# Factorizations to support known members of OEIS sequence A321576, n = 1..95 # A simple summary file giving the factorization of only the corresponding value for each n. # # Kevin P. Thompson n=2 ---------- k=2: 3 P_1 = 3 = 1*2 + 1 ---------- a(2) = 2 n=3 ---------- k=2: 7 P_1 = 7 = 2*3 + 1 ---------- a(3) = 2 n=4 ---------- k=3: 65 P_1 = 5 = 1*4 + 1 P_2 = 13 = 3*4 + 1 ---------- a(4) = 3 n=5 ---------- k=2: 31 P_1 = 31 = 6*5 + 1 ---------- a(5) = 2 n=6 ---------- k=4: 3367 P_1 = 7 = 1*6 + 1 P_2 = 13 = 2*6 + 1 P_3 = 37 = 6*6 + 1 ---------- a(6) = 4 n=7 ---------- k=2: 127 P_1 = 127 = 18*7 + 1 ---------- a(7) = 2 n=8 ---------- k=45: 2766901765409 P_1 = 17 = 2*8 + 1 P_2 = 89 = 11*8 + 1 P_3 = 233 = 29*8 + 1 P_4 = 1289 = 161*8 + 1 P_5 = 6089 = 761*8 + 1 ---------- a(8) = 45 n=9 ---------- k=3: 19171 P_1 = 19 = 2*9 + 1 P_2 = 1009 = 112*9 + 1 ---------- a(9) = 3 n=10 ---------- k=6: 50700551 P_1 = 11 = 1*10 + 1 P_2 = 991 = 99*10 + 1 P_3 = 4651 = 465*10 + 1 ---------- a(10) = 6 n=11 ---------- k=2: 2047 P_1 = 23 = 2*11 + 1 P_2 = 89 = 8*11 + 1 ---------- a(11) = 2 n=12 ---------- k=301: 21651726310835924575445943601 P_1 = 13 = 1*12 + 1 P_2 = 37 = 3*12 + 1 P_3 = 61 = 5*12 + 1 P_4 = 73 = 6*12 + 1 P_5 = 313 = 26*12 + 1 P_6 = 577 = 48*12 + 1 P_7 = 601 = 50*12 + 1 P_8 = 1237 = 103*12 + 1 P_9 = 4441 = 370*12 + 1 P_10 = 16953121 = 1412760*12 + 1 ---------- a(12) = 301 n=13 ---------- k=2: 8191 P_1 = 8191 = 630*13 + 1 ---------- a(13) = 2 n=14 ---------- k=15: 18080919199832609 P_1 = 29 = 2*14 + 1 P_2 = 43 = 3*14 + 1 P_3 = 113 = 8*14 + 1 P_4 = 127 = 9*14 + 1 P_5 = 13469 = 962*14 + 1 P_6 = 75013 = 5358*14 + 1 ---------- a(14) = 15 n=15 ---------- k=10: 794108867905351 P_1 = 31 = 2*15 + 1 P_2 = 151 = 10*15 + 1 P_3 = 271 = 18*15 + 1 P_4 = 631 = 42*15 + 1 P_5 = 751 = 50*15 + 1 P_6 = 1321 = 88*15 + 1 ---------- a(15) = 10 n=16 ---------- k=121: 262535085584891125545615254209921 P_1 = 17 = 1*16 + 1 P_2 = 113 = 7*16 + 1 P_3 = 241 = 15*16 + 1 P_4 = 257 = 16*16 + 1 P_5 = 353 = 22*16 + 1 P_6 = 2129 = 133*16 + 1 P_7 = 143729 = 8983*16 + 1 P_8 = 823457 = 51466*16 + 1 P_9 = 24806993 = 1550437*16 + 1 ---------- a(16) = 121 n=17 ---------- k=2: 131071 P_1 = 131071 = 7710*17 + 1 ---------- a(17) = 2 n=18 ---------- k=64: 80102408567383714238190230860927 P_1 = 19 = 1*18 + 1 P_2 = 37 = 2*18 + 1 P_3 = 109 = 6*18 + 1 P_4 = 127 = 7*18 + 1 P_5 = 12097 = 672*18 + 1 P_6 = 36541 = 2030*18 + 1 P_7 = 67537 = 3752*18 + 1 P_8 = 283447 = 15747*18 + 1 P_9 = 972721 = 54040*18 + 1 ---------- a(18) = 64 n=19 ---------- k=2: 524287 P_1 = 524287 = 27594*19 + 1 ---------- a(19) = 2 n=20 ---------- k=2101: 26617203803529829524424072887741571090057040709675215642877942001 P_1 = 41 = 2*20 + 1 P_2 = 241 = 12*20 + 1 P_3 = 401 = 20*20 + 1 P_4 = 4201 = 210*20 + 1 P_5 = 8824201 = 441210*20 + 1 P_6 = 194688001 = 9734400*20 + 1 P_7 = 242726070101 = 12136303505*20 + 1 P_8 = 19466639646301 = 973331982315*20 + 1 P_9 = 196989230867321 = 9849461543366*20 + 1 ---------- a(20) = 2101 n=21 ---------- k=7: 536608913442906151 P_1 = 127 = 6*21 + 1 P_2 = 4999 = 238*21 + 1 P_3 = 543607 = 25886*21 + 1 P_4 = 1554841 = 74040*21 + 1 ---------- a(21) = 7 n=22 ---------- k=12: 470658689525596656480023 P_1 = 23 = 1*22 + 1 P_2 = 67 = 3*22 + 1 P_3 = 727 = 33*22 + 1 P_4 = 1453 = 66*22 + 1 P_5 = 9396553 = 427116*22 + 1 P_6 = 30770521 = 1398660*22 + 1 ---------- a(22) = 12 n=23 ---------- k=2: 8388607 P_1 = 47 = 2*23 + 1 P_2 = 178481 = 7760*23 + 1 ---------- a(23) = 2 n=24 ---------- k=1900081: 61939438383329165644134283930105948773315516399787546547610749649121464533587870395290507576679110016365957524391021645522102744456901201559816321 P_1 = 73 = 3*24 + 1 P_2 = 6361 = 265*24 + 1 P_3 = 29017 = 1209*24 + 1 P_4 = 52057 = 2169*24 + 1 P_5 = 88969 = 3707*24 + 1 P_6 = 658969 = 27457*24 + 1 P_7 = 567568921 = 23648705*24 + 1 P_8 = 298602144721 = 12441756030*24 + 1 P_9 = 7220611812961 = 300858825540*24 + 1 P_10 = 10830917719441 = 451288238310*24 + 1 P_11 = 87302177622001 = 3637590734250*24 + 1 P_12 = 13034308738378815729616321 = 543096197432450655400680*24 + 1 P_13 = 99866494152680543346973966239395593 = 4161103923028355972790581926641483*24 + 1 ---------- a(24) = 1900081 n=25 ---------- k=6: 28132264806052748251 P_1 = 4651 = 186*25 + 1 P_2 = 6048648636003601 = 241945945440144*25 + 1 ---------- a(25) = 6 n=26 ---------- k=27: 10267083688053500835434793512309051513 P_1 = 53 = 2*26 + 1 P_2 = 45746819 = 1759493*26 + 1 P_3 = 2694777749 = 103645298*26 + 1 P_4 = 1571402279815239691 = 60438549223663065*26 + 1 ---------- a(26) = 27 n=27 ---------- k=18: 6137014262176877617115016189300559 P_1 = 109 = 4*27 + 1 P_2 = 919 = 34*27 + 1 P_3 = 21642769 = 801584*27 + 1 P_4 = 86802409 = 3214904*27 + 1 P_5 = 32611480916149 = 1207832626524*27 + 1 ---------- a(27) = 18 n=28 ---------- k=225: 85163080947638313957312537059417541585351658213340045697804370049 P_1 = 29 = 1*28 + 1 P_2 = 113 = 4*28 + 1 P_3 = 449 = 16*28 + 1 P_4 = 2801 = 100*28 + 1 P_5 = 3361 = 120*28 + 1 P_6 = 51577 = 1842*28 + 1 P_7 = 100801 = 3600*28 + 1 P_8 = 6203513 = 221554*28 + 1 P_9 = 348343213 = 12440829*28 + 1 P_10 = 4274031158041 = 152643969930*28 + 1 P_11 = 128039305212001 = 4572832329000*28 + 1 ---------- a(28) = 225 n=29 ---------- k=2: 536870911 P_1 = 233 = 8*29 + 1 P_2 = 1103 = 38*29 + 1 P_3 = 2089 = 72*29 + 1 ---------- a(29) = 2 n=30 ---------- k=9241: 303591841498357924776413378118106297320004922703347590858710742715577308155671461405109505094497555924522230884173201 P_1 = 31 = 1*30 + 1 P_2 = 61 = 2*30 + 1 P_3 = 211 = 7*30 + 1 P_4 = 241 = 8*30 + 1 P_5 = 4111 = 137*30 + 1 P_6 = 18481 = 616*30 + 1 P_7 = 21121 = 704*30 + 1 P_8 = 62311 = 2077*30 + 1 P_9 = 236881 = 7896*30 + 1 P_10 = 3026371 = 100879*30 + 1 P_11 = 7548031 = 251601*30 + 1 P_12 = 45152071 = 1505069*30 + 1 P_13 = 85386841 = 2846228*30 + 1 P_14 = 493958221 = 16465274*30 + 1 P_15 = 3187944031 = 106264801*30 + 1 P_16 = 5658972541 = 188632418*30 + 1 P_17 = 369296714104081 = 12309890470136*30 + 1 P_18 = 459915769780381 = 15330525659346*30 + 1 ---------- a(30) = 9241 n=31 ---------- k=2: 2147483647 P_1 = 2147483647 = 69273666*31 + 1 ---------- a(31) = 2 n=32 ---------- k=31825: 1232421474800658411085657487875728763806131421804644387293718661505355807433564710241924249198745409439528583720000879617162488674002724059649 P_1 = 1153 = 36*32 + 1 P_2 = 2753 = 86*32 + 1 P_3 = 63649 = 1989*32 + 1 P_4 = 1438181377 = 44943168*32 + 1 P_5 = 2025597601 = 63299925*32 + 1 P_6 = 2051522822614075201 = 64110088206689850*32 + 1 P_7 = 419637203198637577121 = 13113662599957424285*32 + 1 P_8 = 531499474353569157929921 = 16609358573549036185310*32 + 1 P_9 = 4576275301719180839812536659761033349599977470177 = 143008603178724401244141770617532292174999295943*32 + 1 ---------- a(32) = 31825 n=33 ---------- k=12: 386961115826114417195424335797191541 P_1 = 67 = 2*33 + 1 P_2 = 199 = 6*33 + 1 P_3 = 397 = 12*33 + 1 P_4 = 727 = 22*33 + 1 P_5 = 107713 = 3264*33 + 1 P_6 = 4767181 = 144460*33 + 1 P_7 = 9396553 = 284744*33 + 1 P_8 = 20840887 = 631542*33 + 1 ---------- a(33) = 12 n=34 ---------- k=52: 10673191331829796240927270278840314072092258097606205911383 P_1 = 103 = 3*34 + 1 P_2 = 239 = 7*34 + 1 P_3 = 1667 = 49*34 + 1 P_4 = 10376689123058321204799419 = 305196738913480035435277*34 + 1 P_5 = 25064830007197515717532463 = 737200882564632815221543*34 + 1 ---------- a(34) = 52 n=35 ---------- k=31: 10760586252479682895732059660839887422817189186451551 P_1 = 4481 = 128*35 + 1 P_2 = 1259231 = 35978*35 + 1 P_3 = 4329151 = 123690*35 + 1 P_4 = 357366921970776551 = 10210483484879330*35 + 1 P_5 = 1232646357287716841 = 35218467351077624*35 + 1 ---------- a(35) = 31 n=36 ---------- k=537850405: 13472710756243975965324503691159735014077290257759682754542199520512275549898445319268233839689326118161260272496469125347965034824624552841023687304600385301646525684247795969891509062145441744974354836173461206988879804343269412356531078616000568480752076641326511327493826364131181727542216435515974921329 P_1 = 37 = 1*36 + 1 P_2 = 397 = 11*36 + 1 P_3 = 1801 = 50*36 + 1 P_4 = 4969 = 138*36 + 1 P_5 = 24877 = 691*36 + 1 P_6 = 30261097 = 840586*36 + 1 P_7 = 