News - November 2010

November 27, 2010

10^12081-1: 1724480816333576801839.
10^12367-1: 1487192139534351057115573561.
10^12373-1: 27325360511416597951.
10^12395-1: 184617062247694121.
10^12509-1: 77681242464095187660961667.
10^12517-1: 5908703072659511.
10^12663-1: 38254844402833106909449.
10^12709-1: 31220830091797747.
10^12745-1: 5832361282182431.
10^12769-1: 22592695963417744550923.
10^12911-1: 9198174861727024769.
10^12965-1: 8808001357546909788241.
10^24321-1: 9667131861564871.
10^24379-1: 1029747750513791.
10^24439-1: 23574215504823631.
10^24659-1: 94176197153701346164519.
10^24773-1: 59453029091324443.
10^25419-1: 95241707878522142932120761779041.
10^25609-1: 26719140674671.
10^31019-1: 1583551991386241.
10^31049-1: 8695473274933. <--- Makoto Kamada, Nov 19, 2010
10^31069-1: 16748753384707.
10^31105-1: 1395792461824726111.
10^31205-1: 1169980565914801.
10^31237-1: 1863835345564121.
10^31253-1: 14066410160112934921001.
10^31321-1: 265282013748282733.
10^31327-1: 12092597064428095717.
10^31339-1: 430056441105523.
10^31351-1: 52585924486759.
10^31435-1: 46588201324591.
10^31505-1: 431967144411601.
10^31709-1: 24790303069517.
10^31729-1: 210043540293733.
10^31771-1: 49443711902573.
10^31805-1: 80656785887681.
10^31837-1: 92936422630707787.
10^31919-1: 138776692786241.
10^31945-1: 326298816330001.
10^31979-1: 52279299068387.
10^99357-1: 6301692885751. <--- Makoto Kamada, Nov 26, 2010
10^99543-1: 50557787767969.
10^99615-1: 111610911769420962511.
10^99627-1: 733724036710068559.
10^99693-1: 12405701812879.
10^99797-1: 135782225399281.



November 22, 2010

10^31061-1: 282355206417733.
10^31093-1: 47621332646130769.
10^31145-1: 7642285102841.
10^31199-1: 67491785852401.
10^31211-1: 8395238587787.
10^31251-1: 499092473998113601.
10^31483-1: 6375979536119.
10^31641-1: 26441225322991.
10^31677-1: 5574449910973.
10^31853-1: 390987284638992919.
10^99197-1: 26073703407258646441.



November 16, 2010

p-1
10^89999-1: 528029339442151.
10^99003-1: 236607740954281.
10^99005-1: 4142811101293121.
10^99011-1: 295303889057180587.
10^99063-1: 55060464584431.
10^99077-1: 36727920585599.
10^99083-1: 34714947331962311.
10^99085-1: 154913309519431.
10^99095-1: 78698145542791.
10^99111-1: 38280413774666554333.
10^99135-1: 1262269938768433921.
10^99155-1: 1046409055525751.
10^99159-1: 347403606470064891067.

ecm
10^99999-1: 1756539274631599.



November 15, 2010 (P-1)

