Wieferich pairs and Barker sequences, II Peter Borwein and Michael J. Mossinghoff 473 known values of u < 5 * 10^49 for which u has exactly six prime factors, counting multiplicity, and n = 4u^2 cannot be eliminated as a possible length of a Barker sequence. Each value is shown with its prime factorization. 31540455528264605 [5, 13, 29, 41, 2953, 138200401] 66687671978077825 [5, 5, 53, 193, 4877, 53471161] 1293740836374709805 [5, 53, 97, 193, 4877, 53471161] 2487505958525418181705 [5, 29, 41, 2953, 1025273, 138200401] 6467515492166087272433 [13, 29, 41, 2953, 1025273, 138200401] 863383081390130269759645 [5, 41, 193, 2953, 53471161, 138200401] 2630496319975038327042325 [5, 5, 193, 24697, 53471161, 412835053] 6839290431935099650310045 [5, 13, 193, 24697, 53471161, 412835053] 79086309600441820327429745 [5, 17, 613, 4073, 1974353, 188748146801] 90731265804262269790349005 [5, 13, 3061, 5333, 453029, 188748146801] 103551998305709852149811645 [5, 17, 613, 5333, 1974353, 188748146801] 118648578359419891264302545 [5, 17, 3061, 5333, 453029, 188748146801] 122879142625828860061880765 [5, 13, 53, 97, 4794006457, 76704103313] 202400516024892755686163165 [5, 29, 3061, 5333, 453029, 188748146801] 223307997688226357888882045 [5, 29, 1301, 3209, 1954369, 188748146801] 258235141135207998634070245 [5, 37, 3061, 5333, 453029, 188748146801] 261876047581400340733502225 [5, 5, 17, 5333, 612142549, 188748146801] 337756644739168029541486645 [5, 13, 113, 123397, 1974353, 188748146801] 364187964333481064194321445 [5, 421, 661, 3061, 453029, 188748146801] 410340061271887544490400045 [5, 13, 3209, 5333, 1954369, 188748146801] 467278303413495791803900145 [5, 13, 3209, 6073, 1954369, 188748146801] 536598541663237558179753905 [5, 17, 3209, 5333, 1954369, 188748146801] 581597766608950657391303465 [5, 13, 53, 453029, 1974353, 188748146801] 776564410129066082172078365 [5, 13, 5333, 6073, 1954369, 188748146801] 893599571353285787696696365 [5, 17, 613, 46021, 1974353, 188748146801] 905739337549207627548430505 [5, 29, 37, 453029, 1974353, 188748146801] 915373982837287599247815485 [5, 29, 3209, 5333, 1954369, 188748146801] 1015507305553394107455794785 [5, 17, 5333, 6073, 1954369, 188748146801] 1023875159324744574512369665 [5, 17, 3061, 46021, 453029, 188748146801] 1042390061460875227870238785 [5, 29, 3209, 6073, 1954369, 188748146801] 1287279813950797179417972665 [5, 13, 30109, 1128713, 2167849, 268813277] 1297410402435351466488292345 [5, 29, 53, 453029, 1974353, 188748146801] 1372857371759876937892740445 [5, 13, 29, 1954369, 1974353, 188748146801] 1642203958173880151504864705 [5, 353, 613, 4073, 1974353, 188748146801] 1655316720348551871036786785 [5, 37, 53, 453029, 1974353, 188748146801] 1732335991826378183306944045 [5, 29, 5333, 6073, 1954369, 188748146801] 1783837381469736300514363745 [5, 17, 5333, 46021, 453029, 188748146801] 1832255072788584089459569145 [5, 13, 613, 123397, 1974353, 188748146801] 2396025864415840732370205805 [5, 17, 613, 123397, 1974353, 188748146801] 2565786110503652384197083805 [5, 193, 4877, 24697, 53471161, 412835053] 2938297146430339660133610085 [5, 421, 3061, 5333, 453029, 188748146801] 3087810588723405845291093105 [5, 401, 1301, 3209, 1954369, 188748146801] 3298832367416482473968952845 [5, 53, 97, 349, 4794006457, 76704103313] 4339614104697554905150495085 [5, 53, 97, 453029, 1974353, 188748146801] 4586545917130067523664665845 [5, 41, 2953, 1025273, 53471161, 138200401] 4613335899739796948570822485 [5, 661, 3061, 5333, 453029, 188748146801] 6405815459257701704146252885 [5, 53, 97, 453029, 2914393, 188748146801] 7695481921434669886254426445 [5, 17, 5333, 46021, 1954369, 188748146801] 