35173729 = 977048*36 + 1 P_8 = 1075700809 = 29880578*36 + 1 P_9 = 91822858453 = 2550634957*36 + 1 P_10 = 1437726129121 = 39936836920*36 + 1 P_11 = 728672689221193 = 20240908033922*36 + 1 P_12 = 15636922033557493 = 434358945376597*36 + 1 P_13 = 867849172862440861 = 24106921468401135*36 + 1 P_14 = 1436136345404251521234577648788169 = 39892676261229208923182712466338*36 + 1 P_15 = 5884458037838564833390060423265041 = 163457167717737912038612789535140*36 + 1 P_16 = 83684687426446974184214461260758881 = 2324574650734638171783735035021080*36 + 1 P_17 = 3897483906401604941733864339321166318225923900979396771169846623697300846980111766571972947137 = 108263441844489026159274009425587953284053441693872132532495739547147245749447549071443692976*36 + 1 ---------- a(36) = 537850405 n=37 ---------- k=2: 137438953471 P_1 = 223 = 6*37 + 1 P_2 = 616318177 = 16657248*37 + 1 ---------- a(37) = 2 n=38 ---------- k=96: 695901001850055116946037464902509356849914548014593013281819906630906229311 P_1 = 191 = 5*38 + 1 P_2 = 419 = 11*38 + 1 P_3 = 5605585771 = 147515415*38 + 1 P_4 = 6470145306463 = 170266981749*38 + 1 P_5 = 12093662787517 = 318254283882*38 + 1 P_6 = 19824725399142905029406822365507499 = 521703299977444869194916378039671*38 + 1 ---------- a(38) = 96 n=39 ---------- k=26: 11965551334004658322078451162424627010050494039420995351 P_1 = 79 = 2*39 + 1 P_2 = 1951 = 50*39 + 1 P_3 = 6007 = 154*39 + 1 P_4 = 3597751 = 92250*39 + 1 P_5 = 73900842913 = 1894893408*39 + 1 P_6 = 275460073201 = 7063078800*39 + 1 P_7 = 176462150902335559 = 4524670535957322*39 + 1 ---------- a(39) = 26 n=40 ---------- k=13568281: 5895595909108050440838371953414805259362247963974805428616629215509828749662779067726632622390295805386780372745337387451766232073242383225536808833102181777468715280599515781926343527393731992089089820804185521599667701266644002280689950447916659026864606036570085702703172843201 P_1 = 41 = 1*40 + 1 P_2 = 14081 = 352*40 + 1 P_3 = 141601 = 3540*40 + 1 P_4 = 27136561 = 678414*40 + 1 P_5 = 24077918785441 = 601947969636*40 + 1 P_6 = 368196471453361 = 9204911786334*40 + 1 P_7 = 142478295818155006001 = 3561957395453875150*40 + 1 P_8 = 7617699922014046161567401 = 190442498050351154039185*40 + 1 P_9 = 33892160397676788642371002441 = 847304009941919716059275061*40 + 1 P_10 = 67784320795353209088270551521 = 1694608019883830227206763788*40 + 1 P_11 = 169460801988382102229497745401 = 4236520049709552555737443635*40 + 1 P_12 = 13964726648396000384891143577321 = 349118166209900009622278589433*40 + 1 P_13 = 50802827689150097640318849720701948878257842333280327867175125812132441 = 1270070692228752441007971243017548721956446058332008196679378145303311*40 + 1 ---------- a(40) = 13568281 n=41 ---------- k=2: 2199023255551 P_1 = 13367 = 326*41 + 1 P_2 = 164511353 = 4012472*41 + 1 ---------- a(41) = 2 n=42 ---------- k=232: 371872180143824583825905785157832702074869858229266836242143378141606869580957963203754445987501263 P_1 = 43 = 1*42 + 1 P_2 = 463 = 11*42 + 1 P_3 = 3739 = 89*42 + 1 P_4 = 53593 = 1276*42 + 1 P_5 = 856927 = 20403*42 + 1 P_6 = 179640679 = 4277159*42 + 1 P_7 = 1039365814033 = 24746805096*42 + 1 P_8 = 1077492216564457 = 25654576584868*42 + 1 P_9 = 22801373552694073 = 542889846492716*42 + 1 P_10 = 23713115435590752181087051129 = 564597986561684575740167884*42 + 1 ---------- a(42) = 232 n=43 ---------- k=2: 8796093022207 P_1 = 431 = 10*43 + 1 P_2 = 9719 = 226*43 + 1 P_3 = 2099863 = 48834*43 + 1 ---------- a(43) = 2 n=44 ---------- k=35421: 182559426550263054602483197521783993757749444371909348266759476647353659532097422132766701650433133538015598458717232991186901260949411762555777431255835612592443474575507034070007125566448890864881 P_1 = 89 = 2*44 + 1 P_2 = 6469 = 147*44 + 1 P_3 = 70841 = 1610*44 + 1 P_4 = 3253493 = 73943*44 + 1 P_5 = 2509223641 = 57027810*44 + 1 P_6 = 36755736469 = 835357647*44 + 1 P_7 = 13398814697929 = 304518515862*44 + 1 P_8 = 3440274860335470453253 = 78188065007624328483*44 + 1 P_9 = 111675116049365954808713 = 2538070819303771700198*44 + 1 P_10 = 480518074488700949933177482322732047241449 = 10920865329288657953026760961880273800942*44 + 1 P_11 = 6030486952794767192644716373377555504261388160889849916495457 = 137056521654426527105561735758580806915031549111132952647624*44 + 1 ---------- a(44) = 35421 n=45 ---------- k=486: 700945189130770350766468669520806227066554156684083941194130223319977309895267432296036610472609044814336900696551181451 P_1 = 3511 = 78*45 + 1 P_2 = 707131 = 15714*45 + 1 P_3 = 27302486041 = 606721912*45 + 1 P_4 = 277797199051 = 6173271090*45 + 1 P_5 = 39288080029484161 = 873068445099648*45 + 1 P_6 = 879216726825199261 = 19538149485004428*45 + 1 P_7 = 352569263206050821899499851 = 7834872515690018264433330*45 + 1 P_8 = 3056483820514866364996592851 = 67921862678108141444368730*45 + 1 ---------- a(45) = 486 n=46 ---------- k=24: 2652289254805992075049881944204301004086575749971106798448665487 P_1 = 47 = 1*46 + 1 P_2 = 967 = 21*46 + 1 P_3 = 4969 = 108*46 + 1 P_4 = 5676517163 = 123402547*46 + 1 P_5 = 142542511978079 = 3098750260393*46 + 1 P_6 = 1271891630065493 = 27649818044902*46 + 1 P_7 = 11411719402958807 = 248080856586061*46 + 1 ---------- a(46) = 24 n=47 ---------- k=2: 140737488355327 P_1 = 2351 = 50*47 + 1 P_2 = 4513 = 96*47 + 1 P_3 = 13264529 = 282224*47 + 1 ---------- a(47) = 2 n=48 ---------- k=4164776161: 6339419402511416691901935102943910870386610903422378477760379533219784864308732926985850522472967744700094215106573467541860618764734477761608401429371691951927314695232306781127525598586068167366853319033193120439740348323585638751666239823059019444962335678033231513968075138563000592789077590586788434590087429785633017030475392113642675565109715768018824986946291069165886887241562520275074352478707443658621401500837883922628472057002931976679508481 P_1 = 97 = 2*48 + 1 P_2 = 1249 = 26*48 + 1 P_3 = 27457 = 572*48 + 1 P_4 = 8329552321 = 173532340*48 + 1 P_5 = 4376635320829873 = 91179902517289*48 + 1 P_6 = 5779506227954489713 = 120406379749051869*48 + 1 P_7 = 17345360467069121761 = 361361676397273370*48 + 1 P_8 = 34690720934138243521 = 722723352794546740*48 + 1 P_9 = 52036081401207365281 = 1084085029191820110*48 + 1 P_10 = 104113229700263402257 = 2169025618755487547*48 + 1 P_11 = 53570759604998459277974433217 = 1116057491770801234957800692*48 + 1 P_12 = 4081687400540621415637777747740529 = 85035154177929612825787036411261*48 + 1 P_13 = 300861529732564341845013143525981984641 = 6267948536095090455104440490124624680*48 + 1 P_14 = 44353058522330539497113579129187927549395089 = 924022052548552906189866231858081823945731*48 + 1 P_15 = 3296706124959707817137254586682644089711254430926821687241374370916228033 = 68681377603327246190359470555888418535651133977642118484195299394088084*48 + 1 P_16 = 288445852919630104464350866001222785082323710265750963082057585361184489177029159480503899881177780914257 = 6009288602492293843007309708358808022548410630536478397542866361691343524521440822510497914191203769047*48 + 1 ---------- a(48) = 4164776161 n=49 ---------- k=7: 256788863974814750745170953957492865272711 P_1 = 197 = 4*49 + 1 P_2 = 1373 = 28*49 + 1 P_3 = 19993 = 408*49 + 1 P_4 = 543607 = 11094*49 + 1 P_5 = 16358161 = 333840*49 + 1 P_6 = 5340008371082265721 = 108979762675148280*49 + 1 ---------- a(49) = 7 n=50 ---------- k=2101: 311022106544137442308433347013984709397956372179877206199392357326861279014100126424571259949640784975562414167997368568663046343261821501428928828292126551002355001 P_1 = 101 = 2*50 + 1 P_2 = 151 = 3*50 + 1 P_3 = 401 = 8*50 + 1 P_4 = 751 = 15*50 + 1 P_5 = 1901 = 38*50 + 1 P_6 = 4201 = 84*50 + 1 P_7 = 8501 = 170*50 + 1 P_8 = 105251 = 2105*50 + 1 P_9 = 174199451 = 3483989*50 + 1 P_10 = 15475209901 = 309504198*50 + 1 P_11 = 242726070101 = 4854521402*50 + 1 P_12 = 945078852451 = 18901577049*50 + 1 P_13 = 19466639646301 = 389332792926*50 + 1 P_14 = 10764190849356438272551 = 215283816987128765451*50 + 1 P_15 = 50057350895695470967947833551 = 1001147017913909419358956671*50 + 1 P_16 = 1461065013018808991750235990769451 = 29221300260376179835004719815389*50 + 1 ---------- a(50) = 2101 n=51 ---------- k=68: 1522091967472161095653566125191238611086438135173581928509162640708729447009612892196621451749 P_1 = 613 = 12*51 + 1 P_2 = 1531 = 30*51 + 1 P_3 = 2551 = 50*51 + 1 P_4 = 13669 = 268*51 + 1 P_5 = 283493599 = 5558698*51 + 1 P_6 = 12010883244473929 = 235507514597528*51 + 1 P_7 = 1240370539504824632502776491 = 24320990970682835931426990*51 + 1 P_8 = 11012562379016507849445315637 = 215932595666990349989123836*51 + 1 ---------- a(51) = 68 n=52 ---------- k=10765: 2226848690400037842256835430262903693686257113564542739399983293759194167257073610582575604678532453751081183456621326792125983490929188500783262491439834589493196258715199847848958662078858662302148901838929 P_1 = 53 = 1*52 + 1 P_2 = 157 = 3*52 + 1 P_3 = 313 = 6*52 + 1 P_4 = 21529 = 414*52 + 1 P_5 = 231748921 = 4456710*52 + 1 P_6 = 23462311832654917 = 451198304474133*52 + 1 P_7 = 1341216585995373063001361226927193 = 25792626653757174288487715902446*52 + 1 P_8 = 1343556282531833781888987635990652466982629 = 25837620817919880420942069922897162826589*52 + 1 P_9 = 7733606679216993582490118535631280573202381997 = 148723205369557568894040741069832318715430423*52 + 1 P_10 = 524108988301931483382080556055460766855150634669949 = 10079019005806374680424626077989630131829819897499*52 + 1 ---------- a(52) = 10765 n=53 ---------- k=2: 9007199254740991 P_1 = 6361 = 120*53 + 1 P_2 = 69431 = 1310*53 + 1 P_3 = 20394401 = 384800*53 + 1 ---------- a(53) = 2 n=54 ---------- k=145180: 205766404524393995525948555869571186314198815116823845981281075630911911399125180573521718162771083835022664906229517816732766266284967885637522599436173583874557266558231986711399908595225495737112805204006509645842624911291112657757522565093503845554439419844132834319443319 P_1 = 2269 = 42*54 + 1 P_2 = 290359 = 5377*54 + 1 P_3 = 8592481 = 159120*54 + 1 P_4 = 275096359 = 5094377*54 + 1 P_5 = 1187885467 = 21997879*54 + 1 P_6 = 21077087221 = 390316430*54 + 1 P_7 = 63231261661 = 1170949290*54 + 1 P_8 = 89907107761 = 1664946440*54 + 1 P_9 = 362415902808519201277 = 6711405607565170394*54 + 1 P_10 = 4263118256854510046204161177 = 78946634386194630485262244*54 + 1 P_11 = 12379939918686521731139972509 = 229258146642342995021110602*54 + 1 P_12 = 9363361227832034236813431526921 = 173395578293185819200248731980*54 + 1 P_13 = 5409045237913959479991344307590926856352689539 = 100167504405814064444284153844276423265790547*54 + 1 P_14 = 958262883437473861744747591645388915903380411705249489867 = 17745608952545812254532362808247942887099637253800916479*54 + 1 ---------- a(54) = 145180 n=55 ---------- k=1925: 124034958551139168959337559803310571921815045686595382342191595932702388451965261086060686181778797444670639646565294113252705241327324698758105578436100438285837453751982055403501 P_1 = 3851 = 70*55 + 1 P_2 = 283344161 = 5151712*55 + 1 P_3 = 68586986968501 = 1247036126700*55 + 1 P_4 = 7025617365037913288791 = 127738497546143877978*55 + 1 P_5 = 235901173866241150198989214957264475959712737524674805540594557990920867106806858542363073733029401580425041862186555288704869824301 = 4289112252113475458163440271950263199267504318630451009828991963471288492851033791679328613327807301462273488403391914340088542260*55 + 1 ---------- a(55) = 1925 n=56 ---------- ---------- a(56) = ? n=57 ---------- k=171: 5424449700437200059630578818911443627080620183589338467335015913111872518264288952651478564233035255366216480403070954654814091 P_1 = 87211 = 1530*57 + 1 P_2 = 220021 = 3860*57 + 1 P_3 = 14084701 = 247100*57 + 1 P_4 = 774724963 = 13591666*57 + 1 P_5 = 831151739449 = 14581609464*57 + 1 P_6 = 693306585184417 = 12163273424288*57 + 1 P_7 = 524698813322685361 = 9205242338994480*57 + 1 P_8 = 85685903160604919594418095789767635571944967164207782419 = 1503261458957981045516106943680133957402543283582592674*57 + 1 ---------- a(57) = 171 n=58 ---------- k=30: P_1 = 59 = 1*58 + 1 P_2 = 33931 = 585*58 + 1 P_3 = 1941377 = 33472*58 + 1 P_4 = 762159731 = 13140685*58 + 1 P_5 = 50304369657631 = 867316718235*58 + 1 P_6 = 4169090358614206931 = 71880868251969085*58 + 1 P_7 = 