MFNWtKUb<ob<R=MDLCdNVZZJ:tN>T:\\WmDqiCB`N\\@Nd\\Qgqxx`JFmodpsqaTOuToexPpWL\\NfHSJ\\RB<K=\\k>uMU]M>IL`Iva<NBYJV@PH@nb`kI]UA=YFmm]\\KrhsAAy>tVV=tS<VRaJY`qk\\kbYl?mqS`R;HJk<yJujZ<N^<lHMQwxXQQxhywyuwyqxsxnHiudEwhPSyyYYyTcQsgXXIiQeiQyyusyOaTTo=n>LJ;@RZ<LB\\J<DjZmMJhl`<LB\\:=>LR:]J<:LZ[>^<Fj:;@BCBK;C>KJ;JBFZK>[>N:J<nbQ``;@bZ:=NbuUFeSIAoSPTSeLtPXd=YaAktiuBaSZyxwXYmLWcqMu=o_dYwLR:]:>>NjtI`xFagpgrytYXtqidug__xqUopGVtqYdI`e[PyDhudVmCQoDgpLI`oO\\<N^J>[>N:BmacgUru[t>ar^OIZuewgThsHaiDkYygwgboyxqYLqV:Ux;Kxkuy`yvVyEWwiaogXES^YvfgHiwCVydeAFIQC[;F<:Kjs]NXtus=WmxyyYXxATchTuywE]r]IlYqqDutHuQtEkdtleLweTMxmPAmQvFyrvvy`]PItg?^>^bZZ<ZbG^:o^@yn`HceHxYxoH?oenwr?bgha\\AbyyxMv^dPwdXqX^niymwwtCQoixnUgi[YiI`tJx[vqx`XbpYwrqxJNZ\\><BJ;C>CDZUXcgF=SBdSeEQdIiRk?t_OCsaY\\WyqwcF?dPYvVwIv;Tw[isUCWUYZIgaEc>?b^=v=wy=sTssERGU;_fj;dhuX[sE<=R>:\\Jk<YjyTiTl]yxwqmIlJ=lvJuJfIq>eMtxwJPMdywE`qYaNT\\S<]SZQMMXLxYyItYtplFappuLBDJK:BK;y]YfPEgGyGhCxCsBjayeWiB_dZYxjqVQ_cvGX?AV:?GjwiAGSvKd:GsAiUYCImWV<YwDCBK;[>:Ke:;D:;eyCw`;TviE^SBxeEjcgtQy=scMob^arOYgNQwwqdLCyJiScOtZQwmutdwxYOYFqWAmITqc:_sPOSd]XvMTOOs_?V[SXWMgu?TZsbVoS?ggh=gQAbm;gliUWEcMawHgxXiUjWCoaXdYWHwUearmMu:kH^GyV[wAUXugUU=CtSEEGWXQC>Kj@EpQQtw<wmqr=pxKUwHMUG]n=hMDYtdeaJQi:`rvyxyQq`HgiaerFreI^ugj:@g:QjAFnfxaYiodHmVau\\?wfNjMY`hIkIhmDObp_wTfd?>lbPbi?nX?omQt;Ij:gysfc`PePW`OPgZfcuHZ=N]<Q[:HjgocNpcfXd]^v]XoEi^EIqFg`thudH]OooN?gVwcuVbUfgNYuW?cfas`>dgwaYNpSacUoxa_uVh`YirFhukouD^Z<FbmFjqO_B@sanus_asVmYOxIx[NibxNm_agHxxwYnIpyVgynIlA?wyy\\gXeaplhfed^Z>ag^^wphl`Pcdgu_vwE^ypPh_Q_ogwoxi]pfbw`hXxB>[HFl;qw[yqwax[gxoX]i_xixuxWygQg\\`wXPesV`uVcygsnvpXqhAP]YHmbWstgwVV]QgllgwcXmf>nnOfWPw?VlIX_yQxMQwsxvp`r`xrRpZHHapA]oqpqxmhPiuQiOAu>aldi_PgdKI^\\NjHYrjAsbfq=A`QipSyuPOZu_uVhefWxP?