The fundamental solutions to Pell's equation (also known as "minimal solutions") presented below were computed in 2012 using a Python program that implements the chakravala method (attributed to Bhaskara II). $N$ is skipped if it is not square-free (i.e., if it is a perfect square or a multiple of a square).
| $N$ | $x$ | $y$ | Fundamental Solution |
|---|---|---|---|
| $4001$ | $3974605393506435201$ | $62836175188298480$ | $3974605393506435201^{2} \, - \, $$4001$$ \, \cdot \, 62836175188298480^{2} = 1$ |
| $4002$ | $5567$ | $88$ | $5567^{2} \, - \, $$4002$$ \, \cdot \, 88^{2} = 1$ |
| $4003$ | $10675090753927503722008879537371122$ | $168724745136660516665415874096719$ | $10675090753927503722008879537371122^{2} \, - \, $$4003$$ \, \cdot \, 168724745136660516665415874096719^{2} = 1$ |
| $4006$ | $3627681448972124688885752841837120064353235414365037445$ | $57315709347413016502127480790113183410147231351775502$ | $3627681448972124688885752841837120064353235414365037445^{2} \, - \, $$4006$$ \, \cdot \, 57315709347413016502127480790113183410147231351775502^{2} = 1$ |
| $4007$ | $7829026470560460024$ | $123679605193772915$ | $7829026470560460024^{2} \, - \, $$4007$$ \, \cdot \, 123679605193772915^{2} = 1$ |
| $4009$ | $3799$ | $60$ | $3799^{2} \, - \, $$4009$$ \, \cdot \, 60^{2} = 1$ |
| $4010$ | $7219$ | $114$ | $7219^{2} \, - \, $$4010$$ \, \cdot \, 114^{2} = 1$ |
| $4011$ | $190$ | $3$ | $190^{2} \, - \, $$4011$$ \, \cdot \, 3^{2} = 1$ |
| $4013$ | $680250298015640073$ | $10738266076189484$ | $680250298015640073^{2} \, - \, $$4013$$ \, \cdot \, 10738266076189484^{2} = 1$ |
| $4015$ | $742212453896$ | $11713467111$ | $742212453896^{2} \, - \, $$4015$$ \, \cdot \, 11713467111^{2} = 1$ |
| $4017$ | $13183$ | $208$ | $13183^{2} \, - \, $$4017$$ \, \cdot \, 208^{2} = 1$ |
| $4019$ | $1708604365567350951677221730$ | $26951473159328913297971289$ | $1708604365567350951677221730^{2} \, - \, $$4019$$ \, \cdot \, 26951473159328913297971289^{2} = 1$ |
| $4021$ | $137067718222878504169143817801$ | $2161564237986730163450249940$ | $137067718222878504169143817801^{2} \, - \, $$4021$$ \, \cdot \, 2161564237986730163450249940^{2} = 1$ |
| $4022$ | $899697265462117$ | $14186503428702$ | $899697265462117^{2} \, - \, $$4022$$ \, \cdot \, 14186503428702^{2} = 1$ |
| $4026$ | $84149464255$ | $1326216632$ | $84149464255^{2} \, - \, $$4026$$ \, \cdot \, 1326216632^{2} = 1$ |
| $4027$ | $489926383300155323805655713528988632537844064331002$ | $7720403744882820167494955973824537167233515551083$ | $489926383300155323805655713528988632537844064331002^{2} \, - \, $$4027$$ \, \cdot \, 7720403744882820167494955973824537167233515551083^{2} = 1$ |
| $4029$ | $40692425$ | $641084$ | $40692425^{2} \, - \, $$4029$$ \, \cdot \, 641084^{2} = 1$ |
| $4030$ | $9579769109$ | $150904614$ | $9579769109^{2} \, - \, $$4030$$ \, \cdot \, 150904614^{2} = 1$ |
| $4031$ | $78541711170201$ | $1237069102220$ | $78541711170201^{2} \, - \, $$4031$$ \, \cdot \, 1237069102220^{2} = 1$ |
| $4033$ | $1183313728990084222121478786725505178753$ | $18633129069962114596023657959628656976$ | $1183313728990084222121478786725505178753^{2} \, - \, $$4033$$ \, \cdot \, 18633129069962114596023657959628656976^{2} = 1$ |
| $4034$ | $18656897487784515$ | $293745673232494$ | $18656897487784515^{2} \, - \, $$4034$$ \, \cdot \, 293745673232494^{2} = 1$ |
| $4035$ | $711506$ | $11201$ | $711506^{2} \, - \, $$4035$$ \, \cdot \, 11201^{2} = 1$ |
| $4037$ | $2235709805703145399$ | $35187309169758540$ | $2235709805703145399^{2} \, - \, $$4037$$ \, \cdot \, 35187309169758540^{2} = 1$ |
| $4038$ | $325733$ | $5126$ | $325733^{2} \, - \, $$4038$$ \, \cdot \, 5126^{2} = 1$ |
| $4039$ | $22288270864881375590235560$ | $350702975339090911793571$ | $22288270864881375590235560^{2} \, - \, $$4039$$ \, \cdot \, 350702975339090911793571^{2} = 1$ |
| $4042$ | $61255554861860333$ | $963490248543642$ | $61255554861860333^{2} \, - \, $$4042$$ \, \cdot \, 963490248543642^{2} = 1$ |
| $4043$ | $221686399$ | $3486480$ | $221686399^{2} \, - \, $$4043$$ \, \cdot \, 3486480^{2} = 1$ |
| $4045$ | $202249$ | $3180$ | $202249^{2} \, - \, $$4045$$ \, \cdot \, 3180^{2} = 1$ |
| $4047$ | $1781249$ | $28000$ | $1781249^{2} \, - \, $$4047$$ \, \cdot \, 28000^{2} = 1$ |
| $4049$ | $2961136453587513397317964548610024257266844801$ | $46535515843436489689330555084695444735046480$ | $2961136453587513397317964548610024257266844801^{2} \, - \, $$4049$$ \, \cdot \, 46535515843436489689330555084695444735046480^{2} = 1$ |
| $4051$ | $5383417627373949351123839808517440621285033901490$ | $84581805341317262274629872520787545399261115657$ | $5383417627373949351123839808517440621285033901490^{2} \, - \, $$4051$$ \, \cdot \, 84581805341317262274629872520787545399261115657^{2} = 1$ |
| $4053$ | $3483649$ | $54720$ | $3483649^{2} \, - \, $$4053$$ \, \cdot \, 54720^{2} = 1$ |
| $4054$ | $13971438861629094598893146979059394329145661881201019971365$ | $219431646813187437183447298305437210029482532725398231934$ | $13971438861629094598893146979059394329145661881201019971365^{2} \, - \, $$4054$$ \, \cdot \, 219431646813187437183447298305437210029482532725398231934^{2} = 1$ |
| $4055$ | $1298859976089$ | $20397028612$ | $1298859976089^{2} \, - \, $$4055$$ \, \cdot \, 20397028612^{2} = 1$ |
| $4057$ | $382725902503889297913541379676115186731788253687652856246148935722378237549603873$ | $6008766835857783307255897900772197522343201654498602681868116689271634627022552$ | $382725902503889297913541379676115186731788253687652856246148935722378237549603873^{2} \, - \, $$4057$$ \, \cdot \, 6008766835857783307255897900772197522343201654498602681868116689271634627022552^{2} = 1$ |
| $4058$ | $576078752499$ | $9043277050$ | $576078752499^{2} \, - \, $$4058$$ \, \cdot \, 9043277050^{2} = 1$ |
| $4061$ | $18577348099802281296876218751$ | $291519240741564348477958000$ | $18577348099802281296876218751^{2} \, - \, $$4061$$ \, \cdot \, 291519240741564348477958000^{2} = 1$ |
| $4062$ | $1951781642507$ | $30623954398$ | $1951781642507^{2} \, - \, $$4062$$ \, \cdot \, 30623954398^{2} = 1$ |
| $4063$ | $7649$ | $120$ | $7649^{2} \, - \, $$4063$$ \, \cdot \, 120^{2} = 1$ |
| $4065$ | $8671$ | $136$ | $8671^{2} \, - \, $$4065$$ \, \cdot \, 136^{2} = 1$ |
| $4066$ | $343977292342747234626065$ | $5394436514982636408492$ | $343977292342747234626065^{2} \, - \, $$4066$$ \, \cdot \, 5394436514982636408492^{2} = 1$ |
| $4069$ | $363483145$ | $5698236$ | $363483145^{2} \, - \, $$4069$$ \, \cdot \, 5698236^{2} = 1$ |
| $4070$ | $18501$ | $290$ | $18501^{2} \, - \, $$4070$$ \, \cdot \, 290^{2} = 1$ |
| $4071$ | $96879480545$ | $1518382712$ | $96879480545^{2} \, - \, $$4071$$ \, \cdot \, 1518382712^{2} = 1$ |
| $4073$ | $9543400575293275373815894331087003649$ | $149536065050952394599162121793192320$ | $9543400575293275373815894331087003649^{2} \, - \, $$4073$$ \, \cdot \, 149536065050952394599162121793192320^{2} = 1$ |
| $4074$ | $154226701$ | $2416290$ | $154226701^{2} \, - \, $$4074$$ \, \cdot \, 2416290^{2} = 1$ |
| $4078$ | $70221293770832713806532587704441992463$ | $1099626547115668509621755638589441916$ | $70221293770832713806532587704441992463^{2} \, - \, $$4078$$ \, \cdot \, 1099626547115668509621755638589441916^{2} = 1$ |
| $4079$ | $189716843606453532684519911280$ | $2970496451095500078889982759$ | $189716843606453532684519911280^{2} \, - \, $$4079$$ \, \cdot \, 2970496451095500078889982759^{2} = 1$ |
| $4081$ | $604530652265$ | $9463134852$ | $604530652265^{2} \, - \, $$4081$$ \, \cdot \, 9463134852^{2} = 1$ |
| $4082$ | $4268206348899$ | $66804990610$ | $4268206348899^{2} \, - \, $$4082$$ \, \cdot \, 66804990610^{2} = 1$ |
| $4083$ | $40819384890026$ | $638817442935$ | $40819384890026^{2} \, - \, $$4083$$ \, \cdot \, 638817442935^{2} = 1$ |
| $4085$ | $8801188553079$ | $137703600188$ | $8801188553079^{2} \, - \, $$4085$$ \, \cdot \, 137703600188^{2} = 1$ |
| $4087$ | $4601182724$ | $71972595$ | $4601182724^{2} \, - \, $$4087$$ \, \cdot \, 71972595^{2} = 1$ |
| $4089$ | $1285759776147201449$ | $20107185282015420$ | $1285759776147201449^{2} \, - \, $$4089$$ \, \cdot \, 20107185282015420^{2} = 1$ |
| $4090$ | $1251270322579$ | $19565434194$ | $1251270322579^{2} \, - \, $$4090$$ \, \cdot \, 19565434194^{2} = 1$ |
| $4091$ | $37831919632484839132490$ | $591484868211020767467$ | $37831919632484839132490^{2} \, - \, $$4091$$ \, \cdot \, 591484868211020767467^{2} = 1$ |
| $4093$ | $648608100085340746633$ | $10138214969111225196$ | $648608100085340746633^{2} \, - \, $$4093$$ \, \cdot \, 10138214969111225196^{2} = 1$ |
| $4094$ | $4095$ | $64$ | $4095^{2} \, - \, $$4094$$ \, \cdot \, 64^{2} = 1$ |
| $4097$ | $8193$ | $128$ | $8193^{2} \, - \, $$4097$$ \, \cdot \, 128^{2} = 1$ |
| $4098$ | $4097$ | $64$ | $4097^{2} \, - \, $$4098$$ \, \cdot \, 64^{2} = 1$ |
| $4099$ | $6290679704195680536253612607008970662569749959960678667690$ | $98255894580947570793022586715791022877883393268276434001$ | $6290679704195680536253612607008970662569749959960678667690^{2} \, - \, $$4099$$ \, \cdot \, 98255894580947570793022586715791022877883393268276434001^{2} = 1$ |
| $4101$ | $15038410460012428677053740572796415$ | $234831877148720411637761404955232$ | $15038410460012428677053740572796415^{2} \, - \, $$4101$$ \, \cdot \, 234831877148720411637761404955232^{2} = 1$ |
| $4102$ | $10141222990572827$ | $158340679489542$ | $10141222990572827^{2} \, - \, $$4102$$ \, \cdot \, 158340679489542^{2} = 1$ |
| $4103$ | $36076932$ | $563221$ | $36076932^{2} \, - \, $$4103$$ \, \cdot \, 563221^{2} = 1$ |
| $4105$ | $3830995270998176489$ | $59793645893686188$ | $3830995270998176489^{2} \, - \, $$4105$$ \, \cdot \, 59793645893686188^{2} = 1$ |
| $4106$ | $149378127699$ | $2331189290$ | $149378127699^{2} \, - \, $$4106$$ \, \cdot \, 2331189290^{2} = 1$ |
| $4109$ | $46013140309107764048945975$ | $717817105677092067911844$ | $46013140309107764048945975^{2} \, - \, $$4109$$ \, \cdot \, 717817105677092067911844^{2} = 1$ |
| $4110$ | $244530751$ | $3814280$ | $244530751^{2} \, - \, $$4110$$ \, \cdot \, 3814280^{2} = 1$ |
| $4111$ | $22600970918684145317406830884887526438186669303416178086560$ | $352495322229152178879614940884523956622557436044222529897$ | $22600970918684145317406830884887526438186669303416178086560^{2} \, - \, $$4111$$ \, \cdot \, 352495322229152178879614940884523956622557436044222529897^{2} = 1$ |
| $4115$ | $82702446$ | $1289239$ | $82702446^{2} \, - \, $$4115$$ \, \cdot \, 1289239^{2} = 1$ |
| $4117$ | $1837945102852582416613765930145532519988909151$ | $28644556460037454057952889000429618179182680$ | $1837945102852582416613765930145532519988909151^{2} \, - \, $$4117$$ \, \cdot \, 28644556460037454057952889000429618179182680^{2} = 1$ |
| $4118$ | $1893364361423$ | $29504688036$ | $1893364361423^{2} \, - \, $$4118$$ \, \cdot \, 29504688036^{2} = 1$ |
| $4119$ | $338590853596324$ | $5275690702755$ | $338590853596324^{2} \, - \, $$4119$$ \, \cdot \, 5275690702755^{2} = 1$ |
| $4121$ | $4850227375566665244801$ | $75554579224619752240$ | $4850227375566665244801^{2} \, - \, $$4121$$ \, \cdot \, 75554579224619752240^{2} = 1$ |
| $4123$ | $34490562553$ | $537147564$ | $34490562553^{2} \, - \, $$4123$$ \, \cdot \, 537147564^{2} = 1$ |
| $4126$ | $21463508140861728553057577651533912660709375$ | $334145868438155779219711421198468455829568$ | $21463508140861728553057577651533912660709375^{2} \, - \, $$4126$$ \, \cdot \, 334145868438155779219711421198468455829568^{2} = 1$ |
