7FC5CC5A26CDA91D3D0D302A1519EA405ADFBDD265F499646F2EF85E1E42ADFA44E01020B88BFED300D63E3DC8C23D61883D35324CA535A5EEF1395F7B5564760B144126C1613873F45DCCA50C9F524253FB96BD2485976B76912EAB49DF754DACB4A5082B1EC3A82E



56C838D9CB9B2D6C8F5F910AD67832220862ED411DFCF68B99D0F12AF73568A061FD638E31A62A79930BC92D4BE25103B9B8FE57587E0881592944D709B78DD5B1E01875518B5947CC6813B58AB59B90D19F0E27B8795C35A95468742FCF3B8B28992FB46D23F9473E8109B519E2F390

DBC5C1B678927AD0914FF779A9EE920CEF9256929F46923CCF8EC675B19F46FBDAF16878561576C5CD5807E91DF786FCF4F72FA37759B02BE1F72EF3288B33DC61B4EA90805E7098F6385128451969DB31F2234CC686AEF5AEE5D66DD81E5DE32C9EFB4C5204CA084BEDD459BE9EC4440C9D67A72CFC3E43ECEB4CBF5515A70



E6B222FA43A3D99601018025893718ADC0724AFF5F51F863BCE35033B5C57AFEC630AFC33CD45E8E5574737CCB42CA2DDCD85A2105E0492F50744DCACD89641268EC2506EDA87F4292A932D3BFD35565ED5902EFF73192B7CB490A104897C4EA363BB8893CF3FED7713CAD19051302AF804575FF8D099FC6C08BDEDE8AC119F



BFAE76CCBD962CF17D2961E743AEA00C4FBB3C19DD0986B4A5B3A278D55B0BE48E150D5565B97EDE0A5F24D50C934D13CE503243C08EDC0CE98CD40E02F63BF2F42AFFC9AC81BC378220AADC76D22F9ED18EBA0318C63D7F27C7EB826EEC8EF7AF20035AE6B845F1D96DD9FFE6CC24D54F8AA90D461161C1B86BA8FAB834001



B87DD521C48DAFFA7F8629C3153F5C6A870744394CA93CED5052B4292052FB2D38DD3BE55EB7763762423B6221A3E5B0373D6D08F631ADF48AD70E1BACEE0E485EC112B87222CA542DC527E86FD17A908D820B9D1C20321BCD4B3891FD3E56DD8F27113D53CEE31A5B161A65B3E50DB500!

8A112793336FDB247E5C729376865D9A

E74565EA800200B3FEA88C9BCA8832048EB4388A1FE02F5899DDC0574CFB46F491E33B39D292745BD3DA57992EFFB93047F238011B7F68C39C834F0492D0BEBD9A55ED3FE57622F99D26DA40CCA609262F373BC274D2A59B6E4D6CAE2E56D59508A065FB053AC9CD5AED19B61A6622B961961D24BE8C47B32926A9566026E9E



4C72D117AD0C185DF15BC85D578C1A1FEDB9FF5DEF845D5819FE686A62AFD737ED1B76F9220D7B45D02295824C1063EBA7B2DFB3F943BB07EB8E1BF68FFF6EE140B6273CD5233265E2E53F9B24893B06C7BA0D7EDBBA8ED29B23A7EFAD0CD094551BE293C6F8E0B9CF1459E7406C42821E0344CCE8F3B77592E2D8557844C68



8FAE670284C5B4D456BB931438B55B3457B350D3196255D28BD63A3D86795985BF01E660D440C71B63E9F4FD7F96B0AF09F3FB375F5D1E3630544C68E4C0012627EE28EBF59CBC7D0A9FC364706BCECFB855EC994F2F94AD6D0B937D4A601A65A26833DD7AB1E14F6C02C1FD6CD032E975C1B8CB74D23C8E6BDBF79DAD90D8D



05884CBB8A11CD7D0AE8DD22A772E566158D5A95F4263D997644E404C6E6EEA344448C3410C9B3A044D0CF2E4A57D876B0D9135742A93CAB728BF73DD58B72FEC6CAEB30A6EE80FF8AE234487260C227C298AF67D919DE9EDCA5B1C88CE28BB7068A0DAC022C4F5D049EFA4E5933BF7C58!