10^17086+1: 12456395205586731109.
10^17255+1: 1791041698862921.
10^17255+1: 58289088726037681.
10^17386+1: 3634682523576029.
10^17411+1: 407206211743333.
10^17421+1: 2283974015136097433251.
10^17437+1: 309112076259639964827167.
10^17463+1: 380173774647910945582520053.
10^17499+1: 12311143940123088518569.
10^36615+1: 44935390256641.
10^36616+1: 30456284604497.
10^36621+1: 19958310875514259.
10^36622+1: 378846367323864961.
10^36625+1: 794764802176667251.
10^36635+1: 2729819567910601.
10^36645+1: 33046192368697201.
10^36646+1: 224770740916829.
10^36654+1: 4869545241568621.
10^36656+1: 58799411155184449.
10^36659+1: 795013032524715813799359041.
10^36660+1: 42914795757601.
10^36674+1: 32312121659929140355129.
10^36680+1: 878464987055041.
10^36691+1: 678625831361419.
10^36697+1: 6439429340899.
10^36704+1: 376102900000769.
10^36706+1: 8705113105621.
10^36719+1: 85087350529813.
10^36720+1: 6520221214130881.
10^36721+1: 5139110064043782647.
10^36731+1: 401370581442223.
10^36760+1: 76733314784405954879041.
10^36761+1: 58053062808413.
10^36769+1: 12457947271249.
10^36778+1: 9429535546369.
10^36798+1: 279745880961954481.
10^36803+1: 6470778964450809997.
10^36811+1: 8868513923933.
10^36817+1: 20182301646765721.
10^36827+1: 13324602766819.
10^36837+1: 1850153215841533.
10^36839+1: 708241656977383.
10^36846+1: 16245149299669.
10^36859+1: 5087788866253.
10^36863+1: 369066347552179.
10^36877+1: 35418378500117.
10^36881+1: 1599996850553877049.
10^36884+1: 28454106023720129.
10^36896+1: 26796909748417.
10^36898+1: 8242515814961.
10^36908+1: 36097305901795249.
10^36911+1: 17749313801927.
10^36920+1: 20432418510401.
10^36929+1: 13475481246607.
10^36936+1: 11759763683377.
10^36945+1: 19300384325750041.
10^36951+1: 8147664462572079435019.
10^36954+1: 147110130929341.
10^36957+1: 5286097402321009.
10^36965+1: 31029263932412521.
10^36968+1: 417649189632907725569.
10^36979+1: 1231770521872643849.
10^36980+1: 12383769336871601.
10^36986+1: 528629916817764701.
10^36992+1: 192243852274433.
10^37002+1: 34763117395861.
10^37002+1: 135843629131981.
10^37016+1: 673296894463201.
10^37018+1: 2754078256156061.
10^37020+1: 96861104571841.
10^37021+1: 41704088053427983.
10^37024+1: 52305056729537.
10^37031+1: 41425289465899.
10^37031+1: 66847333305203797.
10^37032+1: 8408630492929.
10^37034+1: 5217345646267215569.
10^37035+1: 29003364430921.
10^37036+1: 6079949978857.
10^37037+1: 9522450591836183.
10^37047+1: 883696207973629849.
10^37061+1: 35769622449392307622441.
10^37063+1: 172444670293013.
10^37085+1: 6161328601201.
10^37089+1: 30241335746060011.
10^37102+1: 17784249858893129.
10^37112+1: 75304901992018850561.
10^37113+1: 18015816364687.
10^37114+1: 51875559942084341.
10^37117+1: 714537090037698166069487.
10^37118+1: 13133734014941.
10^37119+1: 219888599078014579.
10^37125+1: 5487364872001.
10^37128+1: 39331867437409.
10^37139+1: 4672438779393613.
10^37146+1: 1499007668533069.
10^37148+1: 123022291611841.
10^37151+1: 154649983460801.
10^37156+1: 102646126888637417.
10^37158+1: 8351707221130549.
10^37162+1: 142345623359509.
10^37164+1: 16763096990617.
10^37164+1: 4315277427158473.
10^37164+1: 4663173035455201.
10^37166+1: 12414482789701.
10^37166+1: 51170996110469.
10^37171+1: 3819592943890201.
10^37171+1: 5785257571125889.
10^37180+1: 66379544293062001.
10^37183+1: 25987082837773.
10^37186+1: 2537975619466663501.
10^37188+1: 1372015529955440187409.
10^37191+1: 28213856501131687.
10^37193+1: 39437314213727.
10^37200+1: 1745437380691201.
10^37208+1: 176454287586097.
10^37214+1: 19738266599729.
10^37218+1: 2164885507637320261.
10^37222+1: 121755074499255338914301.
10^37224+1: 583877811816289.
10^37225+1: 1252182167500651.
10^37232+1: 16348981436324161.
10^37234+1: 33014896211412881.
