News - June 2009

June 24, 2009 (Msieve - QS)
336^58+1: 11373080808883743070624943631533587817805002982557.
336^58+1: 26477794324587772709662239079131738880651238573153.
These 50-digit (probable) primes close the factorization of 336^58+1.
Both of these factors are new (at the best of my knowledge).

June 23, 2009 (Kurt Beschorner)
10^9050M+1: 35090207100930655901.

June 23, 2009 (Kurt Beschorner)
2009^61+1: 11935635852897844663728057682156313.          The cofactor (114 digits) is composite.
2009^67-1: 31254348730897293399139660867891857560197.    The cofactor (135 digits) is prime.
2009^73-1: 13690660001489478323241016541.
2009^73-1: 73217186722304906672240690481087145451.       The cofactor (166 digits) is prime.
2009^87-1: 14146307745966763502258887293091600411229551. The cofactor (121 digits) is prime.
2009^93-1: 767196781884782610143036919530629.            The cofactor (142 digits) is composite.

June 23, 2009
10^11405-1: 99625252847889307790831. The cofactor (9062 digits) is composite.
10^34962+1: 633542251584902689.     The cofactor (23287 digits) is composite.
10^46562+1: 51135547716041461.      The cofactor (44984 digits) is composite.

June 20, 2009
10^24999+1: 4737420243610081.
10^24999+1: 18349474964191099.
10^49999-1: 45165736667201.         The cofactor (49985 digits) is composite.

June 6, 2009 (Alfred Reich, Msieve - QS)
2009^69-1: 14364968172046385806763985037022244817.

June 3, 2009 (Kurt Beschorner)
2009^53-1: 1619104489257838954456318958054291593.
2009^67-1: 8746961721843793256402797638515239568371.
2009^69-1: 1904968184434936124789970180632779.
2009^110-1: 2000889798963163344981037437763961.
2009^118-1: 255464630569917750753690834340793.
2009^118-1: 11625138934254920848585005449488582079.
2009^130-1: 413810058286896588970342805618191820041.

June 5, 2009
10^25070M+1: 2304209899704341.
10^25150L+1: 8798989663601.
10^25190L+1: 6592957439641.
10^25350M+1: 28737116636475001.
10^25390L+1: 70146851410301.
10^25410M+1: 3249544127837701.
10^49634+1: 17816849162976709.      The cofactor (43280 digits) is composite, see Phin10.txt.

