http://kenta.blogspot.com/2008/11/another-mersenne-factorization.html m4423 36th factor has small factor 2882790544393664237 gets stuck on 37 38 39 37 largest known factor is 253783861 unfactored part is 284891188934854761075447734204701908097761046072419945476382569947345104294900582040260023671 Yay, gmp ecm finds 61600717972064819860723867 , and the other is prp and easy to p-1 38 largest known factor is 2498237081 unfactored part is 10372370909391536204545067734059960974672158219375926848186934744241095566515227198379857062995673473946359602284090334324384555976087536909351564189749185700645334904314024668472853512903012259377003527538955246398711153026961072390567553734355420908110621886682622643299038572672765733641865781 39 (largest known factor is 638238527) unfactored part is 1309425332388442587762826922143806166428674303514320453854835573709714744339756290446740027272721411377979071210034788826087747458077711674569985029950975939337393712131116009294668834291539762044934806565677168975467574370114790166231173647896541846519820693083546262088214688140161155840768898680679726755298579163383041561032948037274103628845240735417288454181543 ecm finds quickly 553362189986261 7749626983220333 composite 38088970701321403810011501959 (which factors to 20096256262837 1895326681903307) then 52932220372127992211814054099547 p=2^4253-1 ================== p-1=2*(2^2126+1)*(2^2126-1) 2^2126-1 = (2^1063-1)*(2^1063+1) assume these are being tackled by cunningham project Aurifeuillian 2^2126+1 = a4*a5 a4 = 98829225247710262867429368515096341332791332892647518728955741224331220492185227974590031104217345944915565363435943316108305047551656971126471386689813725547601870716934221146297324363107434598312012508259576563530352855351551239307522379530819187475461501477831677599745547307832992983120685542302906135815513033408513 and a5 = 98829225247710262867429368515096341332791332892647518728955741224331220492185227974590031104217345944915565363435943316108305047551656971126471386689813725547629988928150116123689890228780471984929948115248963542487232577680375224186719178720313191763610819335018683291205052902353044645967524915359209355695920307503105 a4 largest prime 118640804957 remaining a6=699652542389221053115110798703314589881048796127345052828504201824175195471825242261424036428589931344419630141787823239548038747848278992468829785078950402244949971433361568757989478923451267737663284684229157431356340335391853950222875799779387571137084614491240494814600203723953339429184797 is prime a6-1 largest 1063 remaining composite 879928844292489037074859768669181901038138449005872106524899514823065579044055068469099205191378868383320878431273390363701810972688887509959238791784615232649184242248204769014631024750166348566592487063941168209431912928539264253403086562321584521580388234402735290111479723570101442579 ecm quickly finds 44443063111687284151 a5 largest prime 6262064969 remaining composite 3156442027892038079793016229726579233540728628382505008435524624284083197993573163599990465196891697880292795902991319351426711381079475706297846514399960245689683100065265902982677605265850827199552426593450871700377357668400620651137137019387995166730146371147261193201620802358463829791911087895300607051109 ecm (slowly) 51799226966893295289509 51114358532758153182876066459473 1603777152900827521607976402498110749 (2^1063-1) 1063 1485761479.P311 P311-1 largest 1063 remaining a3=2607304716555547761549355846631472474523696305068932268443860652900506622021270380500805673863814098789310639317924187611916776956395055215320487031976399301549034990921194820627136343457050440412835283760936562886297374734942115392150967596397779779996972897894237892028265935347184016132893275359371346461 ecm finds 34395645589799529689 5555064079229513572161110958917 (2^1063+1) 1063 (1) 114584129081.26210488518118323164267329859. C281