^J>[TgZrIjvymI_m]poyylGGp`>efHx:HuPWp\\`eKIZ@x`vgdWWx_yoLyyI>uiweoOucwnCFZcHgbHmSOtJ^yZquiytvqZ;p_UhsdPkq@`pO]jX\\Tw`UpkSIcY?_:?c;@^mhx_x\\OqLWGjuGmmBoIFewCQUvMWtKOedoXgWT]?sNMSCWtlCS;yuumwxWUW_ipegtuu_sEJUDMUtneUB=SaEb?oxgYupoB`Yr;ygy[cnWVgAVyWuBaeWieaig:=FJ[hD;t<WRUKB\\ErHSwt;Xwihumxdoy\\uhdiwgiWdYhS_YVwY`yeJ_g;gcIIrwkdogSUahGCB;GILKVdsIpAw]mtYyevMxCMUFIVt;huOuZsV=]WmQbuKggMtYefDcwryWRAh;eIrAbEawk;iyqvtwsMGWKuFPIgK]TmgxQICg=i_XUNyvy@x?DN[dMB\\sA\\koUXx\\YpQme]T_PUcUysTQe=WQxLMaqO>;Ug[MIiWe:gDJ[HP[xwOToivb_MPYNlDwveRqdWTanxIwpYYNyLytxy\\tsuvwyPDYX^uthdpaQt[DNZlNjXPQytQiMjtU;qojtON@pYUQnAxq<oSHuluRL<LeQjXHmuplCaVttoHetl]viimRun`mpAlriyJy<y[TQ[pY\\yQb]SmAy@<PpIp]Ex;xxyxUGesHQK;DwnpyIatHIX>DMRhOQPQd`wEhWXQK>LJ;Un:DYRHOOHwZMrVmPAuNXxKiAu;uqw`Q[utXTR]LlN\\MpyLRYqqTn@pj@Dsi]LIQpsllYaYmiOdar]qkPuLV=X;xOmtxoaq`pNWar>aJS=MOTk?irC=RRINlIxAqvnxMRImu\\wjXrvEJGTq=AV<XpWLwALLA]SVIJldoHMQsiOdiOiEy]dkRhl<uX]tLv`wSQulErFUj?AXNIOUHmgAotdPLykpTTu\\wt<u><TRhqVDX>IL^uksIwIeYDyqHHxHHXyqvMlSF]VPTNbuWZ<w<hkR`O>LXHAyFaTeHlmmpMuu?MJ;@nm<x?xwwLVwpKAhWraSvYymtOtyn>Xw:IyTtnYdyTIYSULsauHTxsyVVTYJDlFtxwMm_xXdtomAKbTPodP_pjwTXV=lH@P<HVTHV?EJIiPCQsmAyayX]lQcDUk<UZtQLmK^UJLExjqnAitumuwmVbqjwywqpq\\pYruuI<s>\\yDXOh@TAiMq]u\\aNZ<td]LlEMYYSYPMwArO]prIpM\\Npuj[pQ<UNAijLTVu]WfavkUvmTQ_UXB`n[yS]Qx<@X;HjRdlQlwgQTkqxMYJwdQ>QmaePaDT^yQJYTF`Ni=WylLlUlNxrfxMFUPnENSdW=Hk?XygewFewiayXEX`IVGXPMdQyPS_QRSMyDhucXw>ys:xUJ\\tJ`uaexNik;ItB@Q<<Ltyo^ILY=m_@VQQnKAk?elDerd<jPdmveSgmJQywZXjHLTY<qnQt:XpiqjY\\WZDvi`Uc`ndYQnxS[XOQLuiESUijAiXRmUppq;AmCyX_UToHNIhutUyrDSwLtFixjPX?ilCxv=ms\\HQZLlXmmUxKtUU\\QUOYN>LYuHXuqsKLjTqXohpW]tvhOeUxilWHQvXQYXiRGAmqXxwtV?LJ;ay\\LsSTyMlK;DRbQUU=uT=QcUvZ<rsAJHYxjTsCxv=@J[eU>Dv:YYSiUqYoXYQtxj<al]iY