June 2, 2009
10^12264+1: 377574726322081.
10^12301+1: 68956401813279980761.
10^12335+1: 618741483308434771.
10^12343+1: 31817343446543.
10^12426+1: 3560549823030090721.
10^12428+1: 49325079349417.
10^12428+1: 33084275965580781761.
10^12433+1: 191035419255413.
10^12441+1: 235819058293842739.
10^12447+1: 19568076638208024238849.
10^12469+1: 5438904533652281.
10^12480+1: 1468645609566721.
10^12487+1: 90295536376841.
10^18790L+1: 4601207806925028961.
10^18850L+1: 813786220101401.
10^18930L+1: 15383753643445501.
10^18950M+1: 43089313107480901.
10^19270L+1: 8867682790854290941.
10^19430L+1: 204822768985841.
10^19450M+1: 21921415460075526001.
10^19508+1: 10411739063009.
10^19511+1: 20788412446379.
10^19529+1: 37731997929289.
10^20526+1: 6314407181149.
10^20536+1: 4724747483420449.
10^20619+1: 20989089358813.
10^20643+1: 6782406279601.
10^20864+1: 13333409847809.
10^20912+1: 962251859677441.
10^20923+1: 11591815110877.
10^20967+1: 239813881513249.
10^22030M+1: 1311562886834261.
10^22250L+1: 7394931635501.
10^22510M+1: 639972481330531602241.
10^24050M+1: 187246609049501.
10^24070L+1: 15476501755836221.
10^24130M+1: 4093785122253361.
10^24150M+1: 132419447251694401.
10^24170L+1: 70067264122381.
10^24170M+1: 533017356511141.
10^24270L+1: 4001646356616001.
10^24290M+1: 254363097259741.
10^25530M+1: 49688494649341.
10^25670M+1: 62730865296493459981.
10^25690L+1: 1175983134163545231581.
10^25710M+1: 2233998208859341.
10^25790L+1: 379095322244501.
10^25810M+1: 163208659243935581.
10^25930M+1: 23638418291971061.
10^26010L+1: 1083769055742944341161361.
10^26010M+1: 33890228735941.
10^26010M+1: 5951313140774517541.
10^26050L+1: 8553918130504501.
10^26090L+1: 22963842141521.
10^26170M+1: 212786317508641.
10^26230M+1: 95001662060881.
10^26250L+1: 568768636915290001.
10^26330L+1: 22788478715921.
10^26350M+1: 36484607050952092801.
10^26390M+1: 24158391994074023756981.
10^26410M+1: 416395830097661.
10^26430L+1: 33888098962981.
10^26530M+1: 608144414537521.
10^26690M+1: 14918932746310921.
10^26750L+1: 3879632161501.
10^26890L+1: 116921779852201.
10^26950L+1: 122769575735683801.
10^27530M+1: 13791376247919681001.
10^27630M+1: 6758232157654741.
10^27770L+1: 74485606355581.
10^27790M+1: 4360414128707841401.
10^27810L+1: 10461000867661.
10^29270L+1: 16715067339941.
10^29290M+1: 29962867224145670561.
10^29370L+1: 24120614433301.
10^29390L+1: 40444599126901.
10^30570L+1: 129601799606701.
10^30730M+1: 2311034893208161.
10^30750M+1: 586057213600501.
10^32410L+1: 6678708411341.
10^32530M+1: 157281123169141.
10^32590M+1: 7090934285761.
10^32630L+1: 240597609764201.
10^32770L+1: 462494144787221.
10^32850L+1: 15987427356601.
10^32870M+1: 1603734071221.
10^33070M+1: 617045920741.
10^33130L+1: 45526771975961.
10^33330L+1: 27192080520001.
10^33390L+1: 56835968101921.
10^33430L+1: 6396100589381.
10^34690M+1: 945592508401.
10^34770L+1: 705197846714341.
10^34830M+1: 47088968744341.
10^34870L+1: 646470196016261.
10^34890M+1: 793379406255143041.
10^34910L+1: 3618536433704261.
10^34970L+1: 9771391046821.
10^35050L+1: 7229098040701.
10^35050M+1: 1252335528882338101.
10^35210M+1: 135458204060713381.
10^35250M+1: 76053408163501.
10^35330M+1: 76307060217541.
10^35370M+1: 4816769082841.
10^35410M+1: 2582118587641.
10^35490M+1: 206851864826881.
10^35630L+1: 1227609701921.
10^35630L+1: 33954427365691141.
10^35730L+1: 74448171288541.
10^35770L+1: 2504416921140961.
10^36710M+1: 10954180543706261.
10^36730M+1: 1781297731504201.
10^36750L+1: 158815859706001.
10^36810M+1: 2052090408327121.
10^36810M+1: 3390339932792821.
10^36850M+1: 187486953600101.
