News - February 2010

February 24, 2010 (Kurt Beschorner)
10^6010L+1: c2348 = p31 · c2318, where
            c2348 = 37910705837697300026153488386531786759487974248900973304216045537237738087051987058724649528050379910701065164765164657967589128518226524567720374848437068621661076731517555062838278422886800121070136823895875857800795982520869551234820930556386242024220092274883816078756443605256977016861238083052891674168424479800249168419268498554317543819355597916624647972144470192601492963770622636992334291519744781809966982345820865009623517035363299826096886306941367964752431158362230242965604210435302388544300261110235871289271480789459022843668144510893408542933893748295909186440973023864418870314653338601463507238352716304192739394132907755562598682094862903862422925861349986744528067304155312877675608374790179131344115757314193478950613024830640672950318494957994123411382625161321482619712609651275802067366735343397629042399647148462973398279120730518338621614329892830086393758185387487563077241913272545915304458722134374226098636864215020028353096878564892428899989018413675696173043319218089865585188927554288978347878767617524472487179284859885804529553519272015478248279835816914835298302420280154167134731198159837980074869893967024576079831916071584660086765015493031536265959325565913562684954592985923294956926018596966719476114138276111670919854057373782819517297535069387398867682403474969031695230381683505714159815000943805631725099276560882420638622018277039793017626939498380233379696665643717965640250692846049213588852078603884513940548702006621572815641772956846229041371479503943258541221932065161812113798441808405932331742141350422157795641820266502091358471744329119441810848001837519073128101187889861376382760041323146029843848449121013347311381740547782755915437455596346189526195809970198078533667136146621173756938787468372276609667399480573442413900096310745076868183392001437928460989075977596164867866565983306991963667044153051016363620942632401824155633353760591635514553328392465252761839219460991504288480140061043326995201527903086067966059747503811221106402395842622969447849312291292500323136778326377321756307925342201288976602218266174181499736080041091532374741458413832872095240199764504609834803740635931731562045336606062691886856891072755175048825271815056054768412958556468909194997512249450501951391989729788328404269713559327637680270382810331736898198459235668204299983814677170077252480415381,
            p31 = 2271081206408614161804095941081 and
            c2318 = 16692800649628723703393008150025747314237740638722567737882339342557377908665738614065127573474586822840856883085413733028226672471533607906739753599431030352242574779019975494345798680478160118836412564499122827792429262551708071487005519348283896708458110012886544985150868521907957698207898883069750152072203083240161324044454188991380553078260475382058399394626223892137086750813585061447180923515240115350048744769569368123432197599541603714566710224460310722494691565246971501881378407311357304731603154224513333105917229421642750657795954420679534071654774252297206323158793446567521536632175087024549926745653417925134977377315199952388388433011642249169243679754811520448080615682604504441346193338280381344490319846631540150555108674833475502021467370437562471331221570575887894216027957952548593213645939770949846259846668606820471704125607453663533563306254859598355355564797151401915891145768876201702859520023994157178801454084712896595919576512159746420320266908485738023588899222764107352670919950862979205030243360220232944093519675483507333553686207072213465897431580138765321427471941413566093215407124435916396952399400987481321891733054800161007909457916885964321412959741421433488552463138007193516326887230012135128727115007966247716201324071248236073779488023962556238440249159275042644860891816036219256090564843878039862622323841584350638721461123054242849756418185771053319504645314167028769130500246779230868244555860728031313665435032579152827228344778203038145719791696709831634007837631672342927085620401009831675395212670147405458035600312259442710065572908598617087671286253266379059169853302250097891493142101905667715580283663218728967314630935260940413401320499146665647437126393799993475733477095602086107511562570199553359459339056745705470642202105776650344268901778102673403497563794803646162656341286730345619788199369977754645940852258110190403741931587820569341607633269437499140955747102774301878707122491661210642874315815773108086540655665868605776040386115111348177008774806562732563780920113973147592433910983090284493055078077925760854042955200494948135632315692587177189988178501571809014952484396215152184020663244558394229249045670451444816518117328197776247879813615198296264820563609328996951635006325846752133077171800135933335569522426806803364524341049240150301.
(386M^2·41)^41-1: c95 = p41 · p55, where            
                  c95 = 76633882041115273911499223590832874162486598905865953062999821909840507218243548596582433508487,
                  p41 = 27069506453896006859364783871186290493513 and
                  p55 = 2831004036650459977847865028946592934553840434171153999.

