News - January 2012
January 27, 2012
GF.20.7.txt: 8 numbers of shape 20^128+b^127
58179035597570809^11-1: c106 = p51.p56
p51 = 213903673740743114768046158075407582454726169828683
p56 = 30353417096016027257044076289410992638146101566454365029
January 27, 2012 (Kurt Beschorner)
3002^41-1: c132 = p50.p83
p50 = 33246321323526028134240575212061653607979565250623
p83 = 19089813479506289246123323502103283508179986442753506333072756234433465240090417139
3026^41-1: c121 = p31.p91
p31 = 1159389645011978150202146886991
p91 = 2651201735562099520924584302447661605331560446474962511990428146517803090706318494727481171
6042^41-1: c110 = p40.p70
p40 = 3013575898687367919857913298674803260279
p70 = 4943913908517550978851556010440520031313350055575431574821596527641399
14627^41-1: c120 = p54.p67
p54 = 198988108094246566171111665384646598335408788140245213
p67 = 1602262110779240225997148173113420942752118273349771735288753484231
31247^41-1: c115 = p47.p69
p47 = 16991675470748513891927719216324496131691376649
p69 = 146923610873314428750885304776738997049331015779990713999019168177191
91939^41-1: c199 = p28.c172
p28 = 3425718709580819397176692099
93923^41-1: c199 = p27.c173
p27 = 482634708313217735423867837
98387^41-1: c200 = p25.c175
p25 = 7445594424346977891266587
January 26, 2012
1964^41-1: c118 = p50.p69
p50 = 13299589106234023167373911662940457096970754998537
p69 = 252609270482072037760793662722573449733169680006769079915557221601147
1971^41-1: c111 = p54.p57
p54 = 557957204526443276728193503107111955202799750506675549
p57 = 739082457158617653174673850458017103368951290045510200871
2002^41-1: c131 = p50.p81
p50 = 15678019758332876849679641956917447444195074800003
p81 = 879853995258082484145714798515035508789837816937593690632485172509059389467864199
January 25, 2012
1985^41-1: c111 = p56.p56
p56 = 15231342081867293239063012206810873042976786469090264437
p56 = 27525455269584529720277951851892659360947816075092462297
January 23, 2012
100^85+3.10^85+3: c161 = p74.p87
p74 = 69136685723927981661937018854215133211949853738339874623757032628655758753
p87 = 242353089597769206323960325688921334265789078469285715193064089537701002020878911632019
1988^41-1: c121 = p59.p63
p59 = 22035440889992318681738978684923618020982377031345033994111
p63 = 200829754681741452207123667148931063148661439580088574356925619
2389^41-1: c121 = p59.p63
p59 = 11186363078531822456182791453886225369983939024749842948639
p63 = 576864914953486423207243331976329103562415284792127927593445543
41^128+33^128: c134 = p64.p71
p64 = 3293093027149879388836980341949059183918261698737046532416824577
p71 = 13676322543265153430628440426670572459899906695039674656540158430589441
January 19, 2012
4111^41-1: c140 = p56.p84
p56 = 93955478006390577037886535130348228456639894152736833091
p84 = 627133627881577486671197556824212674717443920719534250275358403500189825795149034723
17569^41-1: c170 = p37.p54.p80
p37 = 3677900898208646157789336915143950093
p54 = 243115718610762263585571200527642671365544299611716193
p80 = 68943507063334976694629256644222655107367342050089108713014610262963424778427949
January 18, 2012 (Kurt Beschorner)
5035^41-1: c110 = p51.p60
p51 = 165101625099586334465364728676519767110092991960831
p60 = 303653750187882239849124368443845514298747563903757710051661
5169^41-1: c110 = p33.p78
p33 = 327717814820399228566958100895399
p78 = 241726997220049455412821673067351929801407249197766868399100498175187211088071
5297^41-1: c110 = p43.p67
p33 = 3737720647220100888243363979089177739938983
p67 = 5531213989615161309964416028717124424518355108865434455574841742353
5354^41-1: c110 = p33.p34.p44
p33 = 194499804089909292808801097466041
p34 = 3140564731955091808460839469121709
p44 = 27354511916311739796436590400708621563091321
5855^41-1: c110 = p41.p69
p41 = 15038058983615525242523778348620129909953
p69 = 929035504025164435672071639841836069411197009665998087775521327860899
5867^41-1: c110 = p45.p65
p45 = 531976833771822015836212016319376598562507517
p65 = 22368417226897239527998810925065654384426948304685381603938212613
13417^41-1: c105 = p34.p34.p38
p34 = 1595943864238606942356522570407807
p34 = 9161115077564414502638261523751901
p38 = 26957123228387428407292330761692606149
15053^41-1: c120 = p30.p91
p30 = 144644412100124239658088396917
p91 = 1962698873573524560033050839410898402075169861870359415974491380375579998058198265490570547