10^37235+1: 4254425193811799024700001.
10^37239+1: 715972215630103.
10^37239+1: 650482612077314521.
10^37241+1: 5840527268020927.
10^37241+1: 41291010132599413.
10^37251+1: 659986205529583477.
10^37253+1: 36736857673339.
10^37258+1: 254061851550781.
10^37261+1: 20515514986891.
10^37261+1: 36275758739723539.
10^37267+1: 122114156575648571.
10^37273+1: 805804139653509041.
10^37287+1: 783464591954287.
10^37287+1: 1306361165367293432533.
10^37289+1: 267505659382738053936207361.
10^37297+1: 202746989430982201982921.
10^37299+1: 5529233056947139.
10^37301+1: 8337277809521.
10^37303+1: 5195903535481.
10^37303+1: 23188419629957.
10^37305+1: 2001840001403469193801.
10^37307+1: 141141228578893.
10^37307+1: 1998272809183181441.
10^37314+1: 7957069900849.
10^37318+1: 28818981489241.
10^37322+1: 2851995031355320181.
10^37329+1: 372611152817192927089.
10^37333+1: 740458240994677.
10^37335+1: 17101839034036679286121.
10^37336+1: 6221183730529.
10^37345+1: 270301790546476921.
10^37349+1: 1485933403647733.
10^37351+1: 3238167493499893.
10^37354+1: 8022037811607601.
10^37357+1: 39385240699821899.
10^37359+1: 1952759231814133.
10^37365+1: 36866488500451.
10^37367+1: 2970972734739571.
10^37372+1: 239859696582854401.
10^37376+1: 4713611808176129.
10^37376+1: 56142652717310977.
10^37380+1: 5103792383761.
10^37394+1: 64213641522549709.
10^37394+1: 74342195213064211049.
10^37402+1: 8257355215559129.
10^37405+1: 107007022928202110281.
10^37414+1: 16953975530161489.
10^37416+1: 54004713160129.
10^37416+1: 23845885141878193.
10^37422+1: 57192310915741.
10^37422+1: 2017807841175589.
10^37422+1: 5970630680852579281.
10^37422+1: 2344176544266279863189281.
10^37424+1: 81174413620180897.
10^37425+1: 1841001294897400201.
10^37427+1: 11534467729904081.
10^37436+1: 43900587458401448881.
10^37437+1: 405286928774826846103.
10^37441+1: 31751357335029401809673809.
10^37444+1: 318684157007833.
10^37447+1: 105725790254099.
10^37448+1: 142674388060289.
10^37452+1: 193038099123930831409.
10^37456+1: 21446647947553.
10^37460+1: 43823897494241.
10^37464+1: 70092677215888321.
10^37469+1: 900824329441681.
10^37472+1: 8592825234574657.
10^37475+1: 392305694920651.
10^37477+1: 5337221567217494131.
10^37480+1: 439103749216481.
10^37480+1: 3121248527772961.
10^37481+1: 56414558040340961.
10^37486+1: 17038874379148574509.
10^37487+1: 3334616696503414081.
10^37492+1: 123278840072013809.
10^37493+1: 151773188043958681.
10^37496+1: 3505095271822556161.
10^37502+1: 3037273614287201.
10^37511+1: 1558792149561133.
10^37513+1: 4121829378145459.
10^37514+1: 11044859590413601.
10^37515+1: 292725656045041.
10^37520+1: 95854930628801.
10^37520+1: 1656130728145601.
10^37522+1: 29692405526751449.
10^37525+1: 2130134652872801.
10^37529+1: 51996695280379.
10^37534+1: 2921799464396739361.
10^37540+1: 320909907215921.
10^37551+1: 7462775807269543.
10^37554+1: 16083728140261.
10^37554+1: 893755362671029.
10^37556+1: 17076110860572697.
10^37557+1: 35185596937921.
10^37560+1: 61332623637121.
10^37560+1: 2758298514458881.
10^37562+1: 15419797484561.
10^37568+1: 233179326097409.
10^37569+1: 17420850643477.
10^37571+1: 2408376891658495649.
10^37576+1: 9146797080209713.
10^37576+1: 933204327352590833.
10^37582+1: 8585010722021.
10^37582+1: 11620513898009.
10^37583+1: 21536380869277.
10^37583+1: 1570147275482969.
10^37584+1: 5641186182358392762337.
10^37588+1: 87872472384721.
10^37592+1: 11334558872113.
10^37594+1: 14437347880201.
10^37597+1: 402731039221127.
10^37597+1: 3606426929312579.
10^37602+1: 2815769062950229.
10^37603+1: 3857797205427731.
10^37608+1: 57024759178561.
10^37613+1: 21741384541207.
10^37620+1: 4735023088158001.
10^37628+1: 41642307583913.
10^37637+1: 12276784732997921.
10^37651+1: 3557210450316314717.
10^37661+1: 72138743443729.