| $4127$ | $2826522857010387648$ | $43998236250093167$ | $2826522857010387648^{2} \, - \, $$4127$$ \, \cdot \, 43998236250093167^{2} = 1$ |
| $4129$ | $4764726576922744102984571359612477560223126002281056165101651310774602699688985807569801249$ | $74150749020124963306733757010403185701758477080059295307067580181294296734592311006361800$ | $4764726576922744102984571359612477560223126002281056165101651310774602699688985807569801249^{2} \, - \, $$4129$$ \, \cdot \, 74150749020124963306733757010403185701758477080059295307067580181294296734592311006361800^{2} = 1$ |
| $4130$ | $4064509$ | $63246$ | $4064509^{2} \, - \, $$4130$$ \, \cdot \, 63246^{2} = 1$ |
| $4133$ | $62648088393$ | $974484916$ | $62648088393^{2} \, - \, $$4133$$ \, \cdot \, 974484916^{2} = 1$ |
| $4134$ | $69973806395$ | $1088304094$ | $69973806395^{2} \, - \, $$4134$$ \, \cdot \, 1088304094^{2} = 1$ |
| $4135$ | $1874230971572396404$ | $29146429030397403$ | $1874230971572396404^{2} \, - \, $$4135$$ \, \cdot \, 29146429030397403^{2} = 1$ |
| $4137$ | $4496973089503$ | $69916153672$ | $4496973089503^{2} \, - \, $$4137$$ \, \cdot \, 69916153672^{2} = 1$ |
| $4138$ | $729046233628522149364384772900657683$ | $11333389835944837583763268868111274$ | $729046233628522149364384772900657683^{2} \, - \, $$4138$$ \, \cdot \, 11333389835944837583763268868111274^{2} = 1$ |
| $4139$ | $37250$ | $579$ | $37250^{2} \, - \, $$4139$$ \, \cdot \, 579^{2} = 1$ |
| $4141$ | $162267250027170273968445205418073637423098775985631608583049$ | $2521611990381602965333531298891794957337725204918051507020$ | $162267250027170273968445205418073637423098775985631608583049^{2} \, - \, $$4141$$ \, \cdot \, 2521611990381602965333531298891794957337725204918051507020^{2} = 1$ |
| $4142$ | $6524523$ | $101378$ | $6524523^{2} \, - \, $$4142$$ \, \cdot \, 101378^{2} = 1$ |
| $4143$ | $2114208499417$ | $32846594404$ | $2114208499417^{2} \, - \, $$4143$$ \, \cdot \, 32846594404^{2} = 1$ |
| $4145$ | $249494661161$ | $3875243436$ | $249494661161^{2} \, - \, $$4145$$ \, \cdot \, 3875243436^{2} = 1$ |
| $4146$ | $12778583277142710981185$ | $198457747912327754312$ | $12778583277142710981185^{2} \, - \, $$4146$$ \, \cdot \, 198457747912327754312^{2} = 1$ |
| $4147$ | $94627378$ | $1469433$ | $94627378^{2} \, - \, $$4147$$ \, \cdot \, 1469433^{2} = 1$ |
| $4151$ | $203400$ | $3157$ | $203400^{2} \, - \, $$4151$$ \, \cdot \, 3157^{2} = 1$ |
| $4153$ | $1916599612779560209557902914405290722142964324484199267444482089253674273$ | $29740648250653061240852425711771486063436763063214863104698661480624376$ | $1916599612779560209557902914405290722142964324484199267444482089253674273^{2} \, - \, $$4153$$ \, \cdot \, 29740648250653061240852425711771486063436763063214863104698661480624376^{2} = 1$ |
| $4154$ | $41181951$ | $638960$ | $41181951^{2} \, - \, $$4154$$ \, \cdot \, 638960^{2} = 1$ |
| $4155$ | $379214$ | $5883$ | $379214^{2} \, - \, $$4155$$ \, \cdot \, 5883^{2} = 1$ |
| $4157$ | $103123625891102804292906249$ | $1599440771355677463648500$ | $103123625891102804292906249^{2} \, - \, $$4157$$ \, \cdot \, 1599440771355677463648500^{2} = 1$ |
| $4159$ | $5414767271524082813120$ | $83962494925794507231$ | $5414767271524082813120^{2} \, - \, $$4159$$ \, \cdot \, 83962494925794507231^{2} = 1$ |
| $4161$ | $11095$ | $172$ | $11095^{2} \, - \, $$4161$$ \, \cdot \, 172^{2} = 1$ |
| $4162$ | $75602028173705811683$ | $1171878019769582982$ | $75602028173705811683^{2} \, - \, $$4162$$ \, \cdot \, 1171878019769582982^{2} = 1$ |
| $4163$ | $24208609726$ | $375203295$ | $24208609726^{2} \, - \, $$4163$$ \, \cdot \, 375203295^{2} = 1$ |
| $4166$ | $59418908613165155383083738565$ | $920587423974469760615286642$ | $59418908613165155383083738565^{2} \, - \, $$4166$$ \, \cdot \, 920587423974469760615286642^{2} = 1$ |
| $4169$ | $17604635555034997944764892094999$ | $272653508985316114448065655700$ | $17604635555034997944764892094999^{2} \, - \, $$4169$$ \, \cdot \, 272653508985316114448065655700^{2} = 1$ |
| $4170$ | $26856191$ | $415888$ | $26856191^{2} \, - \, $$4170$$ \, \cdot \, 415888^{2} = 1$ |
| $4171$ | $775$ | $12$ | $775^{2} \, - \, $$4171$$ \, \cdot \, 12^{2} = 1$ |
| $4173$ | $16848649$ | $260820$ | $16848649^{2} \, - \, $$4173$$ \, \cdot \, 260820^{2} = 1$ |
| $4174$ | $1424156508991205142208681039557490896776199898778313581829510488975$ | $22043547972406602245188180037336225229518423057650028204781695724$ | $1424156508991205142208681039557490896776199898778313581829510488975^{2} \, - \, $$4174$$ \, \cdot \, 22043547972406602245188180037336225229518423057650028204781695724^{2} = 1$ |
| $4177$ | $44292547942518779144450202494224889059611070169104663096428673$ | $685327921774660535374479530024713742949913230202310151329808$ | $44292547942518779144450202494224889059611070169104663096428673^{2} \, - \, $$4177$$ \, \cdot \, 685327921774660535374479530024713742949913230202310151329808^{2} = 1$ |
| $4178$ | $263218177$ | $4072224$ | $263218177^{2} \, - \, $$4178$$ \, \cdot \, 4072224^{2} = 1$ |
| $4179$ | $2677345$ | $41416$ | $2677345^{2} \, - \, $$4179$$ \, \cdot \, 41416^{2} = 1$ |
| $4181$ | $478597038039566696511234146917608201$ | $7401673482859530298834759919462620$ | $478597038039566696511234146917608201^{2} \, - \, $$4181$$ \, \cdot \, 7401673482859530298834759919462620^{2} = 1$ |
| $4182$ | $37637$ | $582$ | $37637^{2} \, - \, $$4182$$ \, \cdot \, 582^{2} = 1$ |
| $4183$ | $317558171528$ | $4909975899$ | $317558171528^{2} \, - \, $$4183$$ \, \cdot \, 4909975899^{2} = 1$ |
| $4186$ | $18855674947565$ | $291435512322$ | $18855674947565^{2} \, - \, $$4186$$ \, \cdot \, 291435512322^{2} = 1$ |
| $4187$ | $143493953718$ | $2217594427$ | $143493953718^{2} \, - \, $$4187$$ \, \cdot \, 2217594427^{2} = 1$ |
| $4189$ | $2348310155551200245641645845518123357620381521252013751$ | $36282756659471626090344570914713715637788216718375900$ | $2348310155551200245641645845518123357620381521252013751^{2} \, - \, $$4189$$ \, \cdot \, 36282756659471626090344570914713715637788216718375900^{2} = 1$ |
| $4190$ | $25491871648821$ | $393817228654$ | $25491871648821^{2} \, - \, $$4190$$ \, \cdot \, 393817228654^{2} = 1$ |
| $4191$ | $29371924$ | $453705$ | $29371924^{2} \, - \, $$4191$$ \, \cdot \, 453705^{2} = 1$ |
| $4193$ | $19167$ | $296$ | $19167^{2} \, - \, $$4193$$ \, \cdot \, 296^{2} = 1$ |
| $4195$ | $45772086899846122191836963999$ | $706699414022674604276153640$ | $45772086899846122191836963999^{2} \, - \, $$4195$$ \, \cdot \, 706699414022674604276153640^{2} = 1$ |
| $4197$ | $2229399257939085408333751$ | $34412669824993224540300$ | $2229399257939085408333751^{2} \, - \, $$4197$$ \, \cdot \, 34412669824993224540300^{2} = 1$ |
| $4198$ | $113978639776334919899595657028901$ | $1759147488675595201885659246810$ | $113978639776334919899595657028901^{2} \, - \, $$4198$$ \, \cdot \, 1759147488675595201885659246810^{2} = 1$ |
| $4199$ | $324$ | $5$ | $324^{2} \, - \, $$4199$$ \, \cdot \, 5^{2} = 1$ |
| $4201$ | $15342165195784487937181167063910620379274871789035457823176568529478448214293546222453921580416801$ | $236706570861604845270759494315006025078312806937322254908546450590640947579972569674113045597560$ | $15342165195784487937181167063910620379274871789035457823176568529478448214293546222453921580416801^{2} \, - \, $$4201$$ \, \cdot \, 236706570861604845270759494315006025078312806937322254908546450590640947579972569674113045597560^{2} = 1$ |
| $4202$ | $8607991437$ | $132792578$ | $8607991437^{2} \, - \, $$4202$$ \, \cdot \, 132792578^{2} = 1$ |
| $4206$ | $1826014690238699$ | $28155914188610$ | $1826014690238699^{2} \, - \, $$4206$$ \, \cdot \, 28155914188610^{2} = 1$ |
| $4207$ | $383447171307218768$ | $5911793862730983$ | $383447171307218768^{2} \, - \, $$4207$$ \, \cdot \, 5911793862730983^{2} = 1$ |
| $4209$ | $1222672005355632215$ | $18846057234622156$ | $1222672005355632215^{2} \, - \, $$4209$$ \, \cdot \, 18846057234622156^{2} = 1$ |
| $4210$ | $48062281124634499$ | $740735794382310$ | $48062281124634499^{2} \, - \, $$4210$$ \, \cdot \, 740735794382310^{2} = 1$ |
| $4211$ | $174844298319090500142303314489781850$ | $2694380047628390959995251257521897$ | $174844298319090500142303314489781850^{2} \, - \, $$4211$$ \, \cdot \, 2694380047628390959995251257521897^{2} = 1$ |
| $4213$ | $19071901038149286317976796874999$ | $293831434246702011246505462500$ | $19071901038149286317976796874999^{2} \, - \, $$4213$$ \, \cdot \, 293831434246702011246505462500^{2} = 1$ |
| $4215$ | $844$ | $13$ | $844^{2} \, - \, $$4215$$ \, \cdot \, 13^{2} = 1$ |
| $4217$ | $1234201021430800915937244912165153$ | $19005710119463758154382245165432$ | $1234201021430800915937244912165153^{2} \, - \, $$4217$$ \, \cdot \, 19005710119463758154382245165432^{2} = 1$ |
| $4218$ | $231421901$ | $3563290$ | $231421901^{2} \, - \, $$4218$$ \, \cdot \, 3563290^{2} = 1$ |
| $4219$ | $97368731966766164199033274737192581210$ | $1499045280812594827427418555254641461$ | $97368731966766164199033274737192581210^{2} \, - \, $$4219$$ \, \cdot \, 1499045280812594827427418555254641461^{2} = 1$ |
| $4222$ | $559884677381394885476016891268814708946565953599$ | $8616670137323363145176951081959937441003890680$ | $559884677381394885476016891268814708946565953599^{2} \, - \, $$4222$$ \, \cdot \, 8616670137323363145176951081959937441003890680^{2} = 1$ |
| $4223$ | $4224$ | $65$ | $4224^{2} \, - \, $$4223$$ \, \cdot \, 65^{2} = 1$ |
| $4226$ | $8451$ | $130$ | $8451^{2} \, - \, $$4226$$ \, \cdot \, 130^{2} = 1$ |
| $4227$ | $4226$ | $65$ | $4226^{2} \, - \, $$4227$$ \, \cdot \, 65^{2} = 1$ |
| $4229$ | $37763016201$ | $580694660$ | $37763016201^{2} \, - \, $$4229$$ \, \cdot \, 580694660^{2} = 1$ |
| $4231$ | $1448005395154038127926578071623745469720$ | $22261204914463309108155324946001318973$ | $1448005395154038127926578071623745469720^{2} \, - \, $$4231$$ \, \cdot \, 22261204914463309108155324946001318973^{2} = 1$ |
| $4233$ | $39016567127$ | $599687396$ | $39016567127^{2} \, - \, $$4233$$ \, \cdot \, 599687396^{2} = 1$ |
| $4234$ | $404699980122443661698351251$ | $6219532709989911929797350$ | $404699980122443661698351251^{2} \, - \, $$4234$$ \, \cdot \, 6219532709989911929797350^{2} = 1$ |
| $4237$ | $67008760418986958696434461874237094445151$ | $1029443111985341797799944606703773530120$ | $67008760418986958696434461874237094445151^{2} \, - \, $$4237$$ \, \cdot \, 1029443111985341797799944606703773530120^{2} = 1$ |
| $4238$ | $651$ | $10$ | $651^{2} \, - \, $$4238$$ \, \cdot \, 10^{2} = 1$ |
| $4241$ | $1874971609173091637204298392650019925688492420310049$ | $28791252598216053366957368719542322507429225929080$ | $1874971609173091637204298392650019925688492420310049^{2} \, - \, $$4241$$ \, \cdot \, 28791252598216053366957368719542322507429225929080^{2} = 1$ |
| $4242$ | $320573$ | $4922$ | $320573^{2} \, - \, $$4242$$ \, \cdot \, 4922^{2} = 1$ |
| $4243$ | $71495387886939108299769509927142362$ | $1097593460464898075426812651808199$ | $71495387886939108299769509927142362^{2} \, - \, $$4243$$ \, \cdot \, 1097593460464898075426812651808199^{2} = 1$ |
| $4245$ | $303821441$ | $4663152$ | $303821441^{2} \, - \, $$4245$$ \, \cdot \, 4663152^{2} = 1$ |
| $4246$ | $1036159035641953894068021395045$ | $15901438855896510581442030162$ | $1036159035641953894068021395045^{2} \, - \, $$4246$$ \, \cdot \, 15901438855896510581442030162^{2} = 1$ |
| $4247$ | $21409128$ | $328517$ | $21409128^{2} \, - \, $$4247$$ \, \cdot \, 328517^{2} = 1$ |