40039^41-1: c115 = p40.p75
p40 = 2763797754799743434462610218223326667641
p75 = 529332927374756733990059330073287127701859856683119472304993832317068109867
70241^41-1: c115 = p27.p40.p48
p27 = 453525597949755605868516227
p40 = 5728314847975762722304642660711376167877
p48 = 697700527844407389343483217125855778550631550143
91969^41-1: c184 = p31.c154
p31 = 2072489923739362813705010787739
92009^41-1: c199 = p26.c174
p26 = 24427266030721120749485201
93283^41-1: c199 = p29.c171
p29 = 20642236433039945195843517253
96851^41-1: c200 = p33.c167
p33 = 828499195912002102841449248842147
98573^41-1: c200 = p22.p28.c151
p22 = 7265877650843420363873
p28 = 1786391400106875724978558181
99641^41-1: c109 = p45.p64
p45 = 143387282916565870890532261928255567510405801
p64 = 7761000407570646989240248120192763041292358576072246574447763741
103643^41-1: c106 = p46.p60
p46 = 3675603193289882135543507648962930647798967517
p60 = 351303381015063837478091756305928013159455268750504557637251
104059^41-1: c200 = p19.p29.c153
p19 = 1734745720073722711
p29 = 20585094182077728592445576341
January 18, 2012
1997^41-1: c119 = p56.p63
p56 = 20626960128576273602921932175954201175311035506090420853
p63 = 903936007839558238452974121667199162534980457204710248705809203
January 17, 2012 (Kurt Beschorner)
93607^41-1: c199 = p25.p27.p38.p110
p25 = 6906921608202244874855479
p27 = 875941220789914657737633403
p38 = 96808183716132783996229525691795012429
p110 = 12152514524693074391691615166097697649447654797997944507680132889013962204314981411880465051878665471364622937
January 17, 2012
100^80+3.10^80+3: c128 = p63.p66
p63 = 113854936642623739476186023287614150713159843379384185197841791
p66 = 504462334792771771083523313124260852596015039774840173305624124301
100^82+3.10^82+3: c147 = p47.p50.p51
p47 = 44622896508920343127964811363121090282817855749
p50 = 15499067991211550651630486700117313530170529279067
p51 = 415278158990592467949284211711634076335123093976821
January 16, 2012
1726592724217799651378311926538399150693^5-1: c135 = p53.p82
p53 = 41976613497097360332787998590140233254144084562231971
p82 = 4773209449468682971972633266579421728190204279339900577487328871807550093414465431
# 1726592724217799651378311926538399150693 = (1861^13-1)/1860
100^73+3.10^73+3: c115 = p54.p62
p54 = 129251599191455396962113488791813004715691912542440101
p62 = 77275757797354672572577932147564326361607557196335107620115563
January 13, 2012
1840^41-1: c124 = p51.p73
p51 = 429239030914684260820268698098703507612797392242793
p73 = 5357366336028572755515103125104563418756191676791524442910823545274034351
1845^41-1: c113 = p55.p59
p55 = 1128273607292099011517474096590999121660799508907060189
p59 = 15224540204268925975130096026242234208093065538625174129969
1865^41-1: c124 = p58.p66
p58 = 3088909686992066872386617395091729017663788896313180492187
p66 = 894173791369367462171341998231795902609654640519779109765277805477
1875^41-1: c113 = p57.p57
p57 = 128426384005504869339356071548255929677877152894288229689
p57 = 395575488131735671336625209729874544924010804922641306223
1904^41-1: c117 = p52.p66
p52 = 7368707907350625978123401633155309950714810355438513
p66 = 108316982922677102141584995626813511204208630068786951574295249969
1931^41-1: c107 = p42.p66
p42 = 447847507893993914886419943615815561072927
p66 = 177818919923163078394646964998172665751970173427465924933867901021
1945^41-1: c113 = p55.p58
p55 = 3225373257677507897630712056116680552945952506219294883
p58 = 6148228044369667342055455626802885806557680208564936082347
January 12, 2012
4831^43-1: c132 = p62.p71
p62 = 57712486617662636902655432725587694695834089743597860377393749
p71 = 14012431505560441846359960685627835400663141773443163393436298756938229
8731^41-1: c111 = p47.p65
p47 = 12105341810967490685136528620412125474583386669
p65 = 10647865070100338633493573460613543228219525943067211913288406403
4093^41-1: c111 = p47.p65
p47 = 18467404238560415012251693420611039787928260841
p65 = 45259455538536652961751413283750320014068136005666394502169843421
January 11, 2012
1816^41-1: c122 = p33.p90
p33 = 143297198572712192403791321232239
p90 = 534385878366602041100070596625321256702030944561026612223322495458136956238969132311030113
1833^41-1: c108 = p48.p60
p48 = 201539424884504314750416415509967533515289341921
p60 = 690106296708372842324173412531888043288533459279025660717737