65206693447873608898106170077113 = 1124253335308165670657002932364*58 + 1 ---------- a(58) = 30 n=59 ---------- k=2: 576460752303423487 P_1 = 179951 = 3050*59 + 1 P_2 = 3203431780337 = 54295453904*59 + 1 ---------- a(59) = 2 n=60 ---------- ---------- a(60) = ? n=61 ---------- k=2: 2305843009213693951 P_1 = 2305843009213693951 = 37800705069076950*61 + 1 ---------- a(61) = 2 n=62 ---------- k=156: 3095144367534651048912945381163960551398955163437087869869954861140421974894772148263350564650442011862085420563363626657448730920271511 P_1 = 311 = 5*62 + 1 P_2 = 3659 = 59*62 + 1 P_3 = 8867 = 143*62 + 1 P_4 = 18787 = 303*62 + 1 P_5 = 33327716467083280863260963 = 537543813985214207471951*62 + 1 P_6 = 17029058081603933283981471172506484765367 = 274662227122644085225507599556556205893*62 + 1 P_7 = 28769199889240119928326404968206014795744858030552282671 = 464019353052259998843974273680742174124917065008907785*62 + 1 ---------- a(62) = 156 n=63 ---------- k=18298: 116850241778483753234226918441700918899832157801764297517630354935882077669365867301854400413945724548845795244204566203633140206784886593317550940964647540786891150812653282113085279330094993538380576966114398328005675760817677210753002767790678469819437367948216119 P_1 = 7266673 = 115344*63 + 1 P_2 = 1004395519 = 15942786*63 + 1 P_3 = 6524087001001984331821 = 103556936523841021140*63 + 1 P_4 = 29706106074552212675707 = 471525493246860518662*63 + 1 P_5 = 6134262769885966790065867 = 97369250315650266508982*63 + 1 P_6 = 112582734415412079458494009 = 1787027530403366340611016*63 + 1 P_7 = 262693046184664572387405559 = 4169730891820072577577866*63 + 1 P_8 = 455345464566819535891307118950502183499027132823374898047970037271699714350162131848243672144256534079342130007862503446652270923 = 7227705786774913268115986015087336246016303695609125365840794242407931973812097330924502732448516413957811587426388943597655094*63 + 1 ---------- a(63) = 18298 n=64 ---------- ---------- a(64) = ? n=65 ---------- k=442: 1227023564492985260527252098630009965283026936018989196442815421387542006475346562256297214512440685726739547311961096632737566441209207623704548781278163864117262642268231 P_1 = 131 = 2*65 + 1 P_2 = 189973905031 = 2922675462*65 + 1 P_3 = 713056759837969339900900305521191 = 10970103997507220613860004700326*65 + 1 P_4 = 8009004696322051187030829655160291 = 123215456866493095185089687002466*65 + 1 P_5 = 842704730821702461465917914314047465645944321 = 12964688166487730176398737143293037933014528*65 + 1 P_6 = 10244943694437698260499663103118497195162169471 = 157614518375964588623071740047976879925571838*65 + 1 ---------- a(65) = 442 n=66 ---------- ---------- a(66) = ? n=67 ---------- k=2: 147573952589676412927 P_1 = 193707721 = 2891160*67 + 1 P_2 = 761838257287 = 11370720258*67 + 1 ---------- a(67) = 2 n=68 ---------- k=8365: 4325029606919173493519794160130216854265388798588011876461163793297472441570672384887577935233751703177926606991873886622560086087191208951924091491247740174439588867549562442110644701827963605788353263246868316608986159974542833874428878328340685294333227790058769 P_1 = 137 = 2*68 + 1 P_2 = 4421 = 65*68 + 1 P_3 = 5849 = 86*68 + 1 P_4 = 16729 = 246*68 + 1 P_5 = 37537 = 552*68 + 1 P_6 = 53993 = 794*68 + 1 P_7 = 154157 = 2267*68 + 1 P_8 = 2401897 = 35322*68 + 1 P_9 = 139929721 = 2057790*68 + 1 P_10 = 4316051461 = 63471345*68 + 1 P_11 = 2349729420563288403841 = 34554844420048358880*68 + 1 P_12 = 175911315556231082066001232637 = 2586931111121045324500018127*68 + 1 P_13 = 167806966748096927693960724653142742976077 = 2467749511001425407264128303722687396707*68 + 1 P_14 = 4063819142286429722191170500879734467573341582897960369893 = 59762046210094554738105448542349036287843258572028828969*68 + 1 P_15 = 571253900986761043267272804048184732600450079691243465476363329 = 8400792661570015342165776530120363714712501171930050962887696*68 + 1 ---------- a(68) = 8365 n=69 ---------- k=553: 207832917602845701091843056451694251625097069523566138180607795427726641869701686849032197009346657712474480486252054433375770984509715113386273082129027508432778264571829428853811796373321 