| $4249$ | $1406721390390084009875311660957976221637955862015$ | $21580660160397807236549009676230375609895828576$ | $1406721390390084009875311660957976221637955862015^{2} \, - \, $$4249$$ \, \cdot \, 21580660160397807236549009676230375609895828576^{2} = 1$ |
| $4251$ | $326$ | $5$ | $326^{2} \, - \, $$4251$$ \, \cdot \, 5^{2} = 1$ |
| $4253$ | $16112124032124491488315563849$ | $247061517771859154991751460$ | $16112124032124491488315563849^{2} \, - \, $$4253$$ \, \cdot \, 247061517771859154991751460^{2} = 1$ |
| $4254$ | $1879917009784506005$ | $28823049970624234$ | $1879917009784506005^{2} \, - \, $$4254$$ \, \cdot \, 28823049970624234^{2} = 1$ |
| $4255$ | $24444979624$ | $374748495$ | $24444979624^{2} \, - \, $$4255$$ \, \cdot \, 374748495^{2} = 1$ |
| $4258$ | $133197261443$ | $2041232466$ | $133197261443^{2} \, - \, $$4258$$ \, \cdot \, 2041232466^{2} = 1$ |
| $4259$ | $200236646655773016130$ | $3068242939661179281$ | $200236646655773016130^{2} \, - \, $$4259$$ \, \cdot \, 3068242939661179281^{2} = 1$ |
| $4261$ | $487773692171836773724609849913554117111338210033172214202613754243355294551180678058174336686937984132269449$ | $7472442916404366718042414428150210943686325241177441866467283025312332082757122658434098509179768961076260$ | $487773692171836773724609849913554117111338210033172214202613754243355294551180678058174336686937984132269449^{2} \, - \, $$4261$$ \, \cdot \, 7472442916404366718042414428150210943686325241177441866467283025312332082757122658434098509179768961076260^{2} = 1$ |
| $4262$ | $911908936708901$ | $13968338442630$ | $911908936708901^{2} \, - \, $$4262$$ \, \cdot \, 13968338442630^{2} = 1$ |
| $4265$ | $63457357881876356772528129$ | $971678219662798523892224$ | $63457357881876356772528129^{2} \, - \, $$4265$$ \, \cdot \, 971678219662798523892224^{2} = 1$ |
| $4267$ | $424981762433$ | $6505923792$ | $424981762433^{2} \, - \, $$4267$$ \, \cdot \, 6505923792^{2} = 1$ |
| $4269$ | $69744788185238404612918031666935$ | $1067452803720808529835559078764$ | $69744788185238404612918031666935^{2} \, - \, $$4269$$ \, \cdot \, 1067452803720808529835559078764^{2} = 1$ |
| $4270$ | $5489$ | $84$ | $5489^{2} \, - \, $$4270$$ \, \cdot \, 84^{2} = 1$ |
| $4271$ | $1234320$ | $18887$ | $1234320^{2} \, - \, $$4271$$ \, \cdot \, 18887^{2} = 1$ |
| $4273$ | $21141751909673188224599970798390097292353994900204917977410792113131649$ | $323425699296097444314333318890638436656435063061715291977916766062480$ | $21141751909673188224599970798390097292353994900204917977410792113131649^{2} \, - \, $$4273$$ \, \cdot \, 323425699296097444314333318890638436656435063061715291977916766062480^{2} = 1$ |
| $4274$ | $4237501963299$ | $64817556290$ | $4237501963299^{2} \, - \, $$4274$$ \, \cdot \, 64817556290^{2} = 1$ |
| $4277$ | $17482401$ | $267320$ | $17482401^{2} \, - \, $$4277$$ \, \cdot \, 267320^{2} = 1$ |
| $4278$ | $380927$ | $5824$ | $380927^{2} \, - \, $$4278$$ \, \cdot \, 5824^{2} = 1$ |
| $4279$ | $4492490201$ | $68677740$ | $4492490201^{2} \, - \, $$4279$$ \, \cdot \, 68677740^{2} = 1$ |
| $4281$ | $3242990727575$ | $49564769748$ | $3242990727575^{2} \, - \, $$4281$$ \, \cdot \, 49564769748^{2} = 1$ |
| $4282$ | $430276920222724993868470303118671054963$ | $6575438496687221861825403599073752982$ | $430276920222724993868470303118671054963^{2} \, - \, $$4282$$ \, \cdot \, 6575438496687221861825403599073752982^{2} = 1$ |
| $4283$ | $346922$ | $5301$ | $346922^{2} \, - \, $$4283$$ \, \cdot \, 5301^{2} = 1$ |
| $4285$ | $3299010111034016070952535152336459733832929929$ | $50397411800115770613417751386967405602520788$ | $3299010111034016070952535152336459733832929929^{2} \, - \, $$4285$$ \, \cdot \, 50397411800115770613417751386967405602520788^{2} = 1$ |
| $4286$ | $580010189055$ | $8859506672$ | $580010189055^{2} \, - \, $$4286$$ \, \cdot \, 8859506672^{2} = 1$ |
| $4287$ | $1856659687$ | $28356692$ | $1856659687^{2} \, - \, $$4287$$ \, \cdot \, 28356692^{2} = 1$ |
| $4289$ | $9950817865270864101090870147172511903859201$ | $151943019982729350360724331953492473672160$ | $9950817865270864101090870147172511903859201^{2} \, - \, $$4289$$ \, \cdot \, 151943019982729350360724331953492473672160^{2} = 1$ |
| $4290$ | $131$ | $2$ | $131^{2} \, - \, $$4290$$ \, \cdot \, 2^{2} = 1$ |
| $4291$ | $4532168345760066973943482724665$ | $69187362629241754841897352108$ | $4532168345760066973943482724665^{2} \, - \, $$4291$$ \, \cdot \, 69187362629241754841897352108^{2} = 1$ |
| $4294$ | $378769445$ | $5780214$ | $378769445^{2} \, - \, $$4294$$ \, \cdot \, 5780214^{2} = 1$ |
| $4295$ | $910482345639$ | $13892805164$ | $910482345639^{2} \, - \, $$4295$$ \, \cdot \, 13892805164^{2} = 1$ |
| $4297$ | $8188634905849994516050520990507605191704599727481941785633$ | $124919095643684010495765085150574542783018505510792644248$ | $8188634905849994516050520990507605191704599727481941785633^{2} \, - \, $$4297$$ \, \cdot \, 124919095643684010495765085150574542783018505510792644248^{2} = 1$ |
| $4298$ | $10620973$ | $162006$ | $10620973^{2} \, - \, $$4298$$ \, \cdot \, 162006^{2} = 1$ |
| $4299$ | $5771445002054552513999330$ | $88023947094490260086451$ | $5771445002054552513999330^{2} \, - \, $$4299$$ \, \cdot \, 88023947094490260086451^{2} = 1$ |
| $4301$ | $952159246345$ | $14518604268$ | $952159246345^{2} \, - \, $$4301$$ \, \cdot \, 14518604268^{2} = 1$ |
| $4303$ | $68052293272123172$ | $1037425913523681$ | $68052293272123172^{2} \, - \, $$4303$$ \, \cdot \, 1037425913523681^{2} = 1$ |
| $4305$ | $5249$ | $80$ | $5249^{2} \, - \, $$4305$$ \, \cdot \, 80^{2} = 1$ |
| $4306$ | $32633156770317226683242696591299$ | $497304139861593259920104984730$ | $32633156770317226683242696591299^{2} \, - \, $$4306$$ \, \cdot \, 497304139861593259920104984730^{2} = 1$ |
| $4307$ | $80838082$ | $1231767$ | $80838082^{2} \, - \, $$4307$$ \, \cdot \, 1231767^{2} = 1$ |
| $4309$ | $31606044107117492065564284412616218425260286399382514551$ | $481484038757125747386247094446645420403225797916861820$ | $31606044107117492065564284412616218425260286399382514551^{2} \, - \, $$4309$$ \, \cdot \, 481484038757125747386247094446645420403225797916861820^{2} = 1$ |
| $4310$ | $447591232079$ | $6817779252$ | $447591232079^{2} \, - \, $$4310$$ \, \cdot \, 6817779252^{2} = 1$ |
| $4313$ | $788045621202748469015767$ | $11999458032208557223524$ | $788045621202748469015767^{2} \, - \, $$4313$$ \, \cdot \, 11999458032208557223524^{2} = 1$ |
| $4314$ | $4875549054850291162799$ | $74230683596273336860$ | $4875549054850291162799^{2} \, - \, $$4314$$ \, \cdot \, 74230683596273336860^{2} = 1$ |
| $4315$ | $43445954316823546006$ | $661392005585214267$ | $43445954316823546006^{2} \, - \, $$4315$$ \, \cdot \, 661392005585214267^{2} = 1$ |
| $4317$ | $12535327583$ | $190785192$ | $12535327583^{2} \, - \, $$4317$$ \, \cdot \, 190785192^{2} = 1$ |
| $4318$ | $1373633$ | $20904$ | $1373633^{2} \, - \, $$4318$$ \, \cdot \, 20904^{2} = 1$ |
| $4319$ | $34210800$ | $520561$ | $34210800^{2} \, - \, $$4319$$ \, \cdot \, 520561^{2} = 1$ |
| $4321$ | $67049$ | $1020$ | $67049^{2} \, - \, $$4321$$ \, \cdot \, 1020^{2} = 1$ |
| $4322$ | $4153443$ | $63178$ | $4153443^{2} \, - \, $$4322$$ \, \cdot \, 63178^{2} = 1$ |
| $4323$ | $263$ | $4$ | $263^{2} \, - \, $$4323$$ \, \cdot \, 4^{2} = 1$ |
| $4326$ | $120595938049$ | $1833535920$ | $120595938049^{2} \, - \, $$4326$$ \, \cdot \, 1833535920^{2} = 1$ |
| $4327$ | $4329187429727596204348807032540855344698587368$ | $65813189903447616115842796215628380940240557$ | $4329187429727596204348807032540855344698587368^{2} \, - \, $$4327$$ \, \cdot \, 65813189903447616115842796215628380940240557^{2} = 1$ |
| $4330$ | $145544140906477959553751539$ | $2211825082779834332870238$ | $145544140906477959553751539^{2} \, - \, $$4330$$ \, \cdot \, 2211825082779834332870238^{2} = 1$ |
| $4331$ | $153632710$ | $2334477$ | $153632710^{2} \, - \, $$4331$$ \, \cdot \, 2334477^{2} = 1$ |
| $4333$ | $5127697655922033287422869471583008668599$ | $77898315326493545841703327048726091460$ | $5127697655922033287422869471583008668599^{2} \, - \, $$4333$$ \, \cdot \, 77898315326493545841703327048726091460^{2} = 1$ |
| $4334$ | $395$ | $6$ | $395^{2} \, - \, $$4334$$ \, \cdot \, 6^{2} = 1$ |
| $4337$ | $883281795288501612087700423578663510187183714593$ | $13412340442886401936240539191065876960265516648$ | $883281795288501612087700423578663510187183714593^{2} \, - \, $$4337$$ \, \cdot \, 13412340442886401936240539191065876960265516648^{2} = 1$ |
| $4339$ | $21388845912565265365283599310924559907543316972291384810$ | $324707654594357645931797703393486772535229862296036471$ | $21388845912565265365283599310924559907543316972291384810^{2} \, - \, $$4339$$ \, \cdot \, 324707654594357645931797703393486772535229862296036471^{2} = 1$ |
| $4341$ | $4090148923962636091800219541695305354625655$ | $62078930779046078343207677115795412707708$ | $4090148923962636091800219541695305354625655^{2} \, - \, $$4341$$ \, \cdot \, 62078930779046078343207677115795412707708^{2} = 1$ |
| $4342$ | $2519369676651116251$ | $38233758116391150$ | $2519369676651116251^{2} \, - \, $$4342$$ \, \cdot \, 38233758116391150^{2} = 1$ |
| $4343$ | $8227444647$ | $124844684$ | $8227444647^{2} \, - \, $$4343$$ \, \cdot \, 124844684^{2} = 1$ |
| $4345$ | $791$ | $12$ | $791^{2} \, - \, $$4345$$ \, \cdot \, 12^{2} = 1$ |
| $4346$ | $177974132499$ | $2699678350$ | $177974132499^{2} \, - \, $$4346$$ \, \cdot \, 2699678350^{2} = 1$ |
| $4349$ | $49157847299639716933953985593480045276206297903561629298507595906249$ | $745415042102741523222963610458789141537478054318772358952341890500$ | $49157847299639716933953985593480045276206297903561629298507595906249^{2} \, - \, $$4349$$ \, \cdot \, 745415042102741523222963610458789141537478054318772358952341890500^{2} = 1$ |
| $4351$ | $66017606646248095047416982119449$ | $1000841336182292285864737304940$ | $66017606646248095047416982119449^{2} \, - \, $$4351$$ \, \cdot \, 1000841336182292285864737304940^{2} = 1$ |
| $4353$ | $2903$ | $44$ | $2903^{2} \, - \, $$4353$$ \, \cdot \, 44^{2} = 1$ |
| $4354$ | $4355$ | $66$ | $4355^{2} \, - \, $$4354$$ \, \cdot \, 66^{2} = 1$ |
| $4355$ | $66$ | $1$ | $66^{2} \, - \, $$4355$$ \, \cdot \, 1^{2} = 1$ |
| $4357$ | $8713$ | $132$ | $8713^{2} \, - \, $$4357$$ \, \cdot \, 132^{2} = 1$ |
| $4358$ | $4357$ | $66$ | $4357^{2} \, - \, $$4358$$ \, \cdot \, 66^{2} = 1$ |
| $4359$ | $2905$ | $44$ | $2905^{2} \, - \, $$4359$$ \, \cdot \, 44^{2} = 1$ |
| $4362$ | $1453$ | $22$ | $1453^{2} \, - \, $$4362$$ \, \cdot \, 22^{2} = 1$ |
| $4363$ | $2126115375029342505341004003181226$ | $32188016968778036561449612128195$ | $2126115375029342505341004003181226^{2} \, - \, $$4363$$ \, \cdot \, 32188016968778036561449612128195^{2} = 1$ |
| $4366$ | $1602472386855726955$ | $24252063069606642$ | $1602472386855726955^{2} \, - \, $$4366$$ \, \cdot \, 24252063069606642^{2} = 1$ |
| $4367$ | $793$ | $12$ | $793^{2} \, - \, $$4367$$ \, \cdot \, 12^{2} = 1$ |
| $4369$ | $21711903468106532919260705$ | $328478445735747503816136$ | $21711903468106532919260705^{2} \, - \, $$4369$$ \, \cdot \, 328478445735747503816136^{2} = 1$ |
| $4370$ | $4332189$ | $65534$ | $4332189^{2} \, - \, $$4370$$ \, \cdot \, 65534^{2} = 1$ |
| $4371$ | $17534253574$ | $265214265$ | $17534253574^{2} \, - \, $$4371$$ \, \cdot \, 265214265^{2} = 1$ |
| $4373$ | $9784223752097314022022555849$ | $147957381666621072356360140$ | $9784223752097314022022555849^{2} \, - \, $$4373$$ \, \cdot \, 147957381666621072356360140^{2} = 1$ |