10^36890L+1: 32793351334241.
10^36950L+1: 4134046624901.
10^37030M+1: 8096298033189940001.
10^37050L+1: 18157047838503845701.
10^37110L+1: 1730860127401.
10^37130M+1: 574361370901.
10^37210L+1: 1517646241381.
10^37230M+1: 6654699581521.
10^37250M+1: 120990678296083501.
10^37310M+1: 434988672267456581.
10^37410L+1: 1122919958521.
10^37410M+1: 9854724386701.
10^37510L+1: 311525027173979869361.
10^37610L+1: 97304664286421.
10^37710M+1: 17529286622941.
10^37750L+1: 153954535158001.
10^37870L+1: 28569713862078761.
10^37930M+1: 376155994262515121.
10^38030L+1: 598962460081.
10^38030L+1: 83818052154481.
10^38090L+1: 1439052464981.
10^38210M+1: 27859194900301.
10^38270M+1: 384095653809100561.
10^38310M+1: 40740966949741.
10^38450M+1: 18598755314401.
10^38490L+1: 2300768463541.
10^38490M+1: 3397024246801.
10^38570M+1: 3318665396201.
10^38590L+1: 2562291333541.
10^38590L+1: 214870450428841.
10^38610M+1: 1251093590835661.
10^38750M+1: 500292802501.
10^38770L+1: 105864115614983861.
10^38790L+1: 2462912176089601.
10^38830L+1: 517712765030561.
10^38850L+1: 930712666801.
10^38930L+1: 482367004310441.
10^38930L+1: 967389579563021.
10^38970L+1: 1155875218741.
10^38990L+1: 2471097536741.
10^38990M+1: 107305224147241.
10^38990M+1: 369217292637404681.
10^39170M+1: 29744565175736107141.
10^39190M+1: 58245595858693861.
10^39210L+1: 1047916343821.
10^39210L+1: 339422702808421021.
10^39250M+1: 12943670869501.
10^39270L+1: 1497272422801.
10^39290L+1: 5863073588261.
10^39430M+1: 206292123402641.
10^39450M+1: 23138180436965701.
10^39570M+1: 121135946480401.
10^39610L+1: 1014709491881.
10^39630M+1: 42962325564421.
10^39670L+1: 68277591905321.
10^39830L+1: 317379313346621.
10^39910M+1: 17587288245818201.
10^39970L+1: 480023099979361.
10^39970M+1: 170093155424221.
10^40010L+1: 6390302982366038641.
10^40110L+1: 1079551954020358981.
10^40150L+1: 18648106481390101.
10^40150M+1: 29884394680801.
10^40290M+1: 512744722081.
10^40310L+1: 267847593211361.
10^40470L+1: 159041470461121.
10^40510M+1: 811150769701.
10^40510M+1: 1822414214741.
10^40610M+1: 1037756467856341.
10^40650L+1: 399110680723201.
10^40910M+1: 20625983999561.
10^40910M+1: 198227523549101.
10^41110M+1: 31803905949521.
10^41270L+1: 10063580262024301.
10^41310L+1: 2744642926981.
10^41390M+1: 1705306738225481.
10^41430M+1: 2280740617179974229001.
10^41450L+1: 1267635671801.
10^41490L+1: 152655557038561.
10^41490M+1: 1880796715741.
10^41490M+1: 1793897599548961.
10^41510L+1: 63257640111915061.
10^41530M+1: 5720132962141981.
10^41550L+1: 559147407901.
10^41550L+1: 906420895201.
10^41570L+1: 82420125430331281.
10^41590M+1: 109192472487121.
10^41630M+1: 43632186357481.
10^41650M+1: 3161707311001.
10^41750L+1: 99665672979001.
10^41750M+1: 212218716649543501.
10^41850L+1: 2870200307701.
10^41870M+1: 8860836223361.
10^41930M+1: 1249411271501.
10^41950M+1: 25899259212068473601.
10^42130L+1: 1354360103581.
10^42130M+1: 18050659588501.
10^42170M+1: 1709073266261.
10^42310M+1: 51027318506935201.
10^42310M+1: 2296013837981.
10^42310M+1: 2662243846719936701.
10^42330L+1: 142455159019500647521.
10^42370M+1: 2727942538141.
10^42390M+1: 50322963180373777441.
10^42490L+1: 605114026721.
10^42410L+1: 2979553652021.
10^42470L+1: 3107318187219881.
10^42510L+1: 1366624403041.
10^42530M+1: 6461825441530021.
10^42550L+1: 792696458201.
10^42630L+1: 828630259381.
10^42630M+1: 5946704675101.
10^42650L+1: 278605707132652901801.
10^42670L+1: 7641423752266741.
10^42710L+1: 552521969204041.
10^42710M+1: 141309789379841.
10^42730L+1: 8812285155841.
10^42810M+1: 7268325030907921.
