Date: Tue, 12 Feb 2008 16:03:04 -0500 (EST) From: Samuel S Wagstaff Here are the factorizations of some numbers from Sequence A056542. Call the numbers a(n). Tom Mueller factored a(1) through a(50) in a paper cited in the entry for Sequence A056542. Below I give the factorizations of a(50) through a(90). Thanks goes to Tom Womack for finishing the c131 of a(88). I factored the others. The format is: n=n size of a(n) and whether it is prime (n = 70) or composite (all other n) a(n) prime factorization of n Tom Mueller proved that a(70) is prime in his paper. Sam Wagstaff n=50 Composite has 65 digits: 21845890475850502485271364677172235614229203311417732300825298501 31 293 206506391500393 31126232036943157 374179843710832651624027922347 n=51 Composite has 67 digits: 1114140414268375626748839598535784016325689368882304347342090223552 2 2 2 2 2 2 13 1715761 p57 p57 = 780476461955830461412687284674336938316130742648530321451 n=52 Composite has 68 digits: 57935301541955532590939659123860768848935847181879826061788691624705 5 19 29 97 113 7091543 105784713447827191 p37 p37 = 2557454030939887304951103705306991787 n=53 Composite has 70 digits: 3070570981723643227319801933564620748993599900639630781274800656109366 2 37 283 99989 218920359227 p49 p49 = 6698269375180762011538020413684835622425542635291 n=54 Composite has 72 digits: 165810833013076734275269304412489520445654394634540062188839235429905765 5 38892144626596189 621848126148566689 p37 p37 = 1371186960951492283453927305371984693 n=55 Composite has 73 digits: 9119595815719220385139811742686923624510991704899703420386157948644817076 2 2 149 779954992651578239 p53 p53 = 19618228494511705018815835037326247443885315171723079 n=56 Composite has 75 digits: 510697365680276341567829457590467722972615535474383391541624845124109756257 13 161407 4513835703284570207 p50 p50 = 53920281695707215007591762098594372729437683283461 n=57 Composite has 77 digits: 29109749843775751469366279082656660209439085522039853317872616172074256106650 2 5 5 761 8169419 98237768857570184309 p45 p45 = 953266104004173442180550835633641859483303643 n=58 Composite has 79 digits: 1688365490938993585223244186794086292147466960278311492436611737980306854185701 55051 p74 p74 = 30669115746108037732706838872937572290193946709020934995488033604844723151 n=59 Composite has 80 digits: 9961356396540062152817140702085109123670055065642037805376009254083810439695\ 6360 2 2 2 5 1712795320164847899568628632255831 p46 p46 = 1453961877298527985631559693692314696542201539 n=60 Composite has 82 digits: 5976813837924037291690284421251065474202033039385222683225605552450286263817\ 381601 23 193601 98381365099 136241982434346470791031911 p39 p39 = 100140671201113522065999533130809699683 n=61 Composite has 84 digits: 3645856441133662747931073496963149939263240154024985836767619386994674620928\ 60277662 2 2687 1573175047 162350885595817 1136951155521833 69478783225291126051 p22 p22 = 3362607514476546577789 n=62 Composite has 86 digits: 2260430993502870903717265568117152962343208895495491218795924019936698264975\ 7337215045 5 13 43 17421512347 p72 p72 = 464219723051452034889237681469690781939997186689547375777835244331682333 n=63 Composite has 88 digits: 1424071525906808669341877307913806366276221604162159467841432132560119906934\ 712244547836 2 2 19 131 317 32491 52540666771 p66 p66 = 264319372507823601267178513924649712831134688667093209085189280563 n=64 Composite has 89 digits: 9114057765803575483788014770648360744167818266637820594185165648384767404382\ 1583651061505 5 13 23 23 9173 2953243 45389128523 p64 p64 = 2155660317680659206061552761118197741934959128679296052097382629 n=65 Composite has 91 digits: 5924137547772324064462209600921434483709081873314583386220357671450098812848\ 402937318997826 2 1823 136691 2261943611 4651778801 89852678599 p53 p53 = 12572935594491678853375326236822643441139506735284569 n=66 Composite has 93 digits: 3909930781529733882545058336608146759247994036387625034905436063157065216479\ 94593863053856517 71 85411 449913379 p78 p78 = 143307198389000100418054424018904175102376542582438630204978486066873032004283 n=67 Composite has 95 digits: 2619653623624921701305189085527458328696156004379708773386642162315233695041\ 5637788824608386640 2 2 2 2 5 193 34680287972244319323250583 214966928372588659332638672379107 p33 p33 = 227584263840870365590512873017101 n=68 Composite has 97 digits: 1781364464064946756887528578158671663513386082978201965902916670374358912628\ 263369640073370291521 109 131 402299 1245448987 41997288859 5387536999927211 p52 p52 = 1100445586446229671995457766875153673219659990881527 n=69 Composite has 99 digits: 1229141480204813262252394718929483447824236397254959356473012502558307649713\ 50172505165062550114950 2 5 5 13 187714825810009885261234006696505806378855561981 p49 p49 = 1007372158519166277282435362320870032186285141683 n=70 Prime has 100 digits: 8603990361433692835766763032506384134769654780784715495311087517908153547994\ 512075361554378508046501 n=71 Composite has 102 digits: 6108833156617921913394401753079532735686454894357148001670872137714789019076\ 10357350670360874071301572 2 2 19 37 7470383 12837728515133 p79 p79 = 2265227847912220132253090454043524823745645263433408459514656543590041525591029 n=72 Composite has 104 digits: 4398359872764903777643969262217263569694247523937146561203027939154648093734\ 7945729248265982933133713185 5 3947 125826458901057784134691 27041346766974533942512423016540437 