| $4377$ | $44788413053491717783936464727$ | $676982436305117753992863292$ | $44788413053491717783936464727^{2} \, - \, $$4377$$ \, \cdot \, 676982436305117753992863292^{2} = 1$ |
| $4378$ | $397$ | $6$ | $397^{2} \, - \, $$4378$$ \, \cdot \, 6^{2} = 1$ |
| $4379$ | $239756504596375551$ | $3623121730598720$ | $239756504596375551^{2} \, - \, $$4379$$ \, \cdot \, 3623121730598720^{2} = 1$ |
| $4381$ | $5364766507967673500588545$ | $81052086309048552406752$ | $5364766507967673500588545^{2} \, - \, $$4381$$ \, \cdot \, 81052086309048552406752^{2} = 1$ |
| $4382$ | $59052888063$ | $892082368$ | $59052888063^{2} \, - \, $$4382$$ \, \cdot \, 892082368^{2} = 1$ |
| $4385$ | $21550687965457840929$ | $325444053025763048$ | $21550687965457840929^{2} \, - \, $$4385$$ \, \cdot \, 325444053025763048^{2} = 1$ |
| $4386$ | $4826358785$ | $72876128$ | $4826358785^{2} \, - \, $$4386$$ \, \cdot \, 72876128^{2} = 1$ |
| $4387$ | $18082$ | $273$ | $18082^{2} \, - \, $$4387$$ \, \cdot \, 273^{2} = 1$ |
| $4389$ | $265$ | $4$ | $265^{2} \, - \, $$4389$$ \, \cdot \, 4^{2} = 1$ |
| $4390$ | $358110177866616482648163891919$ | $5404859441184919627582287252$ | $358110177866616482648163891919^{2} \, - \, $$4390$$ \, \cdot \, 5404859441184919627582287252^{2} = 1$ |
| $4391$ | $14761361728850117453397896040$ | $222763844413848059028928333$ | $14761361728850117453397896040^{2} \, - \, $$4391$$ \, \cdot \, 222763844413848059028928333^{2} = 1$ |
| $4393$ | $6611923558458073509488382270733865375841503$ | $99757882564862612306762851683594726289416$ | $6611923558458073509488382270733865375841503^{2} \, - \, $$4393$$ \, \cdot \, 99757882564862612306762851683594726289416^{2} = 1$ |
| $4395$ | $43845986$ | $661379$ | $43845986^{2} \, - \, $$4395$$ \, \cdot \, 661379^{2} = 1$ |
| $4397$ | $3650694709357974448965319873067931849$ | $55055065495714292063478365625389980$ | $3650694709357974448965319873067931849^{2} \, - \, $$4397$$ \, \cdot \, 55055065495714292063478365625389980^{2} = 1$ |
| $4398$ | $254049651623093$ | $3830813340874$ | $254049651623093^{2} \, - \, $$4398$$ \, \cdot \, 3830813340874^{2} = 1$ |
| $4399$ | $31484386458134880046876$ | $474698930835526196625$ | $31484386458134880046876^{2} \, - \, $$4399$$ \, \cdot \, 474698930835526196625^{2} = 1$ |
| $4402$ | $7638463$ | $115128$ | $7638463^{2} \, - \, $$4402$$ \, \cdot \, 115128^{2} = 1$ |
| $4403$ | $248898$ | $3751$ | $248898^{2} \, - \, $$4403$$ \, \cdot \, 3751^{2} = 1$ |
| $4405$ | $1816831441153066131955082249$ | $27374215419280725976296540$ | $1816831441153066131955082249^{2} \, - \, $$4405$$ \, \cdot \, 27374215419280725976296540^{2} = 1$ |
| $4406$ | $1034674786992559935467845$ | $15587684965022624903898$ | $1034674786992559935467845^{2} \, - \, $$4406$$ \, \cdot \, 15587684965022624903898^{2} = 1$ |
| $4407$ | $10091353$ | $152012$ | $10091353^{2} \, - \, $$4407$$ \, \cdot \, 152012^{2} = 1$ |
| $4409$ | $220449$ | $3320$ | $220449^{2} \, - \, $$4409$$ \, \cdot \, 3320^{2} = 1$ |
| $4411$ | $22942393559396090$ | $345438068447403$ | $22942393559396090^{2} \, - \, $$4411$$ \, \cdot \, 345438068447403^{2} = 1$ |
| $4413$ | $187223392452151$ | $2818338455940$ | $187223392452151^{2} \, - \, $$4413$$ \, \cdot \, 2818338455940^{2} = 1$ |
| $4414$ | $41412963797857009903593604103647473778878170580810394415763455$ | $623333041253040855586397140112917131415841903435868382975296$ | $41412963797857009903593604103647473778878170580810394415763455^{2} \, - \, $$4414$$ \, \cdot \, 623333041253040855586397140112917131415841903435868382975296^{2} = 1$ |
| $4415$ | $511363844$ | $7695993$ | $511363844^{2} \, - \, $$4415$$ \, \cdot \, 7695993^{2} = 1$ |
| $4417$ | $827473900280606633688486831636112351$ | $12450609288008889777143222741738040$ | $827473900280606633688486831636112351^{2} \, - \, $$4417$$ \, \cdot \, 12450609288008889777143222741738040^{2} = 1$ |
| $4421$ | $953119768266827005449$ | $14334654165139716860$ | $953119768266827005449^{2} \, - \, $$4421$$ \, \cdot \, 14334654165139716860^{2} = 1$ |
| $4422$ | $133$ | $2$ | $133^{2} \, - \, $$4422$$ \, \cdot \, 2^{2} = 1$ |
| $4423$ | $2508906314776260617277955827128$ | $37724715645658986567702541539$ | $2508906314776260617277955827128^{2} \, - \, $$4423$$ \, \cdot \, 37724715645658986567702541539^{2} = 1$ |
| $4426$ | $2392274509299659869315731206278544645152774755752643246451$ | $35958809743336365917031745495328479100876180412609301230$ | $2392274509299659869315731206278544645152774755752643246451^{2} \, - \, $$4426$$ \, \cdot \, 35958809743336365917031745495328479100876180412609301230^{2} = 1$ |
| $4427$ | $1863$ | $28$ | $1863^{2} \, - \, $$4427$$ \, \cdot \, 28^{2} = 1$ |
| $4429$ | $9092598859373815$ | $136626578160684$ | $9092598859373815^{2} \, - \, $$4429$$ \, \cdot \, 136626578160684^{2} = 1$ |
| $4430$ | $774224011$ | $11632278$ | $774224011^{2} \, - \, $$4430$$ \, \cdot \, 11632278^{2} = 1$ |
| $4431$ | $479756185$ | $7207252$ | $479756185^{2} \, - \, $$4431$$ \, \cdot \, 7207252^{2} = 1$ |
| $4433$ | $220207543401$ | $3307374140$ | $220207543401^{2} \, - \, $$4433$$ \, \cdot \, 3307374140^{2} = 1$ |
| $4434$ | $1281425$ | $19244$ | $1281425^{2} \, - \, $$4434$$ \, \cdot \, 19244^{2} = 1$ |
| $4435$ | $2946694047104394730126$ | $44247448622910294345$ | $2946694047104394730126^{2} \, - \, $$4435$$ \, \cdot \, 44247448622910294345^{2} = 1$ |
| $4438$ | $704224752474143379151$ | $10571038069929815460$ | $704224752474143379151^{2} \, - \, $$4438$$ \, \cdot \, 10571038069929815460^{2} = 1$ |
| $4439$ | $4636824$ | $69595$ | $4636824^{2} \, - \, $$4439$$ \, \cdot \, 69595^{2} = 1$ |
| $4441$ | $80251076689920001$ | $1204232881036800$ | $80251076689920001^{2} \, - \, $$4441$$ \, \cdot \, 1204232881036800^{2} = 1$ |
| $4442$ | $16299138820117816794235443$ | $244554343996121175138538$ | $16299138820117816794235443^{2} \, - \, $$4442$$ \, \cdot \, 244554343996121175138538^{2} = 1$ |
| $4443$ | $1150382808482$ | $17258546869$ | $1150382808482^{2} \, - \, $$4443$$ \, \cdot \, 17258546869^{2} = 1$ |
| $4445$ | $16001$ | $240$ | $16001^{2} \, - \, $$4445$$ \, \cdot \, 240^{2} = 1$ |
| $4447$ | $141155198359897378542057170327723913285926988147488$ | $2116719505995393857046417129559580130876704730063$ | $141155198359897378542057170327723913285926988147488^{2} \, - \, $$4447$$ \, \cdot \, 2116719505995393857046417129559580130876704730063^{2} = 1$ |
| $4449$ | $51762301910478302918469654245016003977815$ | $776036911603252165945401837994102606676$ | $51762301910478302918469654245016003977815^{2} \, - \, $$4449$$ \, \cdot \, 776036911603252165945401837994102606676^{2} = 1$ |
| $4451$ | $3654082723779812248370$ | $54770862229934724207$ | $3654082723779812248370^{2} \, - \, $$4451$$ \, \cdot \, 54770862229934724207^{2} = 1$ |
| $4453$ | $357951625630266921683401$ | $5364113907104115104340$ | $357951625630266921683401^{2} \, - \, $$4453$$ \, \cdot \, 5364113907104115104340^{2} = 1$ |
| $4454$ | $267725526085$ | $4011572766$ | $267725526085^{2} \, - \, $$4454$$ \, \cdot \, 4011572766^{2} = 1$ |
| $4457$ | $257865434685013483729770273$ | $3862529545034802873590152$ | $257865434685013483729770273^{2} \, - \, $$4457$$ \, \cdot \, 3862529545034802873590152^{2} = 1$ |
| $4458$ | $248859648767$ | $3727215056$ | $248859648767^{2} \, - \, $$4458$$ \, \cdot \, 3727215056^{2} = 1$ |
| $4461$ | $177773572737429116905135022956942175$ | $2661650874238562247249634140442728$ | $177773572737429116905135022956942175^{2} \, - \, $$4461$$ \, \cdot \, 2661650874238562247249634140442728^{2} = 1$ |
| $4462$ | $136356796793404943$ | $2041324309766052$ | $136356796793404943^{2} \, - \, $$4462$$ \, \cdot \, 2041324309766052^{2} = 1$ |
| $4463$ | $1128409251969153189024$ | $16890915718751495705$ | $1128409251969153189024^{2} \, - \, $$4463$$ \, \cdot \, 16890915718751495705^{2} = 1$ |
| $4465$ | $337816148176173079$ | $5055564715778844$ | $337816148176173079^{2} \, - \, $$4465$$ \, \cdot \, 5055564715778844^{2} = 1$ |
| $4466$ | $5226495$ | $78208$ | $5226495^{2} \, - \, $$4466$$ \, \cdot \, 78208^{2} = 1$ |
| $4467$ | $23804642$ | $356167$ | $23804642^{2} \, - \, $$4467$$ \, \cdot \, 356167^{2} = 1$ |
| $4469$ | $7122262882301310874364403345801$ | $106540031802634506220621975420$ | $7122262882301310874364403345801^{2} \, - \, $$4469$$ \, \cdot \, 106540031802634506220621975420^{2} = 1$ |
| $4470$ | $73009$ | $1092$ | $73009^{2} \, - \, $$4470$$ \, \cdot \, 1092^{2} = 1$ |
| $4471$ | $59176$ | $885$ | $59176^{2} \, - \, $$4471$$ \, \cdot \, 885^{2} = 1$ |
| $4474$ | $1732222655397408727390761453482911779145122059355687533299$ | $25897373745061168088257688696329361669663744934738706710$ | $1732222655397408727390761453482911779145122059355687533299^{2} \, - \, $$4474$$ \, \cdot \, 25897373745061168088257688696329361669663744934738706710^{2} = 1$ |
| $4478$ | $11522923262214399$ | $172195035009520$ | $11522923262214399^{2} \, - \, $$4478$$ \, \cdot \, 172195035009520^{2} = 1$ |
| $4479$ | $2199569250676$ | $32866019495$ | $2199569250676^{2} \, - \, $$4479$$ \, \cdot \, 32866019495^{2} = 1$ |
| $4481$ | $4323933245322465640449$ | $64593900257366205440$ | $4323933245322465640449^{2} \, - \, $$4481$$ \, \cdot \, 64593900257366205440^{2} = 1$ |
| $4483$ | $35069904978168463226$ | $523781578010154255$ | $35069904978168463226^{2} \, - \, $$4483$$ \, \cdot \, 523781578010154255^{2} = 1$ |
| $4485$ | $150281$ | $2244$ | $150281^{2} \, - \, $$4485$$ \, \cdot \, 2244^{2} = 1$ |
| $4486$ | $16133208167005702950089618527500638518654823862842384211845$ | $240874653498782655935372826951351834752032412247514186722$ | $16133208167005702950089618527500638518654823862842384211845^{2} \, - \, $$4486$$ \, \cdot \, 240874653498782655935372826951351834752032412247514186722^{2} = 1$ |
| $4487$ | $4488$ | $67$ | $4488^{2} \, - \, $$4487$$ \, \cdot \, 67^{2} = 1$ |
| $4490$ | $8979$ | $134$ | $8979^{2} \, - \, $$4490$$ \, \cdot \, 134^{2} = 1$ |
| $4493$ | $45289664649$ | $675664180$ | $45289664649^{2} \, - \, $$4493$$ \, \cdot \, 675664180^{2} = 1$ |
| $4494$ | $207926251$ | $3101650$ | $207926251^{2} \, - \, $$4494$$ \, \cdot \, 3101650^{2} = 1$ |
| $4495$ | $867149366759$ | $12933887028$ | $867149366759^{2} \, - \, $$4495$$ \, \cdot \, 12933887028^{2} = 1$ |
| $4497$ | $41982080443063231092168983$ | $626040619715230176778852$ | $41982080443063231092168983^{2} \, - \, $$4497$$ \, \cdot \, 626040619715230176778852^{2} = 1$ |
| $4498$ | $340790624968576483$ | $5081336001433566$ | $340790624968576483^{2} \, - \, $$4498$$ \, \cdot \, 5081336001433566^{2} = 1$ |
| $4499$ | $423922094650$ | $6320159751$ | $423922094650^{2} \, - \, $$4499$$ \, \cdot \, 6320159751^{2} = 1$ |
| $4501$ | $30215708926147463095$ | $450379154966232468$ | $30215708926147463095^{2} \, - \, $$4501$$ \, \cdot \, 450379154966232468^{2} = 1$ |
| $4502$ | $617346257768391889703717$ | $9200810256130213252638$ | $617346257768391889703717^{2} \, - \, $$4502$$ \, \cdot \, 9200810256130213252638^{2} = 1$ |
| $4503$ | $99438247$ | $1481844$ | $99438247^{2} \, - \, $$4503$$ \, \cdot \, 1481844^{2} = 1$ |
| $4505$ | $51422962209$ | $766142744$ | $51422962209^{2} \, - \, $$4505$$ \, \cdot \, 766142744^{2} = 1$ |
| $4506$ | $349354687501$ | $5204403750$ | $349354687501^{2} \, - \, $$4506$$ \, \cdot \, 5204403750^{2} = 1$ |
| $4507$ | $780478327361831846309355990987026$ | $11625645311400303513583583104395$ | $780478327361831846309355990987026^{2} \, - \, $$4507$$ \, \cdot \, 11625645311400303513583583104395^{2} = 1$ |
| $4510$ | $47806710740821$ | $711869839098$ | $47806710740821^{2} \, - \, $$4510$$ \, \cdot \, 711869839098^{2} = 1$ |