DCAC42A9111AB95376F3A43449B49D73



1C2CDB96449530B41EFDA37EEEADB77492AF5D74B8984785C8E6E0D1B53B9F769AFFD12A7BF35FA31F568EDAE5E09F6E868EBCAD4F2A81F028412F992F14DD68F64A1BEF4285C7E4B0D46D7C25BE6FDCD54796D1DACC851DCB57B558D55FF8DD18D1C957A54C3694CD578A92049319AF310161C3ED2F9D02EC5CD69F058023E



584ACA1D000EA2894D086434E153AFE822791FD1F8ABD2C919BC29DFBCF025747BC17D65C3BA21918F1B541B702D86F97E53C252DDC481602F401EA62135171674327E771074FEC9FD2CBE106C452F704C65EC639E0B89DC84F981E88E4CF0FA0AE6856F0D0ED8A2D48CDD0D754380AB4AB550ADB20350402F33476CA266E97



F8E6A364E7689C9F8B9BECF46E104A3EC7DDAFDAFB556C881678EC2E67AD6A6A327BD27CC9B1564D57C00B2D9FB1B9B8689F48325A63FCDDCC459457F0E6971512CB37D8DB9F1519B45EC727CBEEC56A95D5075428CCC0AA398213E79998017C1DC99B12FF5D82816288B72D926DBCE4C4835E9D69FE236ED981B42588E247E



4BE367A2C273AFC2C556578CCC1B028C87A89FF8DD9F0090EE7DFE2BBFFC441FE3C4A454F185F1EE6A0614EA36BF023FF8DBC008841980801D0029985CD0D85EB8C82E22F27C04FE261631144783B4CABC0127E87FC8EBEA4D8A8161253947E97C546EB34B7DA7FA2D73A542C5D0E50846!

CE866EABEC628FD660CEF6FBA5368F5D

4CFE78CDF7E891EB36760D8F85498C9C6FEF723D7973FD05D16C68457E870A1D508D78AC957314C8D7DD9F9B22F0E5B7F9928280773BA103003F0EC2B350DDBF514F36BA46B92937F9FCE9A01CCD6EAAD2B93443E1A1A1D2E0770047D11CF8D779F836BA47283F86BB7617ED028A6375FBF53FFB4FCFE61C8B0AF73CAB471B9



598DE7578AE6D7051C4CD0842E3F3E20B42F08DB6C68A5C65CBAE23548A46328595EF8F8C378FA79DD944DF30786E0BAC61869C57AD46410F6CFA5294B52713B428BC6B7CD2D518B6AA599CB861CD5D218BB04194D0C2DA52B9122ABA0B76D6DA6399C0F74C51A3FAA9C7CB1826E6946B75E57CC8FAFBA724E81D20F8378A12



76207B3E9CB06466C84D77FBE94845751C056DBDF08A4D590BA81A004228ED68E589B3DEBDC0BEA50D156EAAA7D7593811878045488B53306759864A935CA8B8F798084F43AD0BA208711D76ABC11D9C5AB9B17DF99F1F7F7290B01EAD45353C7670D956935457A7D31A71378D942286BFA0CB6C6119ADD6279EEB87BBB0B87



6C09C1E4D998BA5F2ADBF271AC1BACCADA9A58EAE45DF924B31B3EC872CF6DE09E14D7ED712B875227D6913D8D75762F6152CEAEFF9D9C0689DE5177B98C421A409425449ACE29DBC3BE44118B2CEA7230A00861D8B871AA1D6F4C2740BC1CA06D19FA06319D593020E0C6AAF91C6AEFD1!

B6D483CBA7CD9749CDEE887F053680BD



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