7774170495965861510255271965 [5, 17, 5333, 46021, 1974353, 188748146801] 8576964155282854432319277397 [13, 53, 97, 349, 4794006457, 76704103313] 8796560705126088244810991885 [5, 17, 613, 453029, 1974353, 188748146801] 12657412659232838872357724465 [5, 401, 3209, 5333, 1954369, 188748146801] 14413738436062447116412612165 [5, 401, 3209, 6073, 1954369, 188748146801] 14641522455954531095065638845 [5, 53, 97, 1549, 4794006457, 76704103313] 15005897673450385829383456745 [5, 29, 613, 453029, 1974353, 188748146801] 15926524863470000162225485645 [5, 113, 613, 123397, 1974353, 188748146801] 15940320233575071695086267945 [5, 13, 5333, 123397, 1974353, 188748146801] 19111154160961835048282209565 [5, 193, 30109, 1128713, 2167849, 268813277] 19133227731015598349019926501 [29, 53, 97, 349, 4794006457, 76704103313] 19145455652333250885765099985 [5, 37, 613, 453029, 1974353, 188748146801] 20845034151598170678189735005 [5, 17, 5333, 123397, 1974353, 188748146801] 27424571610098980998528386465 [5, 53, 613, 453029, 1974353, 188748146801] 29019364444441536652698272165 [5, 13, 613, 1954369, 1974353, 188748146801] 33590014407358452118392073705 [5, 13, 3061, 453029, 1974353, 188748146801] 37180928413211433358801452965 [5, 13, 29, 1954369, 53471161, 188748146801] 37948399658115855622759278985 [5, 17, 613, 1954369, 1974353, 188748146801] 38067958385481780847170660997 [13, 53, 97, 1549, 4794006457, 76704103313] 41065570747286591952462342965 [5, 1301, 3209, 5333, 1954369, 188748146801] 43925403455776437385589634845 [5, 17, 3061, 453029, 1974353, 188748146801] 46763774826227540395144160665 [5, 1301, 3209, 6073, 1954369, 188748146801] 49689000818500771125533744869 [13, 193, 30109, 1128713, 2167849, 268813277] 63762807996294933072428993885 [5, 17, 613, 1974353, 3283829, 188748146801] 64735505299138812532942299445 [5, 29, 613, 1954369, 1974353, 188748146801] 74931570601030393187182318265 [5, 29, 3061, 453029, 1974353, 188748146801] 75754035752930772123594805805 [5, 17, 5333, 453029, 1954369, 188748146801] 76528643132850617633893996285 [5, 17, 5333, 453029, 1974353, 188748146801] 94634681144810673370048608785 [5, 37, 3061, 453029, 1954369, 188748146801] 95171341959546507138576663425 [5, 5, 193, 1954369, 53471161, 188748146801] 95602348697866363721577440545 [5, 37, 3061, 453029, 1974353, 188748146801] 96144497027867575165472974225 [5, 5, 193, 1974353, 53471161, 188748146801] 115288992508248815859596899285 [5, 53, 97, 12197, 4794006457, 76704103313] 129227472754999552446132315785 [5, 29, 5333, 453029, 1954369, 188748146801] 129973995276209409474376742093 [53, 97, 197, 349, 4794006457, 76704103313] 130548861814862818316642699545 [5, 29, 5333, 453029, 1974353, 188748146801] 135557786504728802394934493665 [5, 53, 3061, 453029, 1954369, 188748146801] 136943904891538304790367685105 [5, 53, 3061, 453029, 1974353, 188748146801] 138558168184152546272672944445 [5, 113, 5333, 123397, 1974353, 188748146801] 151913769171636037713717382345 [5, 13, 3209, 1954369, 1974353, 188748146801] 153400431205736659226481764245 [5, 53, 97, 16229, 4794006457, 76704103313] 164876430756378739327823989105 [5, 37, 5333, 453029, 1954369, 188748146801] 166562340936204285438475168385 [5, 37, 5333, 453029, 1974353, 188748146801] 191691937854167158283861497945 [5, 3209, 5333, 6073, 1954369, 188748146801] 193210806003891284642166507365 [5, 421, 3061, 350677, 453029, 188748146801] 236174346759137113091207335745 [5, 53, 5333, 453029, 1954369, 188748146801] 238589299178887219682140106065 [5, 53, 5333, 453029, 1974353, 188748146801] 247445489094820918560299324905 [5, 13, 193, 1954369, 53471161, 188748146801] 252463736675704265854551199765 [5, 13, 5333, 1954369, 