News - July 2010

July 31, 2010

10^62969-1: 46870969361511707.
The first yet known factor of the repunit (1)62969.
The remaining cofactor (62952 digits) is composite.
P+1.



July 23, 2010 (Kurt Beschorner)

(181L^2·41)^41-1: c109 = p43 · p67, where
                  c109 = 8972850469601776463689365386933194785768817859138973115139049033680226350880013798249620219765594776702032661,
                  p43 = 4243838935475778877326819962130455836128041 and
                  p67 = 2114323989677008269772065586976281944099609130092616482804150071821.
                  GMP-ECM, B1 = 6e6, sigma = 1782539146.

(206M^2·41)^41-1: c110 = p39 · p71, where
                  c110 = 11155452272045305743827942218833925038462770450095405666179928455232862252733839687402043330516900896850593429,
                  c39 = 178780222782639507024104107998382393579,
                  c71 = 62397574510286147813362639131422554312594612622569901631902505708097151.
                  GMP-ECM, B1 = 6e6, sigma = 4178883682.

(498M^2·41)^41-1: c108 = p45 · p64, where
                  c108 = 180398600125025525932487840169434894314187781571621278347234600434536254249954943679133256275093338713452839,
                  p45 = 105394811449076334339596582006898601801251179 and
                  p64 = 1711645930617645357544482902934090316159219766075018575780735541.
                  Msieve - QS.

(794M^2·41)^41-1: c109 = p41 · p69, where
                  c109 = 4998733418369888368525641330145175303172460096770386390456336272165126165054434973807538962532071981694191363,
                  p41 = 31530102344439603124400795802213464856427 and
                  p69 = 158538445697478842679502332301543533437275430436682248960271843437769.
                  GMP-ECM, B1 = 6e6, sigma = 3479853553.



July 22, 2010 (Kurt Beschorner)

(704L^2·41)^41-1: c109 = p39 · p70, where
                  c109 = 1787666521104559351137280106026558415708089380725231244965792913244291071570634273564507083069655209329009443,
                  p39 = 242362892515755121224002739964401864787 and
                  p70 = 7375991029601817936377148502777954503426581830516210219813187534178289.
                  GMP-ECM, B1 = 6e6, sigma = 947989910.

(962M^2·41)^41-1: c109 = p35 · p75, where
                  c109 = 3594861637232478044274570152927808055854078147439217126683000656232662431750535814263938673531689967300893927,
                  p35 = 20079297591200564141037344941780847 and
                  p75 = 179033236641099912116468229795449055022015170638295041694099301871109893641.
                  GMP-ECM, B1 = 6e6, sigma = 26593205.



July 22, 2010 (Msieve - QS)

(418M^2·41)^41-1: c111 = p55 · p57, where
                  c111 = 960310915528084914728044157360356619217318385455826184819343050707577003776021495143003192330125260698415533359,
                  p55 = 4577072001657400636307454889709485239867397824413425649 and
                  p57 = 209809003480903804627884633165045819869648555564792405791.



July 21, 2010 (Kurt Beschorner (Msieve - QS))

(551L^2·41)^41-1: c108 = p40 · p69, where
                  c108 = 548000975125759903714291186924428657377180355054306734546842464087547486850974550642478386815802286693662987,
                  p40 = 1500327274951291607070038052012285176681 and
                  p69 = 365254291030302607303563045734141302886207073529870169959522296364627.

(585L^2·41)^41-1: c108 = p42 · p63, where
                  c108 = 128653473182369282550845463551059967956634868709208482053756457471162312353178455883825391516079110726293321,
                  p42 = 527470056275725907594872058541523319554999 and
                  p66 = 243906685605519738344742013812737905557229292798905649378056551679.



July 18, 2010 (Kurt Beschorner (Msieve - QS))

(410L^2·41)^41-1: c106 = p51 · p55, where
                  c106 = 1867077333305035052577196832227742327244448014667537329504966428011342986595416863598371435186940350798033,
                  p51 = 627167213204371519268027228769797700739611876138799 and
                  p55 = 2977000860369626598897528866991451189335528545118701567.

(465L^2·41)^41-1: c105 = p42 · p63, where
                  c105 = 191266802900403059365567976263071048897598619100540735606345286229760924935103753314198924053014975281081,
                  p42 = 468008764496911636160093845068112895768317 and
                  p63 = 408682096169729356368486595106734133273302186634873785133622893.

(564M^2·41)^41-1: c105 = p52 · p53, where
                  c105 = 725877634566986975779670505074294831104727898178213892307850961841046911951256772425563972886288958254589,
                  p52 = 7382185446612038804312663568143878570787886005708219 and
                  p53 = 98328285006727836920020661774714590257898995469624231.



July 16, 2010 (Msieve - QS)

(488L^2·41)^41-1: c108 = p51 · p57, where
                  c108 = 118668389816416929451528359054677035821862468048799160016130015680600932925176367885254778600538376757305367,
                  p51 = 503713935364531398082449690275348234664915212502217 and
                  p57 = 235586870810985441697042544006455563988401839973070441951.