P_1 = 967 = 14*69 + 1 P_2 = 915769 = 13272*69 + 1 P_3 = 4674199 = 67742*69 + 1 P_4 = 212915945196555316570672734596918593 = 3085738336181961109719894704303168*69 + 1 P_5 = 49324811567243602678508717061129091931687589691020384025930969 = 714852341554255111282735029871436114951994053493049043854072*69 + 1 P_6 = 4781025967389771846675928789985237919688661222542176993705499099701031364569 = 69290231411445968792404765072249824923024075689017057879789842024652628472*69 + 1 ---------- a(69) = 553 n=70 ---------- ---------- a(70) = ? n=71 ---------- k=2: 2361183241434822606847 P_1 = 228479 = 3218*71 + 1 P_2 = 48544121 = 683720*71 + 1 P_3 = 212885833 = 2998392*71 + 1 ---------- a(71) = 2 n=72 ---------- ---------- a(72) = ? n=73 ---------- k=2: 9444732965739290427391 P_1 = 439 = 6*73 + 1 P_2 = 2298041 = 31480*73 + 1 P_3 = 9361973132609 = 128246207296*73 + 1 ---------- a(73) = 2 n=74 ---------- k=75: 3577930195898019120696236704349981289493064314680404991035402504264626012617837942628437889624387704914900958948371519517049562990210953049 P_1 = 149 = 2*74 + 1 P_2 = 223 = 3*74 + 1 P_3 = 302617816301 = 4089429950*74 + 1 P_4 = 833165427901292639 = 11258992268936387*74 + 1 P_5 = 82775850355896784905941 = 1118592572376983579810*74 + 1 P_6 = 13529808332903100791252308849 = 182835247741933794476382552*74 + 1 P_7 = 381346445708645283097522464637009137778386327175476437 = 5153330347414125447263817089689312672680896313182114*74 + 1 ---------- a(74) = 75 n=75 ---------- ---------- a(75) = ? n=76 ---------- ---------- a(76) = ? n=77 ---------- k=1914: 202060932846084380944111750740646737382428944766849023284472986496233194087665403752160273335745046286895984847314495816971994830604235460380163450100022651772379910063251696490689120238934105692477690692096623058943533178343936750376096271704950669671 P_1 = 7443393343 = 96667446*77 + 1 P_2 = 343612526385779044087 = 4462500342672455118*77 + 1 P_3 = 7238986980789552114648237893179927 = 94012817932331845644782310301038*77 + 1 P_4 = 10913513769807991519561657077596924925973172071362555950102440029374043347568330417400220269471906502140923704850913690000024532610585042731561186785287160571085899845243255687746207744553 = 141733945062441448305995546462297726311339897030682544806525195186675887630757537888314548954180603923908100062998879090909409514423182373137158269938794293130985712275886437503197503176*77 + 1 ---------- a(77) = 1914 n=78 ---------- ---------- a(78) = ? n=79 ---------- k=2: 604462909807314587353087 P_1 = 2687 = 34*79 + 1 P_2 = 202029703 = 2557338*79 + 1 P_3 = 1113491139767 = 14094824554*79 + 1 ---------- a(79) = 2 n=80 ---------- ---------- a(80) = ? n=81 ---------- ---------- a(81) = ? n=82 ---------- k=42: 11006144782298318018805714255022922800863740473646858590847074735682799730656650661898188144550690213558505863971072972259492384095983 P_1 = 83 = 1*82 + 1 P_2 = 67733 = 826*82 + 1 P_3 = 511859827 = 6242193*82 + 1 P_4 = 42145114587920339 = 513964812047809*82 + 1 P_5 = 1535536325585717256184039907840401699 = 18726052751045332392488291559029289*82 + 1 P_6 = 59101491116428708061599179657118474057789822844385576304517879251 = 720749891663764732458526581184371634851095400541287515908754625*82 + 1 ---------- a(82) = 42 n=83 ---------- k=2: 9671406556917033397649407 P_1 = 167 = 2*83 + 1 P_2 = 57912614113275649087721 = 697742338714164446840*83 + 1 ---------- a(83) = 2 n=84 ---------- ---------- a(84) = ? n=85 ---------- k=391: 4230708923985000870814100120023139009663804086065856499388507144080621716928777333833967115502743064917170387489318889698773617367977140126818393685085156444556989260588266961004345452097702609796996846753463685780810151 P_1 = 316201 = 3720*85 + 1 P_2 = 774181 = 9108*85 + 1 P_3 = 15555511 = 183006*85 + 1 P_4 = 116266762951 = 1367844270*85 + 1 P_5 = 8345685468513265897751 = 98184534923685481150*85 + 1 P_6 = 319543310442897788194157177331881521 = 3759333064034091625813613850963312*85 + 1 P_7 = 