News - September 2010

September 25, 2010 (Kurt Beschorner)

(447L^2·41)^41-1: c125 = p36 · p90, where
                  c125 = 18564125970107220420745415030547772680740266465651451256623562582853579776539114129676281434639269804329396393923027026865963,
                  p36 = 111021180392096786690007978181150537 and
                  p90 = 167212471571133973023971411553782947929696786798198703806404046690611593395155829273804499.
                  GMP-ECM, B1=45e6.

(487L^2·41)^41-1: c117 = p34 · p84, where
                  c117 = 813823825537343387247294737509231190599241974336554737897244369747536793808331722445895281134464345821593689117284573,
                  p34 = 5974547940186133482416095418459591 and
                  p84 = 136215130196442810818933524453068374037241016305967993612664772487729261786540063803.
                  GMP-ECM, B1=45e6.

(677M^2·41)^41-1: c144 = p40 · p46 · p59, where
                  c144 = 363736848343785832496155982919613836329113422899093105848344199023997050512449392462335104713805038463579894413544322245907959878761286376425407,
                  p40 = 1174692734065303298851570782564885855503,
                  p46 = 4786707881484991894361351544677695864511172149 and
                  p59 = 64688352773711079356000753761077916264175742689805671227181.
                  GMP-ECM, B1=45e6 for p46 and Msieve (QS) for p40 · p59.   

(726L^2·41)^41-1: c115 = p51 · p65, where
                  c115 = 5406594050562415132010476205331561237290675134116181641738091297800548871790879433554234088624328621645222742508207,
                  p51 = 129489279149655135369128093927842663507330041194381 and
                  p65 = 41753217610500647690024891757833560978433461777069032373533218347.
                  Msieve - QS.

(888M^2·41)^41-1: c115 = p51 · p65, where
                  c115 = 8765783347314979444408351412131634191076866752482438150112953375541114574086795064377470880064756181081464965028997,
                  p51 = 689791949157434676885359101050339109264799295995131 and
                  p65 = 12707865549927316907047516195015874007691455835532777208140354687.
                  Msieve - QS.
                  


September 16, 2010 (Kurt Beschorner)

(134L^2·41)^41-1: c114 = p54 · p60, where
                  c114 = 256995706372851463433218111128203053070352050326302377457662741911346302471982831175269169207314445072899895349241,
                  p54 = 563097203482075756778718482785197282417586773565813159 and
                  p60 = 456396701641641217844964029956803249391901041647037125813599.

(204L^2·41)^41-1: c115 = p55 · p60, where
                  c115 = 2635490917798155956300272960365145346538037830981714181832397475760130083110112533154404705066285228616994036029441,
                  p55 = 4496908810767912734981782991852516569484749087836690061 and
                  p60 = 586067236117271291105021267729693793623081865592386963264581.

(510L^2·41)^41-1: c139 = p37 · p103, where
                  c139 = 4350654025461906633973820136792386618322722454310869703544583522804170311885755611076922049053664533989014748037505552411927099536751334677,
                  p37 = 1392093998307585565068575087578304449 and
                  p103 = 3125258804901924545530956315219213107897672243114251367672320461065065991752962964719747958638498585173.

(607M^2·41)^41-1: c124 = p40 · p85, where
                  c124 = 4144194634255045647402513460418297845211912828068986634718716250945490078817014904659919065424715923182945922689216996389593,
                  p40 = 1359980806131616015561787532271137741761 and
                  p85 = 3047244943142219177426632576456564903507712268004275773476508512893537637187504274713.

(625M^2·41)^41-1: c128 = p38 · p40 · p51, where
                  c128 = 21007223637103229511019261268625758200377514041071151217034864080690556086922802939995584138679695999254338425412027579049696343,
                  p38 = 69494172510086283145900677941727741707,
                  p40 = 2282975658219921119203623019917944131079 and
                  p51 = 132409452531386193033615583165598811189157190241331.

(669M^2·41)^41-1: c138 = p39 · p100, where
                  c138 = 372653615104840645540664436155115715566088243153045556697356936714957241486950286212402723404770833111042726998808512324167312168935648929,
                  p39 = 316828905383145868897273864779495370037 and
                  p100 = 1176198284857201181481749124578234777682854707330953424351748727883717467099390448133067126579225917.

(751L^2·41)^41-1: c143 = p38 · p106, where
                  c143 = 31115286553171642283775746776337502090346966940924239611460922206603348781603493456074915427135776624622658879122146228068503828398655651333509,
                  p38 = 28220538802199380362883861789992155803 and
                  p106 = 1102575920724329276631176985990060932576916588124318359349387172655652195452602452117932825360370750468703.