1974353, 188748146801] 274957547189099034412857682645 [5, 401, 3209, 115849, 1954369, 188748146801] 285678883018267382245711316377 [53, 97, 349, 433, 4794006457, 76704103313] 287495269610266642890434921465 [5, 13, 6073, 1954369, 1974353, 188748146801] 292885252509715569315651635525 [5, 5, 5333, 19013, 612142549, 188748146801] 299751380521446921234951938141 [13, 53, 97, 12197, 4794006457, 76704103313] 330144886422074809194413107385 [5, 17, 5333, 1954369, 1974353, 188748146801] 338884561998265007207523391385 [5, 29, 3209, 1954369, 1974353, 188748146801] 398841121134915313988852587037 [13, 53, 97, 16229, 4794006457, 76704103313] 551993783365369741403744647865 [5, 29, 193, 1954369, 53471161, 188748146801] 554726027804634385114622878285 [5, 17, 5333, 1974353, 3283829, 188748146801] 563188335661186439213998830245 [5, 29, 5333, 1954369, 1974353, 188748146801] 570897082453582273539295198105 [5, 13, 24697, 16110317, 53471161, 412835053] 574059608574454076643755779045 [5, 613, 4073, 123397, 1974353, 188748146801] 641335601438287126447893286345 [5, 29, 6073, 1954369, 1974353, 188748146801] 751647407937039919160606326945 [5, 613, 5333, 123397, 1974353, 188748146801] 995809858533032935673215560785 [5, 17, 5333, 19013, 612142549, 188748146801] 1021978267425626270435581591381 [53, 97, 349, 1549, 4794006457, 76704103313] 1038260936297832125180719030465 [5, 17, 613, 1974353, 53471161, 188748146801] 1074680601600615522171019794865 [5, 10853, 30109, 1128713, 2167849, 268813277] 1075225013988298098913434756545 [5, 401, 3209, 453029, 1954369, 188748146801] 1076789209782845769967309845905 [5, 421, 3061, 453029, 1954369, 188748146801] 1087799697345992949372543309985 [5, 421, 3061, 453029, 1974353, 188748146801] 1354102256721597816417257993785 [5, 13, 123397, 453029, 1974353, 188748146801] 1583898371670056242198026244705 [5, 613, 3061, 453029, 1974353, 188748146801] 1690635790181617705340598119105 [5, 661, 3061, 453029, 1954369, 188748146801] 1707923040251072065404396978385 [5, 661, 3061, 453029, 1974353, 188748146801] 1846812436088071210327084667545 [5, 41, 2953, 53471161, 138200401, 412835053] 2052144066646828922300824807273 [53, 89, 97, 12197, 4794006457, 76704103313] 2107552455998738671830304114565 [5, 613, 4073, 453029, 1974353, 188748146801] 2410359517148725016179301179345 [5, 17, 5333, 46021, 612142549, 188748146801] 2759532837672789918210412924865 [5, 613, 5333, 453029, 1974353, 188748146801] 2794169564161600357644651466649 [13, 10853, 30109, 1128713, 2167849, 268813277] 3020689649609718205853883216905 [5, 29, 123397, 453029, 1974353, 188748146801] 3488448237403430989242839447045 [5, 1301, 3209, 453029, 1954369, 188748146801] 3853983346053778400572195828465 [5, 37, 123397, 453029, 1974353, 188748146801] 4114262044068809987875650433265 [5, 13, 3209, 1954369, 53471161, 188748146801] 4685955495217388547938513101565 [5, 401, 3209, 1954369, 1974353, 188748146801] 5213357494672937133818599112345 [5, 89, 5333, 19013, 612142549, 188748146801] 5520570738941898790008821051585 [5, 53, 123397, 453029, 1974353, 188748146801] 5681973898688482044723641729185 [5, 97, 5333, 19013, 612142549, 188748146801] 5841602796657018431212085954885 [5, 13, 123397, 1954369, 1974353, 188748146801] 6837444525091606003534074091805 [5, 13, 5333, 1954369, 53471161, 188748146801] 6978673174103189115421045852325 [5, 5, 5333, 453029, 612142549, 188748146801] 7163318500170222393731442721345 [5, 613, 3209, 1954369, 1974353, 188748146801] 7469402087122255871122436577305 [5, 17, 71809, 1974353, 3283829, 188748146801] 7786199250118380509931076684705 [5, 13, 6073, 1954369, 53471161, 188748146801] 8047171677075767346999863570093 [53, 