?xuYUpFEtS<NMUtMMonTU\\dK=LjN@rQIqLmuYpq]IQJqVjpj>\\N=\\n<lQ[TStQyvMV=ElodpGlSVuMY`X=LjjHUf\\Vg\\qYExvynXPYDeQyQviYNeAYgitYXTqpumyOELQPLu=UJ\\aX>mQQxNgtJ]aj]ykahM_=W<=ufTwCxrYdTalmjMjMAy_Uo:hr[@TsulHlVWMyq=lVpOiutx`vf<l]Xvm\\pJHn]asvQvlQrw=UjINZMNiHxcPLgqxUQx\\XYn@p<YX<IS`<puLs<uR;YMbend=qc\\JpurKqWodVcps?hOHQY<`jg`Q`iyrmNApQ@@x:Dq=lV:=sQuuk=rw=ywXOMeK>PSpHlDQX_mtqxUVXOYmNPWZ;yjUqm>Ffiha`?^NaleFpoWbXVnMXl;XgB@`?PidiiT_h>N^NxZ<P\\xwb>Qnxqu\\gu<gkGW^Nnt@?_qNuOVvfi_ewtLFwJi]MYnBq`qi]Ihlvxx<NoPxfWpae@eui_fhe`^]lfoUH[KAaBQqwgjv_sv`xsGjxHtaArnaZtif`^pY_sl?wmO_Gw]aFwYo_Uvka_soO[Afww`nM`scN]]Ius`arok]_ceiw[XlN@pbQ^MXtmpit>a^XxwofsIgXYgoCnWw:ueE]GnqiAywtEEc[roEG]QeiIW^whXIIEysBMbbGYU_vW_d`mslAIcmrVgDBLQA<L`yLl<nA<S:]mc]XXAUX]W_ivoeM[QYkpLfPuYiNh<Q=]rvuP@HWvMrhXvxicxOmxXwlfhR>\\SVgZGsLhrC?brwfHNZQpwyIh^Idy?buXqBVdDytYphTf\\<Q]hx\\fVwGn\\n?o:AbNc][iZEFvMWmYt^GV[qC;ob_aimyGNUR=cYd]Vf]UGkxqiBtkuPwDv=Tj?cAev?gRNqh:Qbosrpgbm?gPofact]SepCtmqhIsCMeYk?heYbRgBD;CRuiVay>=fflKgQuYyuieoUTKylppEvtArF<KIqm;@V[Im<DqFqq\\pUvmysdPdaxQLsq\\QV\\T_LrqHJQITx]KdiLetKF]TalME<Oi\\jH\\pw\\t=@sYuWa=KrEToUJJyJbXu=xKw\\vYUQdAw]EwXpUA=JwhwpxYhHsQlnJUyfyiLNgtYiOWt>NmFFy?`jIW`XicKyrs>jtxmuoss^pmYmEi\\dOyXNZ`ycxOxyGgH?woAtuisFpq>p`AAms?w;ymrytRWt<`yFqhsfwnYt<FikNiuhmnxpYq]B>];YhZNoY_sxnMoFdQw]]t][gyEFZOvtGuh;wYidekTJiiweROUR<=YH]bGIG^IbGEd]scvKtYWD?uw_[xLYCIYyKefdmv=YdIMtRwfvkTgOfkkrHobIaWxifyYEDyC<IcteccUVY;bI=DDiClYvQGxQsS>wsUyhvIDSWSGwSPEgFGWaawxuBf_XCWbmsWqKWmqD]efOUxpKgIUv`awHItksvWYui[F>=FbAVVyisIIoEucuWF_SM]wHKWZEVdcxZygXmX?gwgUr^mg>cC<GGByWsEvqiHx=Ej=CAixusYxaGWyx@iD=_V<kB:UG[eu^GbIwb`sx]qyYgyh]rqCg<mIa\\YyAsJYw]Xn]`pxDxutL`@uF]M<AjaaQwatMpqfLqQqquYy_epKTMwiMIIjU@nWmtwiRjqK_]xnyOLMJ<QWymLnIJbeQJASJaXfpXP\\tu]qeApIxqfQpEaTsmpVDmITmm@NYxsymytdX=XxyeuSylqEmkewFYpHQTaamumU:@Q>uvoipNEYGIlEPOG\\mbLN@hmAyUwqvqDJm]mMmSsdrsIpN<L:ENNqksTkr\\TbmpmtNr\\pe\\Su=vE=nQxJ<yK>@mCHxCdXO]rwAoIlX_yoVuqXINYdqx@t>dOLqrGXMctYUiYQuUwepyyYnxr;xJxpTwqN`pStqKb\\TGxXXIXU=WxAJxURXALJYr>hufXN^HwIaRU=nwIvRhVPImeYs[@X;MR@TymeSsDPnLWAIuWiOkmUFlkjip`esT@RWHx<DPiivx<rh<tOxYspQnpMbypEuQrEoe<XemY^lOcas?Lu?LrdAshHPeAU<MQwtONxJ<xoXyrpHQ:pYkps;tSJeJC=q]qsuLLoIpgmQKpN[XOYuTyqYJISADVq=namsVLKg]RTANamSVUMmtNjqM:Uikpj@Q\\mo`GairvtcwbvX[:_aoQp\\`yZVipxhOfZl>oFq^hVnxvgkq_EWaawsmovfNsbWiQflaO_GvsUqfqIwuw_x`ncXhPC>SC=gU]YvC_HZ;YiaYsquyUFLQD`mgoUuAosZKF:_hr[CJuSAyVh=e`mTIcgy?cBGSRWtroiPsY_UrIag`aVBYy\\ihAUgqmEqQi:qRQku?yhVQXEOixqriMyQAV`cXvIHAWtu]w<iXQCd@]Ryuh\\AB;]iyAvIIV\\erliIbiEsqhMuu`QspUTMMwMwevaDwWEyToeayHXyXiXpIux`KEhX[ItGUM=lLQ<rQhMSqlCDKpLuZ_f=iiqIqUFliwiuWstYi;yuPagehynxnlNvW^iPakvIrKybANtmXntGul?mPos\\OZ]WeJihZGd>QrChe?guhQqSHi;`s>hb<ItYXlCHkdfj;^kWasWXn[av=a\\ZFhR@]po\\AiqJqo>AvmIy>wx]yxIIa=n\\dwbB^^NqwOahKNhrqqr>xhaiR@\\]WgeYahaqM`ZYnoU_\\ppgWQc<pdNgmKypqwUIvQwfsMEJ?Xj?rn=seqCCkwr=TJiBgguWGxHoi=WJnISNeQjYMVTuAqnVeWCtsO\\k=UtKmYruvB]vR=roYMi=qKPxDTNYlVy@VQTM]mSYXJnXx]IKd@wq`nw]smIOhxQLpxiySVxkXmPlyOjmv`AuRAU\\IQ;ppWpmVtSNyqc=Kc\\pDETiyLJplnTxPlXCISayUgaqg`pfmupTqIuqqiuuPmttV?LZ?HZvO^f_j<HjGg\\L>mWNx;Fvy^_gnoYxxOYiWieyWs``ZxwpKxZrymZgcBVt:@`<AsAvvwGryQqUgiiWtiXj>hveveKw]yPxiHkr^empymNwPygyexSXsybNYFIgyLOr_qDnghSSe\\utyiuoQwnYhIyxWGsiIieqHoYduqiIuxw]vLyIaKdkqeEwIFEwZaXXWXBqCB]BYKXfwWbYxo;WJ?xXeRX_SL=R<?xy]d;swMiwTox>CWUEc?st:?bv=RZktQkUbeIj?XlWtGowAKBUqHRwV?Gy;?eECHYybWwhmysysexwyryrykCj@UNDp=dkWmUF<UU=MDaPseowdvNujCqK?lsfDsUMvaYmIIs@`rRyVLPRHQyH@LlUugxPAlL_]lAlvGTSApJOYpIqya=NHyQB=KUxXj]pk<mhAxwAWU