July 15, 2010 (Kurt Beschorner (Msieve - QS))

(207L^2·41)^41-1: c106 = p44 · p62, where
                  c106 = 1570187203757327021614158932815427581348741600869276547949004178632464105158520808617109483604956189685397,
                  p44 = 76786909527315453785770085811355340939607601 and
                  p62 = 20448631328218299729668917060802936099689743072978504058188197.

(318M^2·41)^41-1: c106 = p45 · p61, where
                  c106 = 2246329240011466460261819070284528374178850591948913470098315848166005769071517899648215497161071540222257,
                  p45 = 680880562687057155468388176713564233196382653 and
                  p61 = 3299153130684849386020303117335281240555508242397062366286469.

(524M^2·41)^41-1: c105 = p52 · p54, where
                  c105 = 276315551799108744975502397342139195006483605764893661389429116661143061238275743980922025974093965993247,
                  p52 = 1310128017198638058736269556484794696753030751514869 and
                  p54 = 210907291632413452915506592919707191199049500764938563.



July 15, 2010 (Juno Fernadez (gnfs))

(562M^2·41)^41-1: c106 = p46 · p61, where
                  c106 = 5888847347314827850461604789477898298967641136454458088458583507219971682890635834951369265402645564341977,
                  p46 = 3437335058782984404855288863423342194856266097 and
                  p61 = 1713201432681927932757236963922198300019754594696945748056041.



July 12, 2010 (Kurt Beschorner (Msieve - QS))

(407L^2·41)^41-1: c106 = p36 · p71, where
                  c106 = 5020479432414075520007798960455553785507925690565710580522315593145327842604290539621108267217819351445413,
                  p36 = 130783173212841858729202096348227181 and
                  p71 = 38387808684252850839690334468082858209270448172779247176521936603925273.

(492L^2·41)^41-1: c106 = p37 · p69, where
                  c106 = 5589541801325419337233099738487079822950841656555662747282962717875629848490783188703125284100031723979603,
                  p37 = 5929476948578578614192690422309783939 and
                  p69 = 942670297869249843089414178334263003603750988745010033964890365281777.



July 12, 2010 (Msieve - QS)

(170L^2·41)^41-1: c107 = p50 · p58, where
                  c107 = 71785935780750769579631109256817578216625553909399067185750671409720575033479044662721233410597403800071943,
                  p50 = 13642151130189676748179186966911061820415647221079 and
                  p58 = 5262068650001290339715157530900705901678106342026789758417.

99624^41-1: c200 = p4 · p4 · p16 · p22 · p26 · p27 · p50 · p54, where 
            c200 = 86012854929767003947551857160691916926299317095187802474115707733405639295303742305802065021573876177171030378379024117305534775347116068331577623614823491014678870714665836464159174685652093608945001,
            p4 = 1723,
            p4 = 9431,
            p16 = 5599359927661529,
            p22 = 1405630818045636505469,
            p26 = 13990894534856375743167259,
            p27 = 572324477794727531901570563,
            p50 = 97718400208691243166338276089991183320800424737373 and
            p54 = 859501291368003078605757926415167629801474508639915197.



July 10, 2010 (Kurt Beschorner (Msieve - QS))

(503M^2·41)^41-1: c106 = p44 · p62, where
                  c106 = 3469869704869283629366819919571257697167959398368536358395696189823847034496893116597306627447053396155709,
                  p44 = 56307815310829708548911401964386357244025367 and
                  p62 = 61623234460704106918461120721875468895666541467770411642772427.

(734M^2·41)^41-1: c106 = p50 · p56, where
                  c106 = 5657625180019628006663341237445724383422024531769646253568901783209735004253082286378459978576982259302859,
                  p50 = 99349452097087745228837002407474164134310659890461 and
                  p56 = 56946717476517128737506137730634440757859458324069658119.



July 9, 2010 (Kurt Beschorner (Msieve - QS))

(240M^2·41)^41-1: c105 = p39 · p67, where
                  c105 = 800256106948034656711311363682492115939531162708978457252551332277819397140434768959766391212542521110481,
                  p39 = 751344361515960087747910267171398995801 and
                  p67 = 1065098971839473348680403136839044022196471088630698496001478970681.

(458M^2·41)^41-1: c105 = p48 · p58, where
                  c105 = 733115010703116027487979751403281952276425749584220082381115115458409478735682279081843238580360494372801,
                  p48 = 168967494712610188739602346811393076191327441883 and
                  p58 = 4338793162259054473687458684038948265616622084460227552147.


July 4, 2010 (Kurt Beschorner (Msieve - QS))

(277L^2·41)^41-1: c105 = p40 · p66, where
                  c105 = 584261262811371280050372184682223509082824455031802235899363345155161875613724590018270595427075023551361,
                  p40 = 1447753026769824822987154544591187133217 and
                  p66 = 403564179806934526667356179433218724835699578048625320931903425633.

 
Alfred Reich