| $4511$ | $24985$ | $372$ | $24985^{2} \, - \, $$4511$$ \, \cdot \, 372^{2} = 1$ |
| $4513$ | $2937225177063436709999743082645399579147734857113491422134584259713$ | $43722458624396355128949493716386601526225064117216425602227656656$ | $2937225177063436709999743082645399579147734857113491422134584259713^{2} \, - \, $$4513$$ \, \cdot \, 43722458624396355128949493716386601526225064117216425602227656656^{2} = 1$ |
| $4514$ | $40789972010660451$ | $607117330101910$ | $40789972010660451^{2} \, - \, $$4514$$ \, \cdot \, 607117330101910^{2} = 1$ |
| $4515$ | $10751$ | $160$ | $10751^{2} \, - \, $$4515$$ \, \cdot \, 160^{2} = 1$ |
| $4517$ | $16508345748902771170411995848649$ | $245628361284807382107768383660$ | $16508345748902771170411995848649^{2} \, - \, $$4517$$ \, \cdot \, 245628361284807382107768383660^{2} = 1$ |
| $4519$ | $848247818120463021285124851606930862336855497344396380221506360$ | $12618321268387781268413231790858143635939216630980890973034611$ | $848247818120463021285124851606930862336855497344396380221506360^{2} \, - \, $$4519$$ \, \cdot \, 12618321268387781268413231790858143635939216630980890973034611^{2} = 1$ |
| $4521$ | $91340689174094999$ | $1358460548846900$ | $91340689174094999^{2} \, - \, $$4521$$ \, \cdot \, 1358460548846900^{2} = 1$ |
| $4522$ | $143687501$ | $2136750$ | $143687501^{2} \, - \, $$4522$$ \, \cdot \, 2136750^{2} = 1$ |
| $4523$ | $930393727314945033145202$ | $13834181840015741762019$ | $930393727314945033145202^{2} \, - \, $$4523$$ \, \cdot \, 13834181840015741762019^{2} = 1$ |
| $4526$ | $8433289622368680975$ | $125354445643493468$ | $8433289622368680975^{2} \, - \, $$4526$$ \, \cdot \, 125354445643493468^{2} = 1$ |
| $4529$ | $855537772996595350355455$ | $12712706736520481090784$ | $855537772996595350355455^{2} \, - \, $$4529$$ \, \cdot \, 12712706736520481090784^{2} = 1$ |
| $4530$ | $4043260861$ | $60073462$ | $4043260861^{2} \, - \, $$4530$$ \, \cdot \, 60073462^{2} = 1$ |
| $4531$ | $2000272293075168006487124629625$ | $29716118959015468960659096252$ | $2000272293075168006487124629625^{2} \, - \, $$4531$$ \, \cdot \, 29716118959015468960659096252^{2} = 1$ |
| $4533$ | $4178245618449447708492479342935259999$ | $62058476099474951996375422601873400$ | $4178245618449447708492479342935259999^{2} \, - \, $$4533$$ \, \cdot \, 62058476099474951996375422601873400^{2} = 1$ |
| $4534$ | $40805$ | $606$ | $40805^{2} \, - \, $$4534$$ \, \cdot \, 606^{2} = 1$ |
| $4535$ | $15076089604$ | $223872147$ | $15076089604^{2} \, - \, $$4535$$ \, \cdot \, 223872147^{2} = 1$ |
| $4537$ | $16800177062917315732093072338120779921836033$ | $249418963031170569826547831079332655701568$ | $16800177062917315732093072338120779921836033^{2} \, - \, $$4537$$ \, \cdot \, 249418963031170569826547831079332655701568^{2} = 1$ |
| $4538$ | $44765454948444180723$ | $664524131910167734$ | $44765454948444180723^{2} \, - \, $$4538$$ \, \cdot \, 664524131910167734^{2} = 1$ |
| $4539$ | $8392610$ | $124571$ | $8392610^{2} \, - \, $$4539$$ \, \cdot \, 124571^{2} = 1$ |
| $4541$ | $64250542797199083490595174199$ | $953456864957772921307176260$ | $64250542797199083490595174199^{2} \, - \, $$4541$$ \, \cdot \, 953456864957772921307176260^{2} = 1$ |
| $4542$ | $15264149$ | $226490$ | $15264149^{2} \, - \, $$4542$$ \, \cdot \, 226490^{2} = 1$ |
| $4543$ | $190523332$ | $2826681$ | $190523332^{2} \, - \, $$4543$$ \, \cdot \, 2826681^{2} = 1$ |
| $4546$ | $94991260351715$ | $1408863553338$ | $94991260351715^{2} \, - \, $$4546$$ \, \cdot \, 1408863553338^{2} = 1$ |
| $4547$ | $1720494010053289010308156068122$ | $25514713016240883113423806383$ | $1720494010053289010308156068122^{2} \, - \, $$4547$$ \, \cdot \, 25514713016240883113423806383^{2} = 1$ |
| $4549$ | $1137519905470712029552742904895572109039840141629134555584985135847213160285764535644698665801$ | $16865570513612540176750318810766858998322327580957894937920975419322459735491354770797969780$ | $1137519905470712029552742904895572109039840141629134555584985135847213160285764535644698665801^{2} \, - \, $$4549$$ \, \cdot \, 16865570513612540176750318810766858998322327580957894937920975419322459735491354770797969780^{2} = 1$ |
| $4551$ | $2187511705$ | $32426268$ | $2187511705^{2} \, - \, $$4551$$ \, \cdot \, 32426268^{2} = 1$ |
| $4553$ | $35598774441249$ | $527577446600$ | $35598774441249^{2} \, - \, $$4553$$ \, \cdot \, 527577446600^{2} = 1$ |
| $4555$ | $7289$ | $108$ | $7289^{2} \, - \, $$4555$$ \, \cdot \, 108^{2} = 1$ |
| $4558$ | $32771052151296521771591893$ | $485403859009338336642366$ | $32771052151296521771591893^{2} \, - \, $$4558$$ \, \cdot \, 485403859009338336642366^{2} = 1$ |
| $4559$ | $589381505$ | $8728944$ | $589381505^{2} \, - \, $$4559$$ \, \cdot \, 8728944^{2} = 1$ |
| $4561$ | $47388207439720057910539589091581234136127936204419300867157346055297037596874043191820733191273671201$ | $701681852816353768053261208942820320581472902241922325347568663208649480240945177072379900143870280$ | $47388207439720057910539589091581234136127936204419300867157346055297037596874043191820733191273671201^{2} \, - \, $$4561$$ \, \cdot \, 701681852816353768053261208942820320581472902241922325347568663208649480240945177072379900143870280^{2} = 1$ |
| $4562$ | $770617601$ | $11409360$ | $770617601^{2} \, - \, $$4562$$ \, \cdot \, 11409360^{2} = 1$ |
| $4565$ | $4205626175871$ | $62245831984$ | $4205626175871^{2} \, - \, $$4565$$ \, \cdot \, 62245831984^{2} = 1$ |
| $4566$ | $19500325967119400646544325$ | $288585108852187497504842$ | $19500325967119400646544325^{2} \, - \, $$4566$$ \, \cdot \, 288585108852187497504842^{2} = 1$ |
| $4567$ | $82076268218693069814120771897556088$ | $1214512799882649510466208417020827$ | $82076268218693069814120771897556088^{2} \, - \, $$4567$$ \, \cdot \, 1214512799882649510466208417020827^{2} = 1$ |
| $4569$ | $19556621483899492751854844034001175$ | $289323194149567893225974773375564$ | $19556621483899492751854844034001175^{2} \, - \, $$4569$$ \, \cdot \, 289323194149567893225974773375564^{2} = 1$ |
| $4570$ | $75225941359931539$ | $1112780562659106$ | $75225941359931539^{2} \, - \, $$4570$$ \, \cdot \, 1112780562659106^{2} = 1$ |
| $4571$ | $23324353311225$ | $344988009388$ | $23324353311225^{2} \, - \, $$4571$$ \, \cdot \, 344988009388^{2} = 1$ |
| $4573$ | $47746656498313$ | $706061229204$ | $47746656498313^{2} \, - \, $$4573$$ \, \cdot \, 706061229204^{2} = 1$ |
| $4574$ | $30055896909975469428735$ | $444407738075478042176$ | $30055896909975469428735^{2} \, - \, $$4574$$ \, \cdot \, 444407738075478042176^{2} = 1$ |
| $4577$ | $1476827384552227049343$ | $21829273419253668368$ | $1476827384552227049343^{2} \, - \, $$4577$$ \, \cdot \, 21829273419253668368^{2} = 1$ |
| $4578$ | $11773$ | $174$ | $11773^{2} \, - \, $$4578$$ \, \cdot \, 174^{2} = 1$ |
| $4579$ | $41210$ | $609$ | $41210^{2} \, - \, $$4579$$ \, \cdot \, 609^{2} = 1$ |
| $4582$ | $2843$ | $42$ | $2843^{2} \, - \, $$4582$$ \, \cdot \, 42^{2} = 1$ |
| $4583$ | $231039908800008$ | $3412809726419$ | $231039908800008^{2} \, - \, $$4583$$ \, \cdot \, 3412809726419^{2} = 1$ |
| $4585$ | $193810658197866932942999$ | $2862252783935637561780$ | $193810658197866932942999^{2} \, - \, $$4585$$ \, \cdot \, 2862252783935637561780^{2} = 1$ |
| $4586$ | $5732499$ | $84650$ | $5732499^{2} \, - \, $$4586$$ \, \cdot \, 84650^{2} = 1$ |
| $4587$ | $555026$ | $8195$ | $555026^{2} \, - \, $$4587$$ \, \cdot \, 8195^{2} = 1$ |
| $4589$ | $819705642774721010443946585184201$ | $12100376845682204451552319498660$ | $819705642774721010443946585184201^{2} \, - \, $$4589$$ \, \cdot \, 12100376845682204451552319498660^{2} = 1$ |
| $4591$ | $8206729280$ | $121120167$ | $8206729280^{2} \, - \, $$4591$$ \, \cdot \, 121120167^{2} = 1$ |
| $4593$ | $2694951235085372753065531351$ | $39765155800346868881989420$ | $2694951235085372753065531351^{2} \, - \, $$4593$$ \, \cdot \, 39765155800346868881989420^{2} = 1$ |
| $4594$ | $640971759666626022629562499$ | $9456782487812439696267750$ | $640971759666626022629562499^{2} \, - \, $$4594$$ \, \cdot \, 9456782487812439696267750^{2} = 1$ |
| $4595$ | $1485473439$ | $21914024$ | $1485473439^{2} \, - \, $$4595$$ \, \cdot \, 21914024^{2} = 1$ |
| $4597$ | $758911034851849$ | $11193183298980$ | $758911034851849^{2} \, - \, $$4597$$ \, \cdot \, 11193183298980^{2} = 1$ |
| $4601$ | $289029478941964075981405845184215$ | $4261044044370876818374452685732$ | $289029478941964075981405845184215^{2} \, - \, $$4601$$ \, \cdot \, 4261044044370876818374452685732^{2} = 1$ |
| $4602$ | $4758703$ | $70148$ | $4758703^{2} \, - \, $$4602$$ \, \cdot \, 70148^{2} = 1$ |
| $4603$ | $15307156914706802928575294692236683931832945589668202$ | $225618156720756309327949976781404554685767245006549$ | $15307156914706802928575294692236683931832945589668202^{2} \, - \, $$4603$$ \, \cdot \, 225618156720756309327949976781404554685767245006549^{2} = 1$ |
| $4605$ | $45949352164001$ | $677118337560$ | $45949352164001^{2} \, - \, $$4605$$ \, \cdot \, 677118337560^{2} = 1$ |
| $4607$ | $543$ | $8$ | $543^{2} \, - \, $$4607$$ \, \cdot \, 8^{2} = 1$ |
| $4609$ | $14859478542441508057804415825755620789959166551$ | $218877044156100394775531604536232961984428780$ | $14859478542441508057804415825755620789959166551^{2} \, - \, $$4609$$ \, \cdot \, 218877044156100394775531604536232961984428780^{2} = 1$ |
| $4610$ | $275366594499$ | $4055653010$ | $275366594499^{2} \, - \, $$4610$$ \, \cdot \, 4055653010^{2} = 1$ |
| $4611$ | $20326826$ | $299345$ | $20326826^{2} \, - \, $$4611$$ \, \cdot \, 299345^{2} = 1$ |
| $4613$ | $367141691258093151$ | $5405575989635240$ | $367141691258093151^{2} \, - \, $$4613$$ \, \cdot \, 5405575989635240^{2} = 1$ |
| $4614$ | $459280000805$ | $6761432854$ | $459280000805^{2} \, - \, $$4614$$ \, \cdot \, 6761432854^{2} = 1$ |
| $4615$ | $15009461822044$ | $220942502037$ | $15009461822044^{2} \, - \, $$4615$$ \, \cdot \, 220942502037^{2} = 1$ |
| $4618$ | $1313817000528196515358820321040893587388083$ | $19333385601182416948505063138945299420254$ | $1313817000528196515358820321040893587388083^{2} \, - \, $$4618$$ \, \cdot \, 19333385601182416948505063138945299420254^{2} = 1$ |
| $4619$ | $148955001$ | $2191700$ | $148955001^{2} \, - \, $$4619$$ \, \cdot \, 2191700^{2} = 1$ |
| $4621$ | $8784966228052956337831539614153017127496883947504004927423017979424284055063479878882987198859573520634598388198267578873801$ | $129232608969077740795814231703764974438150305306333833482132886687546327961918802044374224308962502943121562397133146250340$ | $8784966228052956337831539614153017127496883947504004927423017979424284055063479878882987198859573520634598388198267578873801^{2} \, - \, $$4621$$ \, \cdot \, 129232608969077740795814231703764974438150305306333833482132886687546327961918802044374224308962502943121562397133146250340^{2} = 1$ |
| $4622$ | $4623$ | $68$ | $4623^{2} \, - \, $$4622$$ \, \cdot \, 68^{2} = 1$ |
| $4623$ | $68$ | $1$ | $68^{2} \, - \, $$4623$$ \, \cdot \, 1^{2} = 1$ |
| $4627$ | $1429983238007499902$ | $21022346837639433$ | $1429983238007499902^{2} \, - \, $$4627$$ \, \cdot \, 21022346837639433^{2} = 1$ |
| $4629$ | $3516183047258935$ | $51680640251084$ | $3516183047258935^{2} \, - \, $$4629$$ \, \cdot \, 51680640251084^{2} = 1$ |
| $4630$ | $1035777672251$ | $15222151830$ | $1035777672251^{2} \, - \, $$4630$$ \, \cdot \, 15222151830^{2} = 1$ |
| $4631$ | $34670972075636249$ | $509481745110300$ | $34670972075636249^{2} \, - \, $$4631$$ \, \cdot \, 509481745110300^{2} = 1$ |