97, 349, 12197, 4794006457, 76704103313] 8207640318748579752553675286245 [5, 3061, 3209, 453029, 1954369, 188748146801] 8475625916426259907160305633405 [5, 193, 24697, 16110317, 53471161, 412835053] 8941273609735177081544558427745 [5, 17, 5333, 1954369, 53471161, 188748146801] 9032700772065805421841394110065 [5, 17, 5333, 1974353, 53471161, 188748146801] 9091990106323875291264620194465 [5, 613, 4073, 1954369, 1974353, 188748146801] 9177969175230422280645681735745 [5, 29, 3209, 1954369, 53471161, 188748146801] 9815354556966171781249473875785 [5, 13, 123397, 1974353, 3283829, 188748146801] 10707350098160418814008427144301 [53, 97, 349, 16229, 4794006457, 76704103313] 11770273462272350250396165638285 [5, 113, 123397, 453029, 1974353, 188748146801] 11787315335616564715286986639985 [5, 193, 613, 1974353, 53471161, 188748146801] 11904636198631285766833837342765 [5, 613, 5333, 1954369, 1974353, 188748146801] 13031267777157964192703884053205 [5, 29, 123397, 1954369, 1974353, 188748146801] 13556507713161034776295123604465 [5, 613, 6073, 1954369, 1974353, 188748146801] 13640182555277711380607276504065 [5, 3061, 5333, 453029, 1954369, 188748146801] 13779657448803278857491148389905 [5, 3061, 5333, 453029, 1974353, 188748146801] 14299688278303226337918572460485 [5, 3209, 5333, 453029, 1954369, 188748146801] 15203062591715268081965101110065 [5, 1301, 3209, 1954369, 1974353, 188748146801] 15252760863665890315576011435565 [5, 29, 5333, 1954369, 53471161, 188748146801] 15276818645229956612000193652565 [5, 613, 4073, 1974353, 3283829, 188748146801] 15532876178173924848008248679765 [5, 3061, 6073, 453029, 1954369, 188748146801] 17369213711802541137538555681265 [5, 29, 6073, 1954369, 53471161, 188748146801] 18641019768602173906094467209701 [193, 4877, 30109, 1128713, 2167849, 268813277] 20002767943778875180897872022865 [5, 613, 5333, 1974353, 3283829, 188748146801] 20103709177719512605101275751725 [5, 5, 193, 53471161, 412835053, 188748146801] 23727488791950842992431555897905 [5, 17, 5333, 453029, 612142549, 188748146801] 25115883103451827737425433995225 [5, 5, 820957, 1974353, 3283829, 188748146801] 26351723678324505211731576182485 [5, 17, 5333, 46021, 6692367337, 188748146801] 27062015242796975241564191509045 [5, 5333, 6073, 453029, 1954369, 188748146801] 27547547162670557612486528334665 [5, 53, 97, 2914393, 4794006457, 76704103313] 29938221415615131458624077920805 [5, 41, 2953, 53471161, 138200401, 6692367337] 30106025249153753089352588821825 [5, 5, 5333, 1954369, 612142549, 188748146801] 30413868245322382760483077555025 [5, 5, 5333, 1974353, 612142549, 188748146801] 30861417707644993303485858421685 [5, 41, 2953, 1954369, 138200401, 188748146801] 31176984814711047639272427587845 [5, 41, 2953, 1974353, 138200401, 188748146801] 31789573048563236468369822342585 [5, 30109, 321037, 1128713, 2167849, 268813277] 35716529879055483153303119398493 [53, 97, 1549, 12197, 4794006457, 76704103313] 40476304409798496869442065943485 [5, 29, 5333, 453029, 612142549, 188748146801] 41482671221783759155801364081789 [193, 10853, 30109, 1128713, 2167849, 268813277] 47523453587537217028364050563101 [53, 97, 1549, 16229, 4794006457, 76704103313] 50777008924787929440535824069385 [5, 113, 123397, 1954369, 1974353, 188748146801] 51642181488363599454115739307205 [5, 37, 5333, 453029, 612142549, 188748146801] 57817816366113115092800864963737 [269, 10853, 30109, 1128713, 2167849, 268813277] 61080967269636948281538502586165 [5, 193, 3209, 1954369, 53471161, 188748146801] 62319702384025768394404215388145 [5, 3209, 5333, 1954369, 1974353, 188748146801] 63851129490026112420290703860785 [5, 613, 123397, 453029, 1974353, 188748146801] 