(858L^2·41)^41-1: c113 = p55 · p58, where
                  c113 = 23049127459900284279400252182148930864011781285638665915619824551214703778465501342427510703429269130947567445941,
                  p55 = 9715290863593206262774327797553879455460243543428390931 and
                  p58 = 2372458816058086644187837345580931496400275773937674674711.

(779L^2·41)^41-1: c141 = p36 · p105, where
                  c141 = 112061934737975997035080404101496701352237790684313838520236926617190023084080190031318383684323886422780096179048486302315734834111074854253,
                  p36 = 226432005750355718095546950443999461 and
                  p105 = 494903246414403812676494251503699137043595966760821679250369103976683767009037397406888852109496485597673.



September 10, 2010 (GMP-ECM)

2009^113-1: 989663675568928687592663133247487340174599.



September 9, 2010 (GMP-ECM)

2009^89-1: 372610250944161968428213958207092099937.
2009^101-1: 196795885698270955375385885818930119209.



September 6, 2010 (Kurt Beschorner, GMP-ECM)

2009^101–1: 130061551347692571630584408611453717.



September 6, 2010 (Kurt Beschorner)

(186L^2·41)^41-1: c114 = p51 · p63, where
                  c114 = 458865097063274023221739188816833871060556284650322842794014145048625866180446794969324502525771128454775683959971,
                  p51 = 551847659475923068870596876081202968022341925194221 and
                  p63 = 831506828350142084568456858292617440752776044086611715821100751.
                  Msieve - QS.

(421M^2·41)^41-1: c114 = p56 · p58, where
                  c114 = 102348241222857176994466304168701862098148556497775597484088738903797675122526253936914851937539926929169096112673,
                  p56 = 35983955008370429045428965124189110781743366619735303621 and
                  p58 = 2844274377262015254684009848116796712957583953684025533613.
                  Msieve - QS.

(629M^2·41)^41-1: c115 = p41 · p75, where
                  c115 = 2522143890052934317679127276042449921026150254669217379793348501960613784634135631902171682658363507852513302554947,
                  p41 = 20592346584849661004575574591145090000797 and
                  p75 = 122479673681703808054877202913582670896904166063871974651448701202563001951.
                  GMP-ECM, B1=45e6.

(716L^2·41)^41-1: c140 = p41 · p100, where
                  c140 = 34920991849113724519030058414905942210966730753539149511690973306546316642146835146371770241637419814367475395749122738371331104982404723623,
                  p41 = 10999051944147089288270619403053371773367 and
                  p100 = 3174909258219858205618698665159467749221695138803833917624852596949943529612075842551284924739693969.
                  GMP-ECM, B1=45e6.
                  
(827M^2·41)^41-1: c134 = p36 · p45 · p53, where
                  c134 = 16585280292032919669617262418158824371897614262305303170750067932992159093424979344526211248496240704000536178788338481337551195990053,
                  p36 = 976629780488721008706811735394598491,
                  p45 = 416613206332251537285249595669462768772232383 and
                  p53 = 40762406883583191061719728646137598484581030535752001.
                  GMP-ECM, B1=45e6 and Msieve - QS.

(891M^2·41)^41-1: c124 = p35 · p37 · p52, where
                  c124 = 1969989894583347350569130332381792689685127473064730139349663512418580867275745133833680154581408372140527827210638555219493,
                  p35 = 63917039242889315136768396429402223,
                  p37 = 8274006135337815855108958100745160351 and
                  p52 = 3725044886592759121698686127425489140942023837377141.
                  GMP-ECM, B1=45e6 and Msieve - QS.
                  


September 3, 2010

P-1 with B1=1e9 and B2=205702360894088-304923019711252.

(684M^2·41)^41-1: 216407336806830457566382551932846407.
(844L^2·41)^41-1: 202819498192920073306512650813147016673933.



September 2, 2010

P-1 with B1=1e9 and B2=205702371522480 (on all composites of the series (k^2·41)^41-1).

(389M^2·41)^41-1: 240240673927835563025699206891418506023751.
(632L^2·41)^41-1: 10913154975249318337750284293315189891.
(654L^2·41)^41-1: 2245042589825625013725712485959985371.
(659L^2·41)^41-1: 7614206386061518779286327973357273681.
(672M^2·41)^41-1: 14661382130639487643541276585432170156049.
(770M^2·41)^41-1: 78839132176680330919656171327062083.
(834M^2·41)^41-1: 1650369551806347483073716663812351257.
(995M^2·41)^41-1: 17950865502058432824767257459343507690177.




Alfred Reich