| $4633$ | $2544431870910977$ | $37381754131104$ | $2544431870910977^{2} \, - \, $$4633$$ \, \cdot \, 37381754131104^{2} = 1$ |
| $4634$ | $87450237077295$ | $1284644543156$ | $87450237077295^{2} \, - \, $$4634$$ \, \cdot \, 1284644543156^{2} = 1$ |
| $4637$ | $16927299571191921871566745875859866249$ | $248581687702547480691089625837214700$ | $16927299571191921871566745875859866249^{2} \, - \, $$4637$$ \, \cdot \, 248581687702547480691089625837214700^{2} = 1$ |
| $4638$ | $519722259851$ | $7631430370$ | $519722259851^{2} \, - \, $$4638$$ \, \cdot \, 7631430370^{2} = 1$ |
| $4639$ | $3038436564712740143065718231393168916237674720$ | $44610592097710753852782012819805266050072721$ | $3038436564712740143065718231393168916237674720^{2} \, - \, $$4639$$ \, \cdot \, 44610592097710753852782012819805266050072721^{2} = 1$ |
| $4641$ | $545$ | $8$ | $545^{2} \, - \, $$4641$$ \, \cdot \, 8^{2} = 1$ |
| $4642$ | $785389834210883966440001$ | $11527435677764495914200$ | $785389834210883966440001^{2} \, - \, $$4642$$ \, \cdot \, 11527435677764495914200^{2} = 1$ |
| $4643$ | $1714097536125823982962$ | $25155687373365409551$ | $1714097536125823982962^{2} \, - \, $$4643$$ \, \cdot \, 25155687373365409551^{2} = 1$ |
| $4645$ | $1098862607505289240922319694241$ | $16123173824034353453539585752$ | $1098862607505289240922319694241^{2} \, - \, $$4645$$ \, \cdot \, 16123173824034353453539585752^{2} = 1$ |
| $4646$ | $15943263695$ | $233903988$ | $15943263695^{2} \, - \, $$4646$$ \, \cdot \, 233903988^{2} = 1$ |
| $4647$ | $375267047527$ | $5504959068$ | $375267047527^{2} \, - \, $$4647$$ \, \cdot \, 5504959068^{2} = 1$ |
| $4649$ | $9420195137863692801$ | $138159300628153120$ | $9420195137863692801^{2} \, - \, $$4649$$ \, \cdot \, 138159300628153120^{2} = 1$ |
| $4651$ | $160017734091375890$ | $2346361622289693$ | $160017734091375890^{2} \, - \, $$4651$$ \, \cdot \, 2346361622289693^{2} = 1$ |
| $4654$ | $7078779885622101808036238549$ | $103763644878709027311485490$ | $7078779885622101808036238549^{2} \, - \, $$4654$$ \, \cdot \, 103763644878709027311485490^{2} = 1$ |
| $4657$ | $200701935223022590342088312477203698350637836387679676316705065033847417760618470889324673$ | $2941023137113257556889756596366858535220211979540040597035457470077739565385246437662352$ | $200701935223022590342088312477203698350637836387679676316705065033847417760618470889324673^{2} \, - \, $$4657$$ \, \cdot \, 2941023137113257556889756596366858535220211979540040597035457470077739565385246437662352^{2} = 1$ |
| $4658$ | $273$ | $4$ | $273^{2} \, - \, $$4658$$ \, \cdot \, 4^{2} = 1$ |
| $4659$ | $4049961429423639009290$ | $59334123594739115881$ | $4049961429423639009290^{2} \, - \, $$4659$$ \, \cdot \, 59334123594739115881^{2} = 1$ |
| $4661$ | $774199$ | $11340$ | $774199^{2} \, - \, $$4661$$ \, \cdot \, 11340^{2} = 1$ |
| $4663$ | $202502337307583851143390548574136013768$ | $2965495931452003980059188669083476139$ | $202502337307583851143390548574136013768^{2} \, - \, $$4663$$ \, \cdot \, 2965495931452003980059188669083476139^{2} = 1$ |
| $4665$ | $7276923901919$ | $106542285608$ | $7276923901919^{2} \, - \, $$4665$$ \, \cdot \, 106542285608^{2} = 1$ |
| $4666$ | $533102430262395380726164440951176332648679844715778550212611889299$ | $7804377984212530223904955072164768356832866618968026531072095730$ | $533102430262395380726164440951176332648679844715778550212611889299^{2} \, - \, $$4666$$ \, \cdot \, 7804377984212530223904955072164768356832866618968026531072095730^{2} = 1$ |
| $4667$ | $7970158$ | $116667$ | $7970158^{2} \, - \, $$4667$$ \, \cdot \, 116667^{2} = 1$ |
| $4669$ | $4307255$ | $63036$ | $4307255^{2} \, - \, $$4669$$ \, \cdot \, 63036^{2} = 1$ |
| $4670$ | $16811$ | $246$ | $16811^{2} \, - \, $$4670$$ \, \cdot \, 246^{2} = 1$ |
| $4673$ | $62196912065683065151741235049785883396209250849$ | $909852374838238645570507874972758676123860360$ | $62196912065683065151741235049785883396209250849^{2} \, - \, $$4673$$ \, \cdot \, 909852374838238645570507874972758676123860360^{2} = 1$ |
| $4674$ | $2051$ | $30$ | $2051^{2} \, - \, $$4674$$ \, \cdot \, 30^{2} = 1$ |
| $4677$ | $2796250463$ | $40887672$ | $2796250463^{2} \, - \, $$4677$$ \, \cdot \, 40887672^{2} = 1$ |
| $4678$ | $33739440558982159421884774595635427621483931655877$ | $493296198254012480627638643098219966907384794674$ | $33739440558982159421884774595635427621483931655877^{2} \, - \, $$4678$$ \, \cdot \, 493296198254012480627638643098219966907384794674^{2} = 1$ |
| $4679$ | $362504918785116480848797400520$ | $5299530320363998104246583709$ | $362504918785116480848797400520^{2} \, - \, $$4679$$ \, \cdot \, 5299530320363998104246583709^{2} = 1$ |
| $4681$ | $5590445260760825825033632937463930398745431551$ | $81710351518659890783921836008773439415721760$ | $5590445260760825825033632937463930398745431551^{2} \, - \, $$4681$$ \, \cdot \, 81710351518659890783921836008773439415721760^{2} = 1$ |
| $4682$ | $8142944897043$ | $119005159642$ | $8142944897043^{2} \, - \, $$4682$$ \, \cdot \, 119005159642^{2} = 1$ |
| $4683$ | $4274017$ | $62456$ | $4274017^{2} \, - \, $$4683$$ \, \cdot \, 62456^{2} = 1$ |
| $4685$ | $67698249$ | $989060$ | $67698249^{2} \, - \, $$4685$$ \, \cdot \, 989060^{2} = 1$ |
| $4686$ | $378005$ | $5522$ | $378005^{2} \, - \, $$4686$$ \, \cdot \, 5522^{2} = 1$ |
| $4687$ | $238965417339133458151$ | $3490499486011239180$ | $238965417339133458151^{2} \, - \, $$4687$$ \, \cdot \, 3490499486011239180^{2} = 1$ |
| $4690$ | $90673436376431$ | $1324017281652$ | $90673436376431^{2} \, - \, $$4690$$ \, \cdot \, 1324017281652^{2} = 1$ |
| $4691$ | $513203446109801846220846539285799890$ | $7493019235436775143682533704699383$ | $513203446109801846220846539285799890^{2} \, - \, $$4691$$ \, \cdot \, 7493019235436775143682533704699383^{2} = 1$ |
| $4694$ | $415829397067499437869677485572878885$ | $6069370450221309645377401001370114$ | $415829397067499437869677485572878885^{2} \, - \, $$4694$$ \, \cdot \, 6069370450221309645377401001370114^{2} = 1$ |
| $4695$ | $978124$ | $14275$ | $978124^{2} \, - \, $$4695$$ \, \cdot \, 14275^{2} = 1$ |
| $4697$ | $11192046249$ | $163304900$ | $11192046249^{2} \, - \, $$4697$$ \, \cdot \, 163304900^{2} = 1$ |
| $4699$ | $1313453305$ | $19160724$ | $1313453305^{2} \, - \, $$4699$$ \, \cdot \, 19160724^{2} = 1$ |
| $4701$ | $7602158272333482711224386544211534755683416055$ | $110877080369225358529302071781197479181974668$ | $7602158272333482711224386544211534755683416055^{2} \, - \, $$4701$$ \, \cdot \, 110877080369225358529302071781197479181974668^{2} = 1$ |
| $4702$ | $230399$ | $3360$ | $230399^{2} \, - \, $$4702$$ \, \cdot \, 3360^{2} = 1$ |
| $4703$ | $1966229341728$ | $28671253681$ | $1966229341728^{2} \, - \, $$4703$$ \, \cdot \, 28671253681^{2} = 1$ |
| $4705$ | $608278366889$ | $8867936148$ | $608278366889^{2} \, - \, $$4705$$ \, \cdot \, 8867936148^{2} = 1$ |
| $4706$ | $235299$ | $3430$ | $235299^{2} \, - \, $$4706$$ \, \cdot \, 3430^{2} = 1$ |
| $4709$ | $961338349290797295451341906249$ | $14009154409397145683145831500$ | $961338349290797295451341906249^{2} \, - \, $$4709$$ \, \cdot \, 14009154409397145683145831500^{2} = 1$ |
| $4710$ | $36558079$ | $532688$ | $36558079^{2} \, - \, $$4710$$ \, \cdot \, 532688^{2} = 1$ |
| $4711$ | $269829866100824$ | $3931275372435$ | $269829866100824^{2} \, - \, $$4711$$ \, \cdot \, 3931275372435^{2} = 1$ |
| $4713$ | $6312553736100912943092112599383$ | $91950981266656629951206946524$ | $6312553736100912943092112599383^{2} \, - \, $$4713$$ \, \cdot \, 91950981266656629951206946524^{2} = 1$ |
| $4714$ | $255939592624493225460600239758293268051$ | $3727714862720804416067096478703943430$ | $255939592624493225460600239758293268051^{2} \, - \, $$4714$$ \, \cdot \, 3727714862720804416067096478703943430^{2} = 1$ |
| $4715$ | $206$ | $3$ | $206^{2} \, - \, $$4715$$ \, \cdot \, 3^{2} = 1$ |
| $4717$ | $8212233269575715849$ | $119571682134708180$ | $8212233269575715849^{2} \, - \, $$4717$$ \, \cdot \, 119571682134708180^{2} = 1$ |
| $4718$ | $345087$ | $5024$ | $345087^{2} \, - \, $$4718$$ \, \cdot \, 5024^{2} = 1$ |
| $4721$ | $2015088471612851438524544788846855562843781249$ | $29327640105241305740457220619942483132822000$ | $2015088471612851438524544788846855562843781249^{2} \, - \, $$4721$$ \, \cdot \, 29327640105241305740457220619942483132822000^{2} = 1$ |
| $4722$ | $113208087897097217$ | $1647458425621152$ | $113208087897097217^{2} \, - \, $$4722$$ \, \cdot \, 1647458425621152^{2} = 1$ |
| $4723$ | $269935075319219492291995696216304202493226$ | $3927808879411109256790363339881410720055$ | $269935075319219492291995696216304202493226^{2} \, - \, $$4723$$ \, \cdot \, 3927808879411109256790363339881410720055^{2} = 1$ |
| $4726$ | $3013278700049685989237821445$ | $43832116634026962986091318$ | $3013278700049685989237821445^{2} \, - \, $$4726$$ \, \cdot \, 43832116634026962986091318^{2} = 1$ |
| $4727$ | $7971033988$ | $115936947$ | $7971033988^{2} \, - \, $$4727$$ \, \cdot \, 115936947^{2} = 1$ |
| $4729$ | $466912095768279936226667730092083201$ | $6789698159289119134886341626287040$ | $466912095768279936226667730092083201^{2} \, - \, $$4729$$ \, \cdot \, 6789698159289119134886341626287040^{2} = 1$ |
| $4730$ | $2751$ | $40$ | $2751^{2} \, - \, $$4730$$ \, \cdot \, 40^{2} = 1$ |
| $4731$ | $6137625650$ | $89232677$ | $6137625650^{2} \, - \, $$4731$$ \, \cdot \, 89232677^{2} = 1$ |
| $4733$ | $56580810122720649$ | $822433721789420$ | $56580810122720649^{2} \, - \, $$4733$$ \, \cdot \, 822433721789420^{2} = 1$ |
| $4735$ | $781789956658484425947244$ | $11361354087502060586841$ | $781789956658484425947244^{2} \, - \, $$4735$$ \, \cdot \, 11361354087502060586841^{2} = 1$ |
| $4737$ | $2781707197246798807$ | $40416594940092852$ | $2781707197246798807^{2} \, - \, $$4737$$ \, \cdot \, 40416594940092852^{2} = 1$ |
| $4738$ | $413$ | $6$ | $413^{2} \, - \, $$4738$$ \, \cdot \, 6^{2} = 1$ |
| $4739$ | $273462438068574$ | $3972412383745$ | $273462438068574^{2} \, - \, $$4739$$ \, \cdot \, 3972412383745^{2} = 1$ |
| $4741$ | $739031291449132980537222118686440057422892507587494022188585843551$ | $10733166084409704363163870331403091508563188689857179240220758840$ | $739031291449132980537222118686440057422892507587494022188585843551^{2} \, - \, $$4741$$ \, \cdot \, 10733166084409704363163870331403091508563188689857179240220758840^{2} = 1$ |
| $4742$ | $12065457941787759264901$ | $175211672518244379870$ | $12065457941787759264901^{2} \, - \, $$4742$$ \, \cdot \, 175211672518244379870^{2} = 1$ |
| $4745$ | $60504681249$ | $878356600$ | $60504681249^{2} \, - \, $$4745$$ \, \cdot \, 878356600^{2} = 1$ |
| $4746$ | $31463931085$ | $456719038$ | $31463931085^{2} \, - \, $$4746$$ \, \cdot \, 456719038^{2} = 1$ |
| $4747$ | $175019914545804617927327$ | $2540258139467269513032$ | $175019914545804617927327^{2} \, - \, $$4747$$ \, \cdot \, 2540258139467269513032^{2} = 1$ |
| $4749$ | $1990935935$ | $28890576$ | $1990935935^{2} \, - \, $$4749$$ \, \cdot \, 28890576^{2} = 1$ |
| $4751$ | $243596108531663468708673120$ | $3534091837089186111975593$ | $243596108531663468708673120^{2} \, - \, $$4751$$ \, \cdot \, 3534091837089186111975593^{2} = 1$ |
| $4754$ | $36500331863161251$ | $529379627977550$ | $36500331863161251^{2} \, - \, $$4754$$ \, \cdot \, 529379627977550^{2} = 1$ |
| $4755$ | $1586$ | $23$ | $1586^{2} \, - \, $$4755$$ \, \cdot \, 23^{2} = 1$ |
| $4757$ | $164151$ | $2380$ | $164151^{2} \, - \, $$4757$$ \, \cdot \, 2380^{2} = 1$ |