p42 p42 = 655018155389422919913287058593563732289113 n=73 Composite has 106 digits: 3210802707118379757680097561418602405876800692474116989678210395582893108426\ 400038235123416754118761062506 2 37 6970751 111362093 74147837500924559 931724992904551844392999877 p45 p45 = 809056239457813722020627793046608501623887681 n=74 Composite has 108 digits: 2375994003267601020683272195449765780348832512430846572361875692731340900235\ 53602829399132839804788318625445 5 131000197213 11075581067263 14385179159299633 30087918315153907643 p47 p47 = 75670995887834027863764664352305395834574740449 n=75 Composite has 110 digits: 1781995502450700765512454146587324335261624384323134929271406769548505675176\ 6520212204934962985359123896908376 2 2 2 13 13 52147613958189799597509377833 p78 p78 = 252752505943062214264117022993026299929006058687214345912248401681255805786011 n=76 Composite has 112 digits: 1354316581862532581789465151406366494798834532085582546246269144856864313134\ 255536127575057186887293416165036577 31 197 739337 p102 p102 = 2999506690205540236987094622907969269644260246678218396863303862863273562253\ 10299708749840119953712603 n=77 Composite has 114 digits: 1042823768034150087977888166582902200995102589705898560609627241539785521113\ 37676281823279403390321593044707816430 2 5 13 3785423206567693 p96 p96 = 2119108182845377318293314360648808654847885764700262186311111618183062075328\ 71952361279179724627 n=78 Composite has 115 digits: 8134025390666370686227527699346637167761800199706008772755092484010327064684\ 338749982215793464445084257487209681541 41 271 19208223443 17761949884346389 p85 p85 = 2145727349171315129248047429414487070732919443926007601563981157713562788962\ 614751453 n=79 Composite has 117 digits: 6425880058626432842119746882483843362531822157767746930476523062368158381100\ 62761248595047683691161656341489564841740 2 2 5 p116 p116 = 3212940029313216421059873441241921681265911078883873465238261531184079190550\ 3138062429752384184558082817074478242087 n=80 Composite has 119 digits: 5140704046901146273695797505987074690025457726214197544381218449894526704880\ 5020899887603814695292932507319165187339201 29837 133999 8252832492389 p97 p97 = 1557983521997772851637893343323753248809377415499133784188992992744144850322\ 861987787330701484143 n=81 Composite has 121 digits: 4163970277989928481693595979849530498920620758233500010948786944414566630953\ 206692890895908990318727533092852380174475282 2 29 31 71 239 94291 7534217629 1184593382979847 2103081302795922368516843780111897854817 p44 p44 = 77113056355266965352393832472405308594284251 n=82 Composite has 123 digits: 3414455627951741354988748703476615009114909021751470008978005294419944637381\ 62948817053464537206135657713613895174306973125 5 5 5 5 13 19 489113 6969212468377 13579304330287 67462484853940987443720124771 p57 p57 = 708291021614353482825896880839260302805886434411807336303 n=83 Composite has 125 digits: 2833998171199945324640661423885590457565374488053720107451744394368554049026\ 7524751815437556588109259590229953299467478769376 2 2 2 2 2 23 15229937 860908793182169521015736623 p88 p88 = 2936746777182160880180526781894900505864578903293012648512976507557627351430\ 182198616991 n=84 Composite has 127 digits: 2380558463807954072698155596063895984354914569965124890259465291269585401182\ 472079152496754753401177805579316077155268216627585 5 9543579297367046782213615326980010283 p89 p89 = 4988816857140213929056721592790122722949322225726810615393571272155594467113\ 9881380202599 n=85 Composite has 129 digits: 2023474694236760961793432256654311586701677384470356156720545497579147591005\ 10126727962224154039100113474241866558197798413344726 2 16757021 50221962946166876325497 64480287135891363959172655829 p70 p70 = 1864448199823180793559862943552162085622539582736141762825189089943331 n=86 Composite has 131 digits: 1740188237043614427142351740722707964563442550644506294779669127918066928264\ 3870898604751277247362609758784800524005010663547646437 269 431 612825493979 16475121351873221009630899997284491854857476894333185801 p59 p59 = 14866243170026478429941045106993407706007720006031598907277 n=87 Composite has 133 digits: 1513963766227944551613846014428755929170195019060720476458312141288718227590\ 016768178613361120520547049014277645588435927728645240020 2 2 5 23 47931099902217821 p113 p113 = 6866576367892014150279051841302928242262161197609816045529231148213249602840\ 4580434754779556598216564804339232547 n=88 Composite has 135 digits: 1332288114280591205420184492697305217669771616773434019283314684334072040279\ 21475599717975778605808140313256432811782361640120781121761 13 313 p60 p72 p60 = 143934227080229954193112325426094569323520033661894401959321 p72 = 227481657290896141632186221920318234470263840916963832032825890411269589 n=89 Composite has 137 digits: 1185736421709726172823964198500601643726096738928356277162150069057324115848\ 5011328374899844295916924487879822520248630185970749519836730 2 5 2293 50327443 17124267098581 28400834478974443309 34432963353381853411405585604962411 p57 p57 = 613566649443066763742457060900625529355486535417626158933 n=90 Composite has 139 digits: 1067162779538753555541567778650541479353487065035520649445935062151591704263\ 651019553740985986632523203909184026822376716737367456785305701 13 19 37 37 167 889697 21485527806063464290535955857587645637101910978689 p75 p75 = 988611467852219784905705739797953889992150041164923098514771563315594496237