70303227631530127911182189183993 [53, 97, 3049, 12197, 4794006457, 76704103313] 70967101552257358233492743306245 [5, 3209, 6073, 1954369, 1974353, 188748146801] 71623622622943449792464973670129 [13, 53, 97, 2914393, 4794006457, 76704103313] 73973935645493804623463086034645 [5, 53, 5333, 453029, 612142549, 188748146801] 78275665647799758032316730936745 [5, 13, 5333, 1954369, 612142549, 188748146801] 80386300083375052280127972886585 [5, 29, 453029, 1974353, 3283829, 188748146801] 82652889926264414817761538090721 [13, 30109, 321037, 1128713, 2167849, 268813277] 85318081918244416252399272920285 [5, 113, 123397, 1974353, 3283829, 188748146801] 92830126947341663062967677504745 [5, 193, 4877, 1954369, 53471161, 188748146801] 93779342400982032816402339059065 [5, 193, 4877, 1974353, 53471161, 188748146801] 98809880269086009513923676763825 [5, 5, 1601, 1954369, 6692367337, 188748146801] 99820240465802911395874450009025 [5, 5, 1601, 1974353, 6692367337, 188748146801] 101509753334052304514005869209105 [5, 193, 5333, 1954369, 53471161, 188748146801] 102360485847122760503798801994205 [5, 17, 5333, 1954369, 612142549, 188748146801] 102547720529923555671493474308385 [5, 193, 5333, 1974353, 53471161, 188748146801] 102561831140857825322921896441505 [5, 37, 453029, 1974353, 3283829, 188748146801] 103407152034096101385642463687085 [5, 17, 5333, 1974353, 612142549, 188748146801] 115595111944065187570515215396005 [5, 193, 6073, 1954369, 53471161, 188748146801] 117939405602427077425745341244065 [5, 5333, 6073, 1954369, 1974353, 188748146801] 124469109880334725296367303508393 [53, 97, 4057, 16229, 4794006457, 76704103313] 126909159974737908087548909518405 [5, 401, 3209, 1954369, 53471161, 188748146801] 129947123784401266665385089761905 [5, 17, 613, 1974353, 6692367337, 188748146801] 146912893255823371408509743551345 [5, 53, 453029, 1974353, 3283829, 188748146801] 155456167249960859485633791819445 [5, 13, 1954369, 1974353, 3283829, 188748146801] 159825132120954484191730872337565 [5, 13, 123397, 1974353, 53471161, 188748146801] 174614946445091767918245015166585 [5, 29, 5333, 1954369, 612142549, 188748146801] 185857534965543525256948211564665 [5, 37, 820957, 1974353, 3283829, 188748146801] 209992589552760273032217267916621 [977, 10853, 30109, 1128713, 2167849, 268813277] 235242840559367949865936685335129 [37, 30109, 321037, 1128713, 2167849, 268813277] 237155667849425298464119518554405 [5, 13, 24697, 53471161, 412835053, 6692367337] 248755105502415896815356977122585 [5, 613, 4073, 1974353, 53471161, 188748146801] 256905688699623624736201559585945 [5, 13, 1601, 1954369, 6692367337, 188748146801] 259405380723314840432966346371765 [5, 17, 5333, 453029, 6692367337, 188748146801] 259532625211087569629273570023465 [5, 13, 1601, 1974353, 6692367337, 188748146801] 269337851729761344058709036581645 [5, 613, 71809, 1974353, 3283829, 188748146801] 275454039565442484487154514641885 [5, 613, 123397, 1954369, 1974353, 188748146801] 318839000601908532004094362998145 [5, 3061, 123397, 453029, 1974353, 188748146801] 325708563133902277858163211145285 [5, 613, 5333, 1974353, 53471161, 188748146801] 346786834634528071160259997135685 [5, 29, 1954369, 1974353, 3283829, 188748146801] 374205011883274006517079615699253 [53, 97, 12197, 16229, 4794006457, 76704103313] 381993445225636496708405541170785 [5, 661, 3061, 453029, 441583073, 188748146801] 411742686102578599555863170282905 [5, 1301, 3209, 1954369, 53471161, 188748146801] 442515061233890021915060237928305 [5, 29, 5333, 453029, 6692367337, 188748146801] 462831718724635638608148268142785 [5, 613, 123397, 1974353, 3283829, 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