| $4758$ | $3173$ | $46$ | $3173^{2} \, - \, $$4758$$ \, \cdot \, 46^{2} = 1$ |
| $4759$ | $4760$ | $69$ | $4760^{2} \, - \, $$4759$$ \, \cdot \, 69^{2} = 1$ |
| $4762$ | $9523$ | $138$ | $9523^{2} \, - \, $$4762$$ \, \cdot \, 138^{2} = 1$ |
| $4763$ | $4762$ | $69$ | $4762^{2} \, - \, $$4763$$ \, \cdot \, 69^{2} = 1$ |
| $4765$ | $54027104329$ | $782672796$ | $54027104329^{2} \, - \, $$4765$$ \, \cdot \, 782672796^{2} = 1$ |
| $4766$ | $1573418482608286046884095$ | $22791201900218366430992$ | $1573418482608286046884095^{2} \, - \, $$4766$$ \, \cdot \, 22791201900218366430992^{2} = 1$ |
| $4767$ | $1588$ | $23$ | $1588^{2} \, - \, $$4767$$ \, \cdot \, 23^{2} = 1$ |
| $4769$ | $622412677627818469773549515799$ | $9012904488597268111605351940$ | $622412677627818469773549515799^{2} \, - \, $$4769$$ \, \cdot \, 9012904488597268111605351940^{2} = 1$ |
| $4771$ | $963973945$ | $13955988$ | $963973945^{2} \, - \, $$4771$$ \, \cdot \, 13955988^{2} = 1$ |
| $4773$ | $2006047351$ | $29036580$ | $2006047351^{2} \, - \, $$4773$$ \, \cdot \, 29036580^{2} = 1$ |
| $4774$ | $3313895270874299$ | $47962031717310$ | $3313895270874299^{2} \, - \, $$4774$$ \, \cdot \, 47962031717310^{2} = 1$ |
| $4777$ | $52952753794318849$ | $766144926115680$ | $52952753794318849^{2} \, - \, $$4777$$ \, \cdot \, 766144926115680^{2} = 1$ |
| $4778$ | $40374099$ | $584090$ | $40374099^{2} \, - \, $$4778$$ \, \cdot \, 584090^{2} = 1$ |
| $4781$ | $129000959559528976970876970495$ | $1865664590602095927934840352$ | $129000959559528976970876970495^{2} \, - \, $$4781$$ \, \cdot \, 1865664590602095927934840352^{2} = 1$ |
| $4782$ | $9701225867$ | $140288422$ | $9701225867^{2} \, - \, $$4782$$ \, \cdot \, 140288422^{2} = 1$ |
| $4783$ | $501072497351868469709693117115455757189644063168$ | $7245199952416725212837969478953288149252705209$ | $501072497351868469709693117115455757189644063168^{2} \, - \, $$4783$$ \, \cdot \, 7245199952416725212837969478953288149252705209^{2} = 1$ |
| $4785$ | $2205134249$ | $31878220$ | $2205134249^{2} \, - \, $$4785$$ \, \cdot \, 31878220^{2} = 1$ |
| $4786$ | $19270120998905353475077724225$ | $278546749290708136742189928$ | $19270120998905353475077724225^{2} \, - \, $$4786$$ \, \cdot \, 278546749290708136742189928^{2} = 1$ |
| $4787$ | $3653683154522$ | $52807933047$ | $3653683154522^{2} \, - \, $$4787$$ \, \cdot \, 52807933047^{2} = 1$ |
| $4789$ | $374308098275810082115773788370209230330090529219031272239912553103131951745022736992360918617477763508328965455430279885758005001$ | $5408873254577040482265152887104956156875861356463842877898638121797514513018435325572914342180391820546453740627525040307724700$ | $374308098275810082115773788370209230330090529219031272239912553103131951745022736992360918617477763508328965455430279885758005001^{2} \, - \, $$4789$$ \, \cdot \, 5408873254577040482265152887104956156875861356463842877898638121797514513018435325572914342180391820546453740627525040307724700^{2} = 1$ |
| $4790$ | $129081992041279$ | $1865081877864$ | $129081992041279^{2} \, - \, $$4790$$ \, \cdot \, 1865081877864^{2} = 1$ |
| $4791$ | $10154010265$ | $146698108$ | $10154010265^{2} \, - \, $$4791$$ \, \cdot \, 146698108^{2} = 1$ |
| $4793$ | $2732286847867485417262353173056735233$ | $39465951433608034511027297239267904$ | $2732286847867485417262353173056735233^{2} \, - \, $$4793$$ \, \cdot \, 39465951433608034511027297239267904^{2} = 1$ |
| $4794$ | $50207122175$ | $725130736$ | $50207122175^{2} \, - \, $$4794$$ \, \cdot \, 725130736^{2} = 1$ |
| $4795$ | $10965480686$ | $158355579$ | $10965480686^{2} \, - \, $$4795$$ \, \cdot \, 158355579^{2} = 1$ |
| $4798$ | $6731165104815806567008363872463103$ | $97176246791344382123515991894064$ | $6731165104815806567008363872463103^{2} \, - \, $$4798$$ \, \cdot \, 97176246791344382123515991894064^{2} = 1$ |
| $4799$ | $3089010803297509275459582253600560$ | $44590675574321070472639773735649$ | $3089010803297509275459582253600560^{2} \, - \, $$4799$$ \, \cdot \, 44590675574321070472639773735649^{2} = 1$ |
| $4801$ | $87854013132174444328933644213624235901434167963506599866248447520891965168514684390501654742712449$ | $1267931383973666765682790248834759737996563007240072221860137060333294115692347724742794794848240$ | $87854013132174444328933644213624235901434167963506599866248447520891965168514684390501654742712449^{2} \, - \, $$4801$$ \, \cdot \, 1267931383973666765682790248834759737996563007240072221860137060333294115692347724742794794848240^{2} = 1$ |
| $4803$ | $22139952026$ | $319462865$ | $22139952026^{2} \, - \, $$4803$$ \, \cdot \, 319462865^{2} = 1$ |
| $4807$ | $208$ | $3$ | $208^{2} \, - \, $$4807$$ \, \cdot \, 3^{2} = 1$ |
| $4809$ | $7396714494301053655$ | $106662428412696444$ | $7396714494301053655^{2} \, - \, $$4809$$ \, \cdot \, 106662428412696444^{2} = 1$ |
| $4810$ | $3329$ | $48$ | $3329^{2} \, - \, $$4810$$ \, \cdot \, 48^{2} = 1$ |
| $4811$ | $47847341149420626010$ | $689826907980715197$ | $47847341149420626010^{2} \, - \, $$4811$$ \, \cdot \, 689826907980715197^{2} = 1$ |
| $4813$ | $9024110188737654433782933231529033$ | $130075785976238175141326776094724$ | $9024110188737654433782933231529033^{2} \, - \, $$4813$$ \, \cdot \, 130075785976238175141326776094724^{2} = 1$ |
| $4814$ | $3233690630805$ | $46606385746$ | $3233690630805^{2} \, - \, $$4814$$ \, \cdot \, 46606385746^{2} = 1$ |
| $4817$ | $17576037363812904270718938254045313$ | $253240197758723866132164426807152$ | $17576037363812904270718938254045313^{2} \, - \, $$4817$$ \, \cdot \, 253240197758723866132164426807152^{2} = 1$ |
| $4818$ | $1392401$ | $20060$ | $1392401^{2} \, - \, $$4818$$ \, \cdot \, 20060^{2} = 1$ |
| $4819$ | $7650468609894886708284425904950$ | $110207099985031869169943709561$ | $7650468609894886708284425904950^{2} \, - \, $$4819$$ \, \cdot \, 110207099985031869169943709561^{2} = 1$ |
| $4821$ | $22587352415$ | $325309512$ | $22587352415^{2} \, - \, $$4821$$ \, \cdot \, 325309512^{2} = 1$ |
| $4822$ | $277566707717$ | $3997180602$ | $277566707717^{2} \, - \, $$4822$$ \, \cdot \, 3997180602^{2} = 1$ |
| $4823$ | $153063$ | $2204$ | $153063^{2} \, - \, $$4823$$ \, \cdot \, 2204^{2} = 1$ |
| $4826$ | $482201738415$ | $6941208868$ | $482201738415^{2} \, - \, $$4826$$ \, \cdot \, 6941208868^{2} = 1$ |
| $4827$ | $973128026$ | $14006555$ | $973128026^{2} \, - \, $$4827$$ \, \cdot \, 14006555^{2} = 1$ |
| $4829$ | $917619438206745128799$ | $13204866110594572840$ | $917619438206745128799^{2} \, - \, $$4829$$ \, \cdot \, 13204866110594572840^{2} = 1$ |
| $4830$ | $139$ | $2$ | $139^{2} \, - \, $$4830$$ \, \cdot \, 2^{2} = 1$ |
| $4831$ | $3007652599669044947731924090089426307152659110384456532480$ | $43272217633712079631875313023619556326930866716738118927$ | $3007652599669044947731924090089426307152659110384456532480^{2} \, - \, $$4831$$ \, \cdot \, 43272217633712079631875313023619556326930866716738118927^{2} = 1$ |
| $4834$ | $23918103056330398383688640047715$ | $344011855562164379477951399094$ | $23918103056330398383688640047715^{2} \, - \, $$4834$$ \, \cdot \, 344011855562164379477951399094^{2} = 1$ |
| $4835$ | $25065606$ | $360479$ | $25065606^{2} \, - \, $$4835$$ \, \cdot \, 360479^{2} = 1$ |
| $4837$ | $121159774548343$ | $1742089298148$ | $121159774548343^{2} \, - \, $$4837$$ \, \cdot \, 1742089298148^{2} = 1$ |
| $4838$ | $391877$ | $5634$ | $391877^{2} \, - \, $$4838$$ \, \cdot \, 5634^{2} = 1$ |
| $4839$ | $2122595649843984315676$ | $30513319661064318405$ | $2122595649843984315676^{2} \, - \, $$4839$$ \, \cdot \, 30513319661064318405^{2} = 1$ |
| $4841$ | $22902242815$ | $329162592$ | $22902242815^{2} \, - \, $$4841$$ \, \cdot \, 329162592^{2} = 1$ |
| $4843$ | $8351$ | $120$ | $8351^{2} \, - \, $$4843$$ \, \cdot \, 120^{2} = 1$ |
| $4845$ | $6059722591$ | $87057432$ | $6059722591^{2} \, - \, $$4845$$ \, \cdot \, 87057432^{2} = 1$ |
| $4846$ | $18053808100646951092220344502927726992568267491668375506740499108082575$ | $259344544663416188690917791416072803638153621248382841266699972691788$ | $18053808100646951092220344502927726992568267491668375506740499108082575^{2} \, - \, $$4846$$ \, \cdot \, 259344544663416188690917791416072803638153621248382841266699972691788^{2} = 1$ |
| $4847$ | $7863276$ | $112945$ | $7863276^{2} \, - \, $$4847$$ \, \cdot \, 112945^{2} = 1$ |
| $4849$ | $12366417996288232700163625$ | $177589723028936049518676$ | $12366417996288232700163625^{2} \, - \, $$4849$$ \, \cdot \, 177589723028936049518676^{2} = 1$ |
| $4853$ | $4564351$ | $65520$ | $4564351^{2} \, - \, $$4853$$ \, \cdot \, 65520^{2} = 1$ |
| $4854$ | $102756872132765847845$ | $1474894615421250066$ | $102756872132765847845^{2} \, - \, $$4854$$ \, \cdot \, 1474894615421250066^{2} = 1$ |
| $4855$ | $26184693821520011643316889$ | $375796631496928624231428$ | $26184693821520011643316889^{2} \, - \, $$4855$$ \, \cdot \, 375796631496928624231428^{2} = 1$ |
| $4857$ | $547223$ | $7852$ | $547223^{2} \, - \, $$4857$$ \, \cdot \, 7852^{2} = 1$ |
| $4858$ | $1216445848158809647$ | $17452756328997876$ | $1216445848158809647^{2} \, - \, $$4858$$ \, \cdot \, 17452756328997876^{2} = 1$ |
| $4859$ | $54213402457772090$ | $777737814073269$ | $54213402457772090^{2} \, - \, $$4859$$ \, \cdot \, 777737814073269^{2} = 1$ |
| $4861$ | $11528406864151354745743592709050320024453682361850769249843760254138488675885373409330452597227977489028845001$ | $165350870183997641437154581073138305989111930547667173013365085216825948812284142275299510964624203294717700$ | $11528406864151354745743592709050320024453682361850769249843760254138488675885373409330452597227977489028845001^{2} \, - \, $$4861$$ \, \cdot \, 165350870183997641437154581073138305989111930547667173013365085216825948812284142275299510964624203294717700^{2} = 1$ |
| $4862$ | $90507$ | $1298$ | $90507^{2} \, - \, $$4862$$ \, \cdot \, 1298^{2} = 1$ |
| $4863$ | $54363272912857$ | $779567024964$ | $54363272912857^{2} \, - \, $$4863$$ \, \cdot \, 779567024964^{2} = 1$ |
| $4865$ | $279$ | $4$ | $279^{2} \, - \, $$4865$$ \, \cdot \, 4^{2} = 1$ |
| $4866$ | $132182707639563641491293185$ | $1894910016382377748043808$ | $132182707639563641491293185^{2} \, - \, $$4866$$ \, \cdot \, 1894910016382377748043808^{2} = 1$ |
| $4867$ | $5023$ | $72$ | $5023^{2} \, - \, $$4867$$ \, \cdot \, 72^{2} = 1$ |
| $4870$ | $114997284860833691$ | $1647870601900698$ | $114997284860833691^{2} \, - \, $$4870$$ \, \cdot \, 1647870601900698^{2} = 1$ |
| $4871$ | $55224613415137727966355886422306120$ | $791268030991721212570358847559037$ | $55224613415137727966355886422306120^{2} \, - \, $$4871$$ \, \cdot \, 791268030991721212570358847559037^{2} = 1$ |
| $4873$ | $18061402049927613329981520477659302934999$ | $258733852134447740092330109223423480900$ | $18061402049927613329981520477659302934999^{2} \, - \, $$4873$$ \, \cdot \, 258733852134447740092330109223423480900^{2} = 1$ |
| $4874$ | $124863132294141145402046212006440051$ | $1788510371468923501629863030925070$ | $124863132294141145402046212006440051^{2} \, - \, $$4874$$ \, \cdot \, 1788510371468923501629863030925070^{2} = 1$ |
| $4877$ | $53480529923177583223559002608721543059849$ | $765806986485704736902188297614875170420$ | $53480529923177583223559002608721543059849^{2} \, - \, $$4877$$ \, \cdot \, 765806986485704736902188297614875170420^{2} = 1$ |
| $4879$ | $46066613243120$ | $659509226391$ | $46066613243120^{2} \, - \, $$4879$$ \, \cdot \, 659509226391^{2} = 1$ |