=mTAlPMr;AubAotqywxxtQr>Lt[dQFyOneoNPXXHK:aKAusE\\vKuwAAT;YU]lUR`mryQFUjnEN@DyW=Y[iJNyu:\\S?]xWAT^hUx`YsdlGDigW`GGbUXx?qc=^cq>nSH^[xwpxiH^aMfx;qk;accfibatdhtIy^XXvM_hqvvsOyrvpKxcdYia`qtWimWyZpqqputWgZp_r^tmaqqwqU`jgA`uGdP>gknjjvZZa\\I>wsGp:WsIibUNfQ`jqvZFyv\\_s[_aGgsNPZw_[<^tFpapH\\cVpyggoEFitMwStCsQ;hKqHRWejSElsvNYIHAI=exI[CRUxsqxqmi=MuNsvg[drmIZoEKMrpoeyKw;;rnEC`aTR]efUxpigieYeCIlWu`iGXiSh]De_SdGIEMET_UvqR=UHaiWLoIgerVgDBLu=<LVyMXeqlLYMltsuLhUMX@NGyjH<WW<QIdQy\\RtMpSPO;tTYXqppj>=vX<c<a`Z>iYIrfYs`AnhoayYwI^ahYm]GvWik=FZ[hwrqsgvpdHnxqaDWhRInAPyxWj=Wb=oy`@uYyigqZDw[yakyxyux_@N^NG^Wnw=Qiwoy?wlrynVXbMoisybyNwL^pyhyUOqHNpminivic>nCHj?Prunusoltqxqpq[ylcQueqo]VtU?gR@fHQ[nPdmItP^Z>hZ\\__JOaZ>uJIrX?kn`fRyr]Gp;@xYG`poxj@j_Oomndmv^pvgZGjBV[YYmYax`fphgutHa;arKNuKIjro_fqnMav?FZYwuS`quqsUI_i^[^nhBOclXddWug`fLPru@uMVv]GZlpb`V\\H@lsVdhPtHFyxYygyb<H\\p?ts`aJnoZox:`aZYr\\XpT?[k^^B>ioIwhIw]Xbe?f<^rII^YY]A?l[Akw>p=xf[Qj?h]@HuqFdoOtMAjfObr^t?@]VNsAFvEhp^?pO`y\\ylx@oxnykxkuys>iabVmxamjvrSo`INj]IyNx<IryiX[uBsQrY;fX?eRqhxkb@AG;_GQUR`GTH_ghGB;?TRws?[BigxeyyDIFPgyXIf?eTdUYBkXfmr<_hroThcTd=SYoyVKE=mu;eRvkCR?Veiw<iWBGh>mSdIFceW:uE<?R?exk;XrYEHOXtAybAuxkCeyUNgs_kD[ix:OgtWguwrYIwAWVtoUpmeM=wuGUigwJqItUu\\mWv=y=yE`oh?Ee=qv=kwM=Xpss>chKCV<lwE\\u=Qu@=QrYniaWmqX@YPAekTxprmODyl`ms@HWtdxk\\LotWkYmXynYMylIPdYVQxYfpwxdRydp\\msD\\ZgYZM@eR@jZqyiysfaoKaivoxWw^M_ZcVxt^ymNrB>stXlPWeG?qZosSfn;FjPpr>hwsAyxasPiedicHFZ[W[Y^qYFmv?`XYh[YiNav^aeXxavxyApac@j`Y^f^ah>cBniAOev?vyyZLAnAO\\>>vuynAvb;Igeiqd>]GFhSqeEIsnhgxh]vy\\NaZEp[O^soGyXVyVIb^A_=@pPHuVgsHOaPV]fqxSq\\hVuH^`lYZ[?RORJAR=ST^SBaEhtStUID^Eb<uDDKRmQr\\GW^iBGYbxWcB_iVeW;eHPUiK[UVYHK[v^_SyWVQWTisCPSVJwChsSx?tGev=?b\\wwJKhssCDIfusCMgUqWhrWxZYFAQUA=y;qCqSB^mbCAFpMtmIy<gxFYcZqsywDH[HUsEoQCrEyOwT=KRK[wfIiv?GQkFgki==F>yWtAY:otAuHoKh;Sib?D^=Rx;DxWDsIr@cY@IY@[hAMIZYy=?gukv>mgAUBLsTymS=OheYVBaFdASmYfYcyb;TYkuWwRY?fYAtp;wIeU?SyUyuxqHJqs`Cy=mI^[WQ]UAgVngH@QDlQb@;rXot[kt?OR^MuyAYvIXy_wvaWnYTNuEMAygQsLmYQwYlYTocYFixjGDckGU;B\\oDOmHraFcIYwSxeyV<siMCW]GXLwxUqD_abpGRAshgkYISeI[XWYuWyvvQf@AGgmFrKbuCDQaGy]urUx`ai_qiaQH<khsUs[GYMosS]v_UEqOyRIceYTVygqIGXixoqxccBC=SjsVSUG];DBKIQUCl?t:=HG?XG;S@QYpwRRIYY[YWWba=uf[EZSG\\;u@siECY=uBTyCwiYhUBnSrBurUOIruyOaB]AsSYbm=e;ASPKBEKS:=hj?r`gUY=U[[bKWDrkDHuSBwItAeZ?V@?sf;EBSh@OsWqh=cS<eU@iU:YXTIfy=UZiW<UDDYDSwdq;C=CYscVnSx<wgDSCP_iU=EYqE[IWVAUMiUoCdA?FvGVaEeEYBmmBnWwkwrgGgSiSIsD:WhoSipIWpUwg=x]=yAatU?cOWt`yCvAyxABkOVMKEWagDwi=aD=uDlGvZUCMGdSACM[C`UytIu;[UI;DBqtGGxrqYISwUkDrAUmafuIS[ir>YV<WwLWxBMVZmgrcW=uteoXlmbWUDFyCBcwVqEvydCkcggCoyvTQtlAi\\syacsKKUiYVpCgKYyRWy`uwwsdPaxkWS\\Ws[iyUGCXgHKsTpcYA?Gd]emUu\\wERqePahmgSlsEvay<MyuQfoUwbmwoaXu]rAIWQkWU_W<KFUcHPQdHIUHDtvhsPqxchWXqPNynctvfMlpMLB\\JgYJptUDMXWhvc\\y`xYZ<w=avcdsmDXptjG<KuiMaYJ\\MJIqktmQu<Y=yu]yOxQv]\\LOQspHUlhY^]rq=QAHyNqyetKF`Yh\\OX=lH<rw=pJHtCtkUAWkYMcHSHIoeEKSYUjLxKmXILoTlMS@KjPRRipOhX;QSU=yGAXvhvl=P`QpGUs:qPGiRglWipOR`jsylnTPiltbar[LU=LTOEU]En@@LDqnslnjej=]WfMRLLt=akCuNpLymEtaDq`lO\\IXseTbuJvtLZUvR`o`EqFayJpjUQMqQvJ<rfxOZiVghYaqyP\\WepTYPTWakp`rhlQpEloylDIrAtMfykClLZaW`TkFPgwiZ=V`=gyJg^UFZD^kywb:sSaUlGIhWIlsVlgHw]EPqIhihFeSYSRmsTc_V=UsPktYoHYoGqUb;ieAqVF[XRiCiiyTgIcEbZYRwAigessWriAJ<]XL=VhpKHlKspQclRB@VPQKkYpKuMnyv<usUUXQdOxmu`xwMUurUWQXl_iJ<DrvQJ<LQ<]wh=yNIYnqovirmyoLIocAXtqS=<WTMrf\\M\\`PZDTsiR;LpTIJqxu=mKYAQvyK^Ev>YvHpnoPMltOFIobpYUQjHuu=HPaYX^YxsMUu<Rf=jgXupHt@ikXLVq\\S=LLZdUdEVplWP\\k:@xhepXlYQ<rHLMPTUP\\wgMRODmP<Q<UOUyVAew:LRJUpgAJtxNsuleuL>qL^il^uRkDWTdUj`Rf<WQ=RcQoctKlQjglPiAKl@LEQr=tQEhsm<NfEwHxytHUVUR>UP[]LXdUrpvWxSUqW`tkAduxELqqXsTLKuuwypCdmELRnXR>Lpn@Rw]xxxjJaS^lqLAyHiRmPsQUmimpchYFHQYaktQmUhL`]Jl\\j^\\VyQMq\\thmr]DNd<xv]lmHUauSjpvQqR>dua]sphuvhRwYUWyns@OMqP;@RJIx:=QVUT:xvjDq`iX>Er<YqRTm>uLwUxxqjFmp<quWixb=Rr`s`<X`DK:tQH\\RxPjIDNBQjE]RVMP<TLd<yl=ra@TQqrMXQ<mN@ULgHUe@NImqydo@\\nJhU^]J>lXHAxyAYTQvyITCqTe]tMMys=NJ\\rZuYw=vdhT;Xl\\hWEhL>dpSTssHNhQjRhoW=LwhjlHqsEo@hPZ<JvuUn]wqxxXmtlArvIJfqM^Xj?XLBlPtajmuKO\\OuHWvDNELmN<yS<mkLnUEOVQTsam@LtYxrTpNUIkOAMYTp_HuTHx:yt]dj^eWQYYx`jSpR>XYqunQiwYUtF=Kkar=AnUHwSXqFIVw=lN]kHTW=Aon`o[ESMyrOPScdXYtncxJahVM<NrYMjXxplmopYwyy^LT:Ilj`usQToiJyIyxtW<yPc]wZIYUQwxdsDIMZLJ;ur;tjqIRruS<mNJdJe=Y^mn@`Y>hmeILc\\y`iw\\yWwLMJXUx\\YPPy]YnPEoyeY\\<yxiUk<QaMkDtJkYrH@QL`sGIp@URELJLAjI\\mBINyLN<PoLquIHp`Ax@DRkpmbmM\\HJ[Ml<DquTmiqUV]J>xK?Ut]LQKIyY<PyMpflYfhYZ=rx=y:MQjToV@uhEQGLmSxTLay\\QtjXxfMT;hnJLplUPsDV\\MjWaJ>mwDPQ=@VxXukLS:Lp@UmD=V<Tl^\\NhUOdyUIDK;YS;hwfIlAHuqISHaUjIkjemu`sGpp[]UTAQMXRUYQ]HU^ukMqvlmo=`PvyOnAsk]MpUMgas[eVKdmiPRKPr`UWBdyv`WTaXraqgeXYPK>LjWYMh]LfxLe=sDlKxYSEpVtAj:Utk\\q]uRGHOR<kCIQEyUmtRppxYylPQM>]O>=vW<lK\\mGLreMQFIpZYt;LT<\\kImS>mJhDJ;EvoTKT`l;iQPHULdNjIJCaO\\tMJ@pjYqZejtqwg]LJpK[Ysnur]IynHjheRxEqBuRkqvNxjoTSJ<Vjmp;pY`<J=Dt;axjmmEDtHHTutmSaJaMoRESiMr=itb`uOQSUak]pTEDVcmXSXtnHNSywA]xI]tmUwcXXwLMJLK\\DTh@lshLFqojmqAHQhGg[ai`or?v\\V?bqAmawsnP\\uXrvhgowmD^Z<ps=VmcFw:p`=NmKV\\r>ni^_I@pB_dp>b]OtFw]JNipqmEO\\axrtHr^_ZiagHVqUYty`rqIw:Ib;@xCFtIwbqFxDqxgqy;PjjI_;_`gPmb?nC^i:on`Wsdxhk@\\Jn[yXyMybXFoS?wMPZcGpuodHHamOnKBemhJwtBMe`]dAwFVKF_H[whqS?q<HsC^jk^]pipJhwRf^f`dfvnDyjsFeANt^OhCYsWa^AwdNh`h^Zm_l=wgpVmcHxoO:kgrOFKYx[Od_aY<Qy\\ccZ=e`gC]awQUthqdqSTbmtMQVk;b:wcm_HjmYIIUaaiUyTMWwm]boOFrocJOhfAgXQWLKhu_sUqTqIg:=FbaSRoyX;FYSUpgt@GcGOt@[f;keOYuuMeweIhobY_bHwXRIBc;c@oi;_D`YHBEfpeI<Khnucw;wBcBrqb:UC<SSYkXJuhPYrSufRUU<gX:CVIYWBgTFoB>otMOxfQbnYy<AW:]E[_C>[FZAGMuBZuxFWXs;GfugQpW]<RALpjptb\\svpvUUJ\\xmy@Jj@NEhMNUTBHvMhugMjhUnBMThUPDImIMPt`w=Ytndw;iq_\\St@M[AQFyY[PTcemtIPCHsLTyB=uVLY=QuJDnchWxyQ[=rExWp`PWlyvAlxESTqjpMVOEkfYvnTq_aVLpRTqsbEJqdo@\\RaDNRxORxPiHUp`kN]vrTj\\Isatm^hkLdUe@jt\\Y^YRQPoUpWtFlP@omyfLW\\PWsR_w^HiUawxfktw[Nqng@_;@bjXiu>adgn:>ZVFjC_b;_dZfk@^vdXqX^cWxyqo]TagooiA`gTfn;FigqmoPq<@pJ^qap]sPjxQv^^hrYayxx\\Ycdo[\\^vG@irI^<@bV@i<I[daymvy>@cBixqr^WHIoxOasr?ERAh^UTf]fycyFwXJyxLGS:MVn;FJAfFesPwD^wcaie:?T^qEaYHlkie;hjEfkIr>shuccD?tZ_yQaBFEFRkyCuiHmYSqgfeUu[W[ubk_Hmsg^Gy?me=Kvf[rVcxdCCsAbjMc?seC;DEkHrSw>uWqYWiWihmGlAeQoilscT_fV=smQfpMugmV:eUsaY:=DmGCIqhvcUU[xVUTdQWmiSKYr=sRqWRh[t[wDHMi`wCNwGrSEHoI>]IGsiMKISQiCMrS=Uy_RowHAEceGgmmFWorIkifKSE_BO_HySUSaxn_wRiSQiexOX=quP?s>_cIEIy_wlWsBIxYuxwGbsoDnkFcURjqd=qHs[iMStGyx_UuHYulEi[aI]Qyn[WvghlUt:=FJ[GfCu:od;CvoeSZiuFsrhUtceiX?WREVHSwRUT=aHZ;uvsbC]tOyvhgCVyWumIvyIR_WZ;RB;C?kHSCvI=cocVruvBOy[iYy;FmYGJ;cEwuqqIDUCmKgIuUkeFwww[McoEw_swMuEr_xLMIBsdGmbYcYnyv^SC]yx]ycs[enKxfMg?WbTexoOfNmhuQibQePWuheiSotl[vIWTSYYv?W]UiWCB[cOaPVb=y:UVVpXTPUsPV?]nZIk?uSYIX]hM]=m[EYppvpnhBp]>heDWu<nf@Hl^hZKIq@Vioqf`i\\a^gcixEP\\vA\\oQ_CGiVYl?X`dqjUnqdylCv^NVrcwuvfhXpsM@_Q_uMykeAawYqKPacEcARSCFrIw;kB`abRsxFodtMrGOv_ITbovVKiKQeCgVUSikmFE]w=abQKcH;IvSw[AgAKR\\IbUgwmcHMeFu?TwAVAMISYI<=SpGWo;wnWXEUISQuj[Ggse=KvLCgVeSYsEs]vKGfw]ckUdpwcMAya?XTUHFggMYVHYCv_SmIfBWxw[Ig?CBcITITqIhZASqMYBWw^ysi\\RPExf]quLulmu`QUYynpHpSasGUJ;@RjtqjhRvPY]Qk;AriAN:lPG<sRarNDW=<vnmW@EbP@kR`^<FivoxWw^MYqEB>qTHaiamSwEySsW`wiqyWxmGn[bjIUemUiyU=gRFKfXExS;Ft;RxkIueKNAj`