Comment on 4096 RSA key in the strongset factored?Comments−ingenter11yAhem. For the first key they mention, there are more factors there!The key is probably corrupted or generated improperly. In[2]:= k = 81702302396037694663397550711015464924940759880679873041484988446177\ 6172171921668594148071323527016137506405823108520062504849249423700259\ 4069053132814039014100827620971595602214630489243361923840267775021772\ 6273104520032220014977312750288854523497313948088764458519260063105896\ 2876114156934248895171959246969597637127280010272143593885240940877456\ 2346621961304914007384387318325143353538246979304530784267221911051575\ 6839282687004365570800854541114336776383656601174049938345659212966258\ 5004880376777597714978023542434421914201119537685489173509942329090631\ 6620146500331426421109143608494218561796112264508065622355348025160815\ 9525991476849744470271874940233007048802875107373034946075277191548484\ 7399385631524708487646079936572410398967582895983187640798072309362094\ 7276541676286201059814590215482904158000967692144374256909343720156287\ 9602749821990244128818939838635984666162324349353489741141768543542401\ 0451956954083531228374002591372549525280610594684910812811287436481207\ 0897631254242477930440433097372694687097106798722692728553899453853864\ 6776550988064892974349821432957828887498719376843935338230526010842568\ 8024147656806932474058888992099083804597481699305852902662863062054067\ 183925164590726103552998367994727700722491707; In[3]:= Mod[k, 231] Out[3]= 0 In[4]:= PrimeQ[k/231] Out[4]= False In[5]:= k/231 Out[5]= 35368962076206794226579026281824876590883445835792152831811683\ 3100336005269230159564566264642219487505414028494852173187231536471611\ 9914542887035988231185720389968667087270823469537008330459707290159209\ 9661353364980311702259746743425433025478148700135908263534397627385308\ 7038512067581886118722465442406600419739236851636368083179044971965775\ 2716260756113403162300436097137367240321798068505185846117222626502991\ 7972189107914583118772974372664303512699903196388139036385254695090568\ 3836616885229600336622387436373827893689140346804994669042932255386289\ 6496240961102381095855593553741821858969074370611369916911524829154989\ 2471064729866440194694575875270536897405648832413466395253223409210905\ 4322444761638801525847830149818154360350822063888699559821489522975025\ 6978765054779946444242883036619140901690111688730602659902275718330614\ 7862718442748840688417371783090839236356998338668549503675212615484217\ 9837233961886127308887977651083372888549578043554369993467884333890665\ 1433796925381495343064039151702639555279085323422856589910272101255174\ 8285128474697397430689599285636983964428089826285444521184129104123814\ 2175622521276041907762975783068827748521127531377359006862728425481845\ 0450507289719327232580534861464796513972730400397−ingenter11yUpdate: some more factors for the key. In[8]:= primes = Table[Prime[i], {i, 1, 10000000}]; In[9]:= r = k/231; Select[primes, Mod[r, #] == 0 &] Out[10]= {19, 7704959} In[11]:= PrimeQ[k/231/19/7704959] Out[11]= False In[13]:= r/19/7704959 Out[13]= 2416008079731972085604323566968184938863361678449872200338542\ 2782524728573078725530058065928860640441907473143687288939310762579324\ 2201448845923773741805403670269789344162077509161854710812642480618084\ 6418886532753250669796572553463393409872248215326471682480854051430439\ 2318772751800215263874553179418646615820937142842296219000273581288825\ 2789449984922109948745889094702540699357374091188011161049671668836093\ 7278541145959209900694985382835863685677859045842263065588173367519102\ 3000601703070615085046450531430050636608745665363730079826233868575064\ 1515845148088351185382897973393486745557331417516226266671518736327371\ 0952774886507742692568074519503781293211406810410464658659799378912020\ 4022428232439503300191599103479511965185485160912786274522509295156878\ 2006686251281732387799849219226976241206277650039929011945237627811183\ 5293192238971567100891050322477609224503267676028587870533168970890197\ 7752061262164585534348926085756033558766611288812716862195529175560192\ 7171277951291635708971328803457524430235472568512308733137100548610807\ 1730859408357205400252076841587686986935644804331821576562378722868016\ 3691408455343059061584335066277570324891522017892861973483415607333423\ 704276600438478560110515119729110048093857
Comments
Ahem. For the first key they mention, there are more factors there!
The key is probably corrupted or generated improperly.
Update: some more factors for the key.