| $4881$ | $6140323831221044062531214092524416568535$ | $87889475339706351050947088141116027052$ | $6140323831221044062531214092524416568535^{2} \, - \, $$4881$$ \, \cdot \, 87889475339706351050947088141116027052^{2} = 1$ |
| $4882$ | $124247583289601$ | $1778234625840$ | $124247583289601^{2} \, - \, $$4882$$ \, \cdot \, 1778234625840^{2} = 1$ |
| $4883$ | $72717054922$ | $1040621799$ | $72717054922^{2} \, - \, $$4883$$ \, \cdot \, 1040621799^{2} = 1$ |
| $4885$ | $41513600901433838664817334643809101245451025929$ | $593961262656104937181054062519768094596842652$ | $41513600901433838664817334643809101245451025929^{2} \, - \, $$4885$$ \, \cdot \, 593961262656104937181054062519768094596842652^{2} = 1$ |
| $4886$ | $699$ | $10$ | $699^{2} \, - \, $$4886$$ \, \cdot \, 10^{2} = 1$ |
| $4889$ | $159987880449$ | $2288110880$ | $159987880449^{2} \, - \, $$4889$$ \, \cdot \, 2288110880^{2} = 1$ |
| $4890$ | $979$ | $14$ | $979^{2} \, - \, $$4890$$ \, \cdot \, 14^{2} = 1$ |
| $4891$ | $35335212074$ | $505252965$ | $35335212074^{2} \, - \, $$4891$$ \, \cdot \, 505252965^{2} = 1$ |
| $4893$ | $1399$ | $20$ | $1399^{2} \, - \, $$4893$$ \, \cdot \, 20^{2} = 1$ |
| $4894$ | $23402368611180560915150125238357815409268209660928954656658340415$ | $334524425196484338738834986339036989925030840584749069283709736$ | $23402368611180560915150125238357815409268209660928954656658340415^{2} \, - \, $$4894$$ \, \cdot \, 334524425196484338738834986339036989925030840584749069283709736^{2} = 1$ |
| $4895$ | $1959$ | $28$ | $1959^{2} \, - \, $$4895$$ \, \cdot \, 28^{2} = 1$ |
| $4897$ | $548405164693140736300953219904408001833751$ | $7836758870741393933962135842207324735300$ | $548405164693140736300953219904408001833751^{2} \, - \, $$4897$$ \, \cdot \, 7836758870741393933962135842207324735300^{2} = 1$ |
| $4898$ | $4899$ | $70$ | $4899^{2} \, - \, $$4898$$ \, \cdot \, 70^{2} = 1$ |
| $4899$ | $70$ | $1$ | $70^{2} \, - \, $$4899$$ \, \cdot \, 1^{2} = 1$ |
| $4902$ | $4901$ | $70$ | $4901^{2} \, - \, $$4902$$ \, \cdot \, 70^{2} = 1$ |
| $4903$ | $503652899701789055912983688$ | $7192839871475509291647309$ | $503652899701789055912983688^{2} \, - \, $$4903$$ \, \cdot \, 7192839871475509291647309^{2} = 1$ |
| $4906$ | $393497103302773939089325$ | $5617948681904637439002$ | $393497103302773939089325^{2} \, - \, $$4906$$ \, \cdot \, 5617948681904637439002^{2} = 1$ |
| $4907$ | $1401$ | $20$ | $1401^{2} \, - \, $$4907$$ \, \cdot \, 20^{2} = 1$ |
| $4909$ | $12165098448733217042597100360612188326460959169855150084680319775011277825702423512631542892425581209064381496987460168611374494519049$ | $173627739800963200208721774390369072669151273741441279258971988046604638720745897758119752051570736240339161634844898670297075170540$ | $12165098448733217042597100360612188326460959169855150084680319775011277825702423512631542892425581209064381496987460168611374494519049^{2} \, - \, $$4909$$ \, \cdot \, 173627739800963200208721774390369072669151273741441279258971988046604638720745897758119752051570736240339161634844898670297075170540^{2} = 1$ |
| $4910$ | $981$ | $14$ | $981^{2} \, - \, $$4910$$ \, \cdot \, 14^{2} = 1$ |
| $4911$ | $3190039584182270869003617676$ | $45520927784382943654912465$ | $3190039584182270869003617676^{2} \, - \, $$4911$$ \, \cdot \, 45520927784382943654912465^{2} = 1$ |
| $4915$ | $6221187475960098264534180304606$ | $88738386526606555824270624153$ | $6221187475960098264534180304606^{2} \, - \, $$4915$$ \, \cdot \, 88738386526606555824270624153^{2} = 1$ |
| $4917$ | $19073$ | $272$ | $19073^{2} \, - \, $$4917$$ \, \cdot \, 272^{2} = 1$ |
| $4918$ | $19974008023383465409268741331281462535782285468260901$ | $284820311967795050643694386464022154779472580430990$ | $19974008023383465409268741331281462535782285468260901^{2} \, - \, $$4918$$ \, \cdot \, 284820311967795050643694386464022154779472580430990^{2} = 1$ |
| $4919$ | $1809338099956399320$ | $25797719546469589$ | $1809338099956399320^{2} \, - \, $$4919$$ \, \cdot \, 25797719546469589^{2} = 1$ |
| $4921$ | $277878089217140165411912575$ | $3961207761643162542469488$ | $277878089217140165411912575^{2} \, - \, $$4921$$ \, \cdot \, 3961207761643162542469488^{2} = 1$ |
| $4922$ | $3749130049773$ | $53439169582$ | $3749130049773^{2} \, - \, $$4922$$ \, \cdot \, 53439169582^{2} = 1$ |
| $4926$ | $141107200007309877493451$ | $2010490246189958501630$ | $141107200007309877493451^{2} \, - \, $$4926$$ \, \cdot \, 2010490246189958501630^{2} = 1$ |
| $4927$ | $9476$ | $135$ | $9476^{2} \, - \, $$4927$$ \, \cdot \, 135^{2} = 1$ |
| $4929$ | $707372812330894931945$ | $10075554458769857084$ | $707372812330894931945^{2} \, - \, $$4929$$ \, \cdot \, 10075554458769857084^{2} = 1$ |
| $4930$ | $13405249$ | $190920$ | $13405249^{2} \, - \, $$4930$$ \, \cdot \, 190920^{2} = 1$ |
| $4931$ | $49748176204195649017372176542210$ | $708450747117826514436383929377$ | $49748176204195649017372176542210^{2} \, - \, $$4931$$ \, \cdot \, 708450747117826514436383929377^{2} = 1$ |
| $4933$ | $2851273$ | $40596$ | $2851273^{2} \, - \, $$4933$$ \, \cdot \, 40596^{2} = 1$ |
| $4934$ | $5373125$ | $76494$ | $5373125^{2} \, - \, $$4934$$ \, \cdot \, 76494^{2} = 1$ |
| $4935$ | $281$ | $4$ | $281^{2} \, - \, $$4935$$ \, \cdot \, 4^{2} = 1$ |
| $4937$ | $10816062733669244756708657736279544830864645933167649$ | $153935091410519657068840930993740461240753146804840$ | $10816062733669244756708657736279544830864645933167649^{2} \, - \, $$4937$$ \, \cdot \, 153935091410519657068840930993740461240753146804840^{2} = 1$ |
| $4938$ | $492916139149$ | $7014512530$ | $492916139149^{2} \, - \, $$4938$$ \, \cdot \, 7014512530^{2} = 1$ |
| $4939$ | $290951$ | $4140$ | $290951^{2} \, - \, $$4939$$ \, \cdot \, 4140^{2} = 1$ |
| $4942$ | $82091704772249999$ | $1167744697939500$ | $82091704772249999^{2} \, - \, $$4942$$ \, \cdot \, 1167744697939500^{2} = 1$ |
| $4943$ | $2536632755162363045946362928$ | $36079647922990257956124041$ | $2536632755162363045946362928^{2} \, - \, $$4943$$ \, \cdot \, 36079647922990257956124041^{2} = 1$ |
| $4945$ | $13048546222618475561$ | $185557699825068564$ | $13048546222618475561^{2} \, - \, $$4945$$ \, \cdot \, 185557699825068564^{2} = 1$ |
| $4946$ | $148343995032722065$ | $2109322157486988$ | $148343995032722065^{2} \, - \, $$4946$$ \, \cdot \, 2109322157486988^{2} = 1$ |
| $4947$ | $44522$ | $633$ | $44522^{2} \, - \, $$4947$$ \, \cdot \, 633^{2} = 1$ |
| $4951$ | $1196867545034626391236630027378156811700697649152669203240829573521238520$ | $17009816455766344033980504339896706830474783136086069058188581145632293$ | $1196867545034626391236630027378156811700697649152669203240829573521238520^{2} \, - \, $$4951$$ \, \cdot \, 17009816455766344033980504339896706830474783136086069058188581145632293^{2} = 1$ |
| $4953$ | $31712407$ | $450604$ | $31712407^{2} \, - \, $$4953$$ \, \cdot \, 450604^{2} = 1$ |
| $4954$ | $1674451$ | $23790$ | $1674451^{2} \, - \, $$4954$$ \, \cdot \, 23790^{2} = 1$ |
| $4955$ | $3037700409$ | $43154204$ | $3037700409^{2} \, - \, $$4955$$ \, \cdot \, 43154204^{2} = 1$ |
| $4957$ | $703188740673772626865637347531589723171508240245797027302174942685741833277603015957764466249$ | $9987630083880166005427153931575066647353177273907689914570850356734395450996237946882329700$ | $703188740673772626865637347531589723171508240245797027302174942685741833277603015957764466249^{2} \, - \, $$4957$$ \, \cdot \, 9987630083880166005427153931575066647353177273907689914570850356734395450996237946882329700^{2} = 1$ |
| $4958$ | $120680533$ | $1713894$ | $120680533^{2} \, - \, $$4958$$ \, \cdot \, 1713894^{2} = 1$ |
| $4962$ | $64534808622737$ | $916148018308$ | $64534808622737^{2} \, - \, $$4962$$ \, \cdot \, 916148018308^{2} = 1$ |
| $4963$ | $20938998116180220677497$ | $297223921754943613596$ | $20938998116180220677497^{2} \, - \, $$4963$$ \, \cdot \, 297223921754943613596^{2} = 1$ |
| $4965$ | $137049136293272543311231$ | $1944986881583814333552$ | $137049136293272543311231^{2} \, - \, $$4965$$ \, \cdot \, 1944986881583814333552^{2} = 1$ |
| $4966$ | $3518687951$ | $49931820$ | $3518687951^{2} \, - \, $$4966$$ \, \cdot \, 49931820^{2} = 1$ |
| $4967$ | $1927823273729013048$ | $27353955685257197$ | $1927823273729013048^{2} \, - \, $$4967$$ \, \cdot \, 27353955685257197^{2} = 1$ |
| $4969$ | $1626563562626510213372630040555809763113291152754536940524746193424503264784577289656968552449$ | $23074725371035972004398977389861848538187174778850936550475853344224806309900887804815396480$ | $1626563562626510213372630040555809763113291152754536940524746193424503264784577289656968552449^{2} \, - \, $$4969$$ \, \cdot \, 23074725371035972004398977389861848538187174778850936550475853344224806309900887804815396480^{2} = 1$ |
| $4970$ | $141$ | $2$ | $141^{2} \, - \, $$4970$$ \, \cdot \, 2^{2} = 1$ |
| $4971$ | $13255$ | $188$ | $13255^{2} \, - \, $$4971$$ \, \cdot \, 188^{2} = 1$ |
| $4973$ | $4265535471900611289009776649$ | $60487317983586033353120980$ | $4265535471900611289009776649^{2} \, - \, $$4973$$ \, \cdot \, 60487317983586033353120980^{2} = 1$ |
| $4974$ | $508719712625121365$ | $7213161835264626$ | $508719712625121365^{2} \, - \, $$4974$$ \, \cdot \, 7213161835264626^{2} = 1$ |
| $4978$ | $39932560618831110401$ | $565978212831451440$ | $39932560618831110401^{2} \, - \, $$4978$$ \, \cdot \, 565978212831451440^{2} = 1$ |
| $4979$ | $226684281394164374$ | $3212553311793975$ | $226684281394164374^{2} \, - \, $$4979$$ \, \cdot \, 3212553311793975^{2} = 1$ |
| $4981$ | $16242330303794825$ | $230138918138052$ | $16242330303794825^{2} \, - \, $$4981$$ \, \cdot \, 230138918138052^{2} = 1$ |
| $4982$ | $847$ | $12$ | $847^{2} \, - \, $$4982$$ \, \cdot \, 12^{2} = 1$ |
| $4983$ | $11442628$ | $162099$ | $11442628^{2} \, - \, $$4983$$ \, \cdot \, 162099^{2} = 1$ |
| $4985$ | $16102604768066758034229249$ | $228067578855232998297920$ | $16102604768066758034229249^{2} \, - \, $$4985$$ \, \cdot \, 228067578855232998297920^{2} = 1$ |
| $4987$ | $5118127609762203222991732874522$ | $72475534312996368114299353803$ | $5118127609762203222991732874522^{2} \, - \, $$4987$$ \, \cdot \, 72475534312996368114299353803^{2} = 1$ |
| $4989$ | $2547476030462150856121523889429542455$ | $36066446456336846316033135905094396$ | $2547476030462150856121523889429542455^{2} \, - \, $$4989$$ \, \cdot \, 36066446456336846316033135905094396^{2} = 1$ |
| $4990$ | $475033495955221$ | $6724716207546$ | $475033495955221^{2} \, - \, $$4990$$ \, \cdot \, 6724716207546^{2} = 1$ |
| $4991$ | $1442400$ | $20417$ | $1442400^{2} \, - \, $$4991$$ \, \cdot \, 20417^{2} = 1$ |
| $4993$ | $203667074024198606471219657591775000843039818342706569573269133151983656322740518913$ | $2882305703590826960866276081589618111319978226159758000157512208959750251493095424$ | $203667074024198606471219657591775000843039818342706569573269133151983656322740518913^{2} \, - \, $$4993$$ \, \cdot \, 2882305703590826960866276081589618111319978226159758000157512208959750251493095424^{2} = 1$ |
| $4994$ | $44945$ | $636$ | $44945^{2} \, - \, $$4994$$ \, \cdot \, 636^{2} = 1$ |
| $4997$ | $158413476054522316599$ | $2240977257041063380$ | $158413476054522316599^{2} \, - \, $$4997$$ \, \cdot \, 2240977257041063380^{2} = 1$ |
| $4999$ | $36602597872432826422774598212839995768873090103501521163739417443181640$ | $517690674949038127261225892293391610962526870191086544534450818687299$ | $36602597872432826422774598212839995768873090103501521163739417443181640^{2} \, - \, $$4999$$ \, \cdot \, 517690674949038127261225892293391610962526870191086544534450818687299^{2} = 1$ |