November 11, 2010 (P-1)

10^36722+1: 8829699140641.
10^36722+1: 8408768466750961.
10^36951+1: 6001519268419.
10^37532+1: 7642781454617.
10^37541+1: 15911748645409.



November 10, 2010 (P-1)

10^28537-1: 56671787993053.
10^28771-1: 7121713448277107.
10^33013+1: 25519641024884915534179.



November 9, 2010

p−1
10^18007−1: 11896280396837.
10^70201−1: 23728981809233206790107.

GMP-ECM, sigma=93e9
10^6057+1: 995539901827070009162143.



November 8, 2010

10^7038+1: 156238450624729908181.
10^7077+1: 122284157927089915051.
10^49740+1: 155524609662001.



November 6, 2010 (Kurt Beschorner)

(366L^2·41)^41−1: 22812598712443368656340194368618050781886978901649. The cofactor (66 digits) is probably prime.
(702L^2·41)^41−1: 73383236203323740377871399292515266385817765989. The cofactor (69 digits) is probably prime.
(915M^2·41)^41−1: 52267572653142986766506382689299127690759. The cofactor (75 digits) is probably prime.



November 6, 2010

ecm
10^7097+1: 4394001804830499637.
10^7309+1: 2436052512587885912915699.
10^7505+1: 3156875107699511443081.

p−1
10^6005+1: 2442638856271163903621761.
10^7128+1: 384968604460972625281.
10^7166+1: 22513288673933375800025821.
10^7181+1: 6173117789805541903545241.
10^7362+1: 77867204524505205255469.
10^7369+1: 197311855283869947402373.
10^7511+1: 8974327105215919414380211.
10^7522+1: 1436076295276259330239781.
10^7524+1: 9356104244617585012801.
10^7534+1: 147558060456282171692111809.
10^7558+1: 151099594304313503010961.
10^7566+1: 83026979924678346339121.
10^7570L+1: 381277271849181567593656104821.
10^7587+1: 4224281125236884368201.
10^7588+1: 12416444050991264173009.
10^7594+1: 25055811155392021750745189.
10^7618+1: 16968225776179351179169.
10^7629+1: 41642545231979343861594481.
10^7637+1: 196343473965722630709961.
10^7655+1: 112030732721431002149258790241001.
10^7658+1: 57537762082503123290801.
10^7704+1: 261467649473976978823842193.



November 3, 2010 (Juno Fernadez - Msieve (NFS))

(844L^2·41)^41−1: 11355540765711596569311849358824170567477822173. The cofactor (59 digits) is probably prime.



November 2, 2010 (GMP-ECM)

10^7044+1: 7034806653138011359093033.
10^8034+1: 1368296044086465469.
10^8133+1: 144765760714756900321.
10^8569+1: 263604275213578322167.
10^8763+1: 1446911685748693.
10^8803+1: 2017926571665167.
10^8956+1: 30015759970061753.
10^9020+1: 11596509745342721.
10^9022+1: 33151171352600549.
10^9503+1: 104663459422923639317.
10^9580+1: 322409873144081.
10^9581+1: 6818255837179821607.
10^9786+1: 192314112075597709.
10^9793+1: 26932124125301543.
10^9856+1: 72399380883225089.
10^10955+1: 22942795783072411.
10^10975+1: 37465005898485836851.
10^11223+1: 1355558247889821913699.
10^11480+1: 18125332129564801.
10^11566+1: 65599853216661299581.

November 2, 2010 (P−1)

10^8938+1: 930717893422366057402421.
10^9057+1: 773103130591216120489357.
10^9733+1: 45938080281148881852301573.
10^10912+1: 27524562432590198977.
10^10949+1: 220356511489392779.
10^11102+1: 19975170627732389409341.
10^11454+1: 81286041571977481.
10^11468+1: 7913885708154126713.
10^11475+1: 178308408770295357601.



November 2, 2010

2010^79−1: 744442872351616714609262547487618790892937.


Alfred Reich