10^42950L+1: 57845102576002051601.
10^43090L+1: 28879983874241.
10^43110L+1: 269478394749541.
10^43130L+1: 5577052784140661.
10^43170L+1: 214330487551851522541.
10^43250L+1: 8405907207001.
10^43450M+1: 2055532635366822701.
10^43470M+1: 2011599114841.
10^43470M+1: 11050695524496601.
10^43530L+1: 128578999405861.
10^43630M+1: 380303581386361.
10^43670M+1: 54226484564341.
10^43750L+1: 1347882068400001.
10^43830M+1: 16692663510721441.
10^43850L+1: 10401614299201.
10^43910L+1: 665508127261.
10^43910M+1: 55947815846801.
10^44190M+1: 1632435163201.
10^44230M+1: 183122321062441.
10^44250L+1: 1049586813001.
10^44330M+1: 3562173057301.
10^44510L+1: 463914466021.
10^44610M+1: 1768994471821.
10^44610M+1: 18430304501341.
10^44630L+1: 20916209390339581.
10^44730L+1: 3881919850695181.
10^45030M+1: 2703000950101.
10^45090M+1: 59733443550241.
10^45110L+1: 845488610201.
10^45250L+1: 10845704710501.
10^45310L+1: 57898754325341.
10^45430M+1: 1376134576741.
10^45530M+1: 3404123844361.
10^45530M+1: 3404123844361.
10^45550M+1: 44227329632617601.
10^45590M+1: 844884618998041.
10^45670M+1: 585445008761.
10^45710L+1: 224303788748201.
10^45750M+1: 7030022317501.
10^45770M+1: 21714916862761.
10^45930M+1: 37515257386741.
10^46130M+1: 32600279511105881.
10^46150L+1: 1776690325413234401.
10^46510L+1: 118123525252841.
10^46530L+1: 68352036021721.
10^46630L+1: 6451376795221.
10^46730M+1: 97254940989388421.
10^46750M+1: 50741646835001.
10^47010M+1: 15400042849861.
10^47030M+1: 121116169763131561.
10^47090M+1: 898452079460990581.
10^47190L+1: 43184900971051983001.
10^47230L+1: 1387802109516345001.
10^47270L+1: 4796874135841.
10^47410L+1: 7078618984141.
10^49513+1: 10932892844917.         The cofactor (48696 digits) is composite.
10^49543+1: 2678687753249.          The cofactor (44052 digits) is composite.
10^49551+1: 24474674955270259.      The cofactor (32445 digits) is composite.
10^49574+1: 584093261501.           The cofactor (42460 digits) is composite.
10^49579+1: 84297277997357.         The cofactor (48371 digits) is composite, see Phin10.txt. 
10^49582+1: 10952478801476134001.   The cofactor (45719 digits) is composite.
10^49591+1: 6269320106503.          The cofactor (48981 digits) is composite.
10^49592+1: 11871704106529.         The cofactor (49535 digits) is composite, see Phin10.txt.
10^49593+1: 1305711316653823.       The cofactor (32369 digits) is composite.
10^49600+1: 5551380973996801.       The cofactor (38378 digits) is composite.
10^49601+1: 2801956965256147021369. The cofactor (49131 digits) is composite, see Phin10.txt.
10^49606+1: 2819397959131337609.    The cofactor (46638 digits) is composite.
10^49617+1: 9466742200249.          The cofactor (31956 digits) is composite.
10^49620+1: 9636598379761.          The cofactor (26420 digits) is composite.
10^49625+1: 102410836625990251.     The cofactor (39578 digits) is composite.

10^24915-1: 276314023123625191.
10^66023-1: 6285164700705307.       I am not able to determine the status of the cofactor (65265 digits).
10^99101-1: 52146269538373.         I am not able to determine the status of the cofactor (98089 digits).
10^99121-1: 1361819454161.          I am not able to determine the status of the cofactor (90088 digits).
1ß^99153-1: 956210697376723.        I am not able to determine the status of the cofactor (63073 digits).
10^99159-1: 11561506273489.         I am not able to determine the status of the cofactor (66086 digits).
10^99235-1: 856003690111.           I am not able to determine the status of the cofactor (78133 digits).

Alfred Reich