February 20, 2010 (Kurt Beschorner)
(164L^2·41)^41-1: c96 = p45 · p52, where
                  c96 = 787304537268398037382411752795574363454304575162707974186177554175510176745752556004163747342237,
                  p45 = 213322192598034905474183162784682727333463757 and
                  p52 = 3690682754006394822039890884277154053403084317082641.
(186M^2·41)^41-1: c96 = p28 · p69, where
                  c96 = 876580058465902431282397677377746851242740013417718206417533054493464241259265860274481876674601,
                  p28 = 1246004766670927471180187141 and
                  p69 = 703512604376263275613220166928615185235242692461122067149972576399061.
(202M^2·41)^41-1: c97 = p44 · p53, where
                  c97 = 2062449977360755507274992069507766655809788292617531988864980216933457270169056191807591521281713,
                  p44 = 38705781800015590484579052147922503636202349 and
                  p53 = 53285320214354248318319727723628298752683667707425237.
(305M^2·41)^41-1: c109 = p42 · p68, where
                  c109 = 1620836074495280086865572234278851671101507610722908874127936996875977038159752737978961053418954819445283639,
                  p42 = 147023027521613721156175494859070841950459 and
                  p68 = 11024368779625371638738038621133492793559013542546085592433184236021.
(317M^2·41)^41-1: c123 = p23 · p100, where
                  c123 = 262943967559995925813411169784599557967781069401396411367110045729199325667965167431608515922765154846787477906706522629293,
                  p23 = 87575093255418405692621 and
                  p100 = 3002497145999067242619824650690076591277544949268137567173259761130693277324548715912270936735956833.
(377M^2·41)^41-1: c134 = p28 · p106, where
                  c134 = 24626634353506552447845041956723383617955290459908696108182317875220623820406531530932284512394666308111235437868629444380629368374607,
                  p28 = 4909048109609194251437430893 and
                  p106 = 5016580364185320826341376354642239191125819745199754593981832481458024179007065765776058256361717483763499.
(378M^2·41)^41-1: c126 = p25 · p101, where
                  c126 = 317554686999384905787979402621658735672550806080523561251161295420797677134916914647433067763140023835933828952327473257316303,
                  p25 = 9692496447249467774850427 and
                  c101 = 32762940768423023787869805546505156251021379007327412444983446467896686131678973879001976813418572989.
                  This c101 is reserved by Kurt Beschorner.
(382L^2·41)^41-1: c90 = p40 · p50, where
                  c90 = 171536394609188209174007724547419101415015790891592784234345387716468483241306673231100989,
                  p40 = 8889669243574317616923526753684495038091 and
                  p50 = 19296150386380139258045496774851034607986047809879.
(413M^2·41)^41-1: c108 = p49 · p60, where
                  c108 = 895471724659801794968852063929150888759836470613753295768246122563238827294100851305102955912684410044486599,
                  p49 = 7908893452552558774394349973744179943731145603681 and
                  p60 = 113223389597035529462881948181274087967440284238972397571879.

February 5, 2010 (Kurt Beschorner)
(205M^2·41)^41-1: c96 = p37 · p60, where
                  c96 = 336837467328904425691879937530957944239753738762428975318846142692015532383871950627651711913839,
                  p37 = 1828032163497191134145983377286499251 and
                  p60 = 184262330857737117633164526534503149491303316419473167605589.
(294M^2·41)^41-1: c99 = p30 · p69, where
                  c99 = 445059033074672132124193182109767278976066745783573553514441615782924549256942618225039029094721453,
                  p30 = 494040850374420340434195869243 and
                  p69 = 900854722311674834812754664465403619764746084363606523648315308956471.
(295M^2·41)^41-1: c92 = p31 · p61, where
                  c92 = 18768894654122600987051040130822474200888192597482162516496355506081197085203256195410887883,
                  p31 = 1951237907023001280669401765549 and
                  p61 = 9618967828868318725354331588069066903093290783755343730298967.
(298L^2·41)^41-1: c122 = p28 · p33 · p63, where
                  c122 = 51371484801926251096949591945642692012461197972445095077917714093554895286247437417586011786551628871918541893258684990471,
                  p28 = 2192483693918755795464230263,
                  p33 = 129606939849894818259006589332377 and
                  p63 = 180782958670430699712336595996843707885747150342333595955767321.
(299L^2·41)^41-1: c105 = p44 · p61, where
                  c105 = 268698177559360540086894492376151072672651296853729843333184598934492391659199662860798948885448139522247,
                  p44 = 44097025325301608410073301091844912276658239 and
                  p61 = 6093340210075105274328343266845908837595902512857839659857273.
(306L^2·41)^41-1: c92 = p35 · p58, where
                  c92 = 30396937309338289973899973965406936804279653943400913307785279803348866407988307135722613889,
                  p35 = 11806712796329613868962865555608407 and
                  p58 = 2574547025382701921026447974325002963551457468799958986727.
(412L^2·41)^41-1: c126 = p26 · p30 · p71, where
                  c126 = 155660860868393573844234838446556684807269289154983682516547507169692253580503631009700238155742125841379973979144246411599631,
                  p26 = 13343606163407535190579303,
                  p30 = 117035903434161340762240774001 and
                  p71 = 99675196553438235907665034724889202069832343625805301488644769328923177.
(413M^2·41)^41-1: c132 = p24 · c108, where
                  c132 = 103864744481445560283866960431010507180707801567581210916777571818059150328846580573798850302652564506167362652229707628717411157809,
                  p24 = 115988859973110554942791 and
                  c108 = 895471724659801794968852063929150888759836470613753295768246122563238827294100851305102955912684410044486599.
                  This c108 is reserved by Kurt Beschorner. Done.
(587M^2·41)^41-1: c142 = p24 · c118, where
                  c142 = 1210216198528749518372610027654269181395662874971239197775536918984733945788019017327327591009973214774731178971668760508417085980409675295167,
                  p24 = 244364926367604776696033 and
                  c118 = 4952495501372355357996496364534993494252881828297102502936914908764168766977698862661017580813649216471973196273866399.
                  This c118 is reserved by Kurt Beschorner.

Alfred Reich