3583239131016114340595482575273206217808605061642596847650800159282064397876649710621897544575247006459822749956043122134273850205541 = 42155754482542521654064500885567131974218883078148198207656472462141934092666467183787029936179376546586149999482860260403221767124*85 + 1 ---------- a(85) = 391 n=86 ---------- k=87: 39626962031561674021228242257535385866030777469516490137016013400069486104350596553989193298166421216899109561037673394140684896214859473820159754458436754564651277873 P_1 = 173 = 2*86 + 1 P_2 = 431 = 5*86 + 1 P_3 = 1549 = 18*86 + 1 P_4 = 169937 = 1976*86 + 1 P_5 = 8386549 = 97518*86 + 1 P_6 = 1423443816716917 = 16551672287406*86 + 1 P_7 = 702283911960395937901 = 8166091999539487650*86 + 1 P_8 = 748288946360769808877 = 8701034260008951266*86 + 1 P_9 = 11718287758552541683190753590169583740059 = 136259159983169089339427367327553299303*86 + 1 P_10 = 27463647331336608133202679490590573294667661946293 = 319344736410890792246542784774308991798461185422*86 + 1 ---------- a(86) = 87 n=87 ---------- ---------- a(87) = ? n=88 ---------- ---------- a(88) = ? n=89 ---------- k=2: 618970019642690137449562111 P_1 = 618970019642690137449562111 = 6954719321827979072466990*89 + 1 ---------- a(89) = 2 n=90 ---------- ---------- a(90) = ? n=91 ---------- k=39: 5545954199767957928387754685269668327763302477189149292866624157375241953379325303976226873209457580449928934161772044478054952198914044578948727 P_1 = 28393 = 312*91 + 1 P_2 = 153427 = 1686*91 + 1 P_3 = 1677783199 = 18437178*91 + 1 P_4 = 22815424087 = 250718946*91 + 1 P_5 = 138382708044670752391 = 1520689099391986290*91 + 1 P_6 = 240334982985715000159864642529418242549753668258067294347600275919986195187198453304351294909179 = 2641043769073791210547963104718881786261029321517223014808794240878969177881301684663201042958*91 + 1 ---------- a(91) = 39 n=92 ---------- ---------- a(92) = ? n=93 ---------- k=63: 168855381936602686741866292678144623085032898545449211118332276940432844152042836049027979425024895112620542232459716104184231802633015020111924520075891420069299533631 P_1 = 11719 = 126*93 + 1 P_2 = 948997879126741 = 10204278270180*93 + 1 P_3 = 277515553917257817151 = 2984038214164062550*93 + 1 P_4 = 643213894074256162586743159 = 6916278430905980242868206*93 + 1 P_5 = 36595537833074945777658387961 = 393500406807257481480197720*93 + 1 P_6 = 10909810170442938727452126009824287 = 117309786778956330402711032363702*93 + 1 P_7 = 213044848409455006212578719521247219003 = 2290804821607043077554609887325238914*93 + 1 ---------- a(93) = 63 n=94 ---------- k=142: 10027215700207791775284711225190686144993499379527849561262179181175241186913894289056065836116962307928536035184773191976658721771000658703954425108771868024886278320830724416418989750639839783885831143 P_1 = 283 = 3*94 + 1 P_2 = 434939 = 4627*94 + 1 P_3 = 5092368973 = 54174138*94 + 1 P_4 = 3059118193877860208308859 = 32543810573168725620307*94 + 1 P_5 = 114787463204876462332126133283686113 = 1221143225583792152469426949826448*94 + 1 P_6 = 1176672848424213579999551866900497377 = 12517796259832059361697360286175504*94 + 1 P_7 = 11285247793141388352823242401430091371169 = 120055827586610514391736621291809482672*94 + 1 P_8 = 3430742795737959703279435294020864090948827482433 = 36497263784446379822121652064051745648391781728*94 + 1 ---------- a(94) = 142 n=95 ---------- k=145: 10300290081150784020499697767234996513733640859267956790747926685978812182072809447039785638213685654642567003664534367109833887274032013001313774083269437713185439858014037055863008506603764898437574911601 P_1 = 571 = 6*95 + 1 P_2 = 6271 = 66*95 + 1 P_3 = 2179976401 = 22947120*95 + 1 P_4 = 2404264833221 = 25308050876*95 + 1 P_5 = 294475215750588547136649044401031 = 3099739113164089969859463625274*95 + 1 P_6 = 25119089222339967108631720431625608451 = 264411465498315443248754951911848510*95 + 1 P_7 = 1795230349975753008082321494641738257441017150391 = 18897161578692136927182331522544613236221233162*95 + 1 P_8 = 41330402176529907379243387432811769247118136534198046917571 = 435056865016104288202561972976965992074927752991558388606*95 + 1 ---------- a(95) = 145