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 2013-09-12, 10:31 #1 kosta   Jan 2013 23×7 Posts looking for help Hi all, I am again looking for help to get factorizations of "Mersenne-Base Cunningham numbers" that is M^k-1 where M is usually the ninth Mersenne number 2^61-1 . Such factorizations are necessary to find primitive polinomials of order k in the prime modulus M. This means that there are many problems in applied math that can benefit from this. I am using it to give rigorous proofs of the period of my random number generator, the open source code for which is at mixmax.hepforge.org This generator has one of the longest periods and largest dimension of equidistribution among those RNGs that pass all tests (BigCrush suite of testU01). Anyway, at the moment the priority is k=256 which has three composite factors left: (the first one has had some ~5000 of ECM curves at 110e6 run on it already, the others much less) Please help attack this with ECM! Code: 27503817001021855161359142123867859536697596095777966914212896065652446437415997206851944428748759308483152015176751478208917632740831052389257949045686226159825984985356043711658640131389761 <191> hard one!!! 18930980212150778658143159711416730136200742355048430944408077805454501544121058050710438623644976643579568478748689225465038938464011530148153580043196665523858714780034943329382234044724038431213136488103194383542836308326302531830690671759473325150693000818485896079142024207488183191603066094867302274851408209161562196472627185861243239471360987259839668553810541197161303141253813264275710055206801996347252332812227469903429800390785873082786173337626096421170452409737152246875948865850487633711435886551375076509185416913355127882371024081834224488258386000239336533732116945580281903921924494316807817691156797500610949770841693483849196558599258677177705676976553150205835940759070498289537318393087261604572708010017854836977479828374989386550569063659418057201167954695411383147945528230357603719723696547333961155112227512439929740133098611028478305869122597767602582146640095838960695926111231800131722592648759637126341795289092147323739014629137162856102558399443776611642484170798487277697210069866968710484937247775411539481031091616532164626919230467431325286071942526953056351268465122294438939927278176983005832078321060029850695918105866066274046788062802911536026896981474014885913129520911433138796475692534782060893070985057746706217173247124181918725967990669403997597529414828421867709782091350185149307531843750815021462069060873453575319897052608945225640084772334413615797146036725174678922568067591496871308977483130768966854798748480320360870622758642995896034268261480756434754667920406093715528336844267867247338256307655462784524683809420997031711433610203696925756126945856673949133388697503272509570318063534023993896121971606390695349925517435873779906704805327266135931150033734455656611126074781992225597935828474911702362536852731103482395923168461628802728519468866722020764976600011998087549286313852498787283147187257577289747120355896768926636307688557050266379529593144392438596569456378549052059250084123434746695852427671287584079849438130271674182791128749594948820888742924263314384082546137614840418774285705037250753181482495539017794111186792812579490234863767435926094417745386364002239819233593542202017050428138443261649137703944886196732584922335620633467343749138099803112003180180690258536226891424336808618740692968322710999691689757811327180679514220956689022977 <2324> 24365121414823865519974600188078325214486272351320529928314106563911512133032811171346414609165922133106336606192803444592124927878301232565928372829350024741449992880412370138518873384617443518879005827840951350608884767033142386127110233509696773041253859206652540664915840753610129687118015922633393354940606382607175246399925639842214537685061012212377583743732389912438048906046363259466539559751651270351991744927420309584378384826777751243942090578631347270681210823481880346979275465839019657471561422751980296359238902125494593628182105541964462430791948530929551097376823042136081183131457591308295169572587394350784620457315592766793383134110304549567556857751048839273721119844014286434235517868064434555564880709409133862088487161556299918877927542836809844574855794130207563549145672555325522080734798030718639277682845735863238580724053654701234623482171059786718115752537591725404839829898229676028891439557715781781990539817629468227436757227411195413777839967484901992264793398973010134979481270840249460764878721045843734818432185838876867604005475815171007208499204508892825711948217539972177886564445126091946810033457579139733887872912106113 <1163>