4349^41-1: c112 = p50.p62
p50 = 32172650887313670958534629128688165149706867277879
p62 = 38489916050392770592447731649745255663597157840966442556861639
7933^41-1: c111 = p44.p68
p44 = 11886980471423119673920193030386872325707529
p68 = 10800305788788771834283877195919943314692347953803755019447762339681
1954228039577198139017863240041341137^5-1: c137 = p65.p73
p65 = 16683380954446625144417120971211644902891204016598785663947903541
p73 = 1686871982079127857426927258381489692524318619640521407004939661535422301
January 10, 2012
1813^41-1: c129 = p60.p70
p60 = 237060226351885544849658661511139442246679444533506385255717
p70 = 1102084736135142382222813073303352884047327844803556292664652198793991
1815^41-1: c123 = p48.p76
p48 = 221253735355022691931136312080006782104296724837
p76 = 3860335773808389814803857250802240066145207590308955405528235529259847164243
5081^41-1: c111 = p45.p66
p45 = 265667040649240765321045814400757372109258149
p66 = 544154786977996360138661381938722786394868193558690017370537679469
5101^41-1: c107 = p35.p72
p35 = 20256953025190123633481273974840711
p72 = 529810353689970201110021827345041146584878572983579161081064987325463971
9173^41-1: c112 = p55.p57
p55 = 1230901653963633860805179583545292166254214949606605859
p57 = 921133944417348718872651551923586332254184405595311481657
January 9, 2012
10^9030+1 (M): c2000 = p27.c1973
p27 = 322696503029308300381108201
11177^41-1: c158 = p76.p83
p76 = 1370838886209845847460683121187715218194359756998913634424925701440473149621
p83 = 71927141321098181169525880995600191010733787903583007275902958467126538047808137617
1751^41-1: c126 = p44.p83
p44 = 29350845103511865027074873513068243765037293
p83 = 28714217093958486345148734974614379427069028720608414916985523303397718407775329321
1762^41-1: c108 = p50.p59
p50 = 16635122575102525079774533709776264138625318203031
p59 = 43938139671591683730827083047478520632540439319402421805297
1781^41-1: c122 = p57.p65
p57 = 176810495422262917890877705214603228255079509275525834811
p65 = 93450790044337213114672997384253634188690158062600339246212951913
1791^41-1: c129 = p63.p67
p63 = 156849699137841340787299230535594698620138209190348153591950637
p67 = 1022125460595475915303825175831967848847839640075584372091049580071
1806^41-1: c121 = p54.p67
p54 = 432985757930351669278916370838605364232006211051914641
p67 = 7965809744147291166817505681381347154066275506831141178536826497947
7069^41-1: c142 = p41.p102
p41 = 11804893656192270888828169519296294416111
p102 = 523539450942229642250659238661980237007210370278256136641188416595377781138288758561253312270513083147
(127^2.41)^41-1 (L): c117 = p53.p64
p53 = 72721312494296531214376781137004011458110926121763251
p64 = 3489353366078004410170569242788735665590491570614458531559899471
(203^2.41)^41-1 (L): c125 = p53.p73
p53 = 13934495737235763981315535186192939454982583588173689
p73 = 2566186057981166253247243101567882327432203638882669746233449702866237269
January 3, 2012 (Robert Backstrom (gnfs))
13723^41-1: c104 = p47.p58
p47 = 16357553096616669848522621337615309146754717257
p58 = 4705097162798799730138678113331394726480849962189260483671
January 3, 2012
41^128+6^128: c207 = p66.p67.p74
p66 = 814554648666414975248663225606036961623298580352499035339733929729
p67 = 5982506453657238715905749897263607992021605120161250203243245476097
p74 = 56044146261093907419662513476200228952804445236761583166959045093982952449
January 2, 2012
17^128+9^128: c128 = p54.p74
p54 = 412173747168531433270119131647482006765971708569292033
p74 = 50478633975904131297173589589073347035841165822905169904070250690301293313
45761002055556680826306341^7-1: c106 = p51.p55
p51 = 892110128322108430329524036596637299178523894528887
p55 = 6011026481504083529342615688381187440693403859272893733
# (306517^17-1)/306516 = 953.4591.8484823421.263568576125993109113.13559457661418573442165599.45761002055556680826306341
January 1, 2012
7925005857343^11-1: c128 = p63.p65
p63 = 995205400528123524477646734701549733650939941857269962382310457
p65 = 42692870758798681927972651508673060380658523729468782997177247263
3571683756931^13-1: c125 = p51.p75
p51 = 376509669997080409886906514336522481238356006814309
p75 = 253891939947459961573240885353633006111013760621198239642085382645255540973
# 3571683756931 is a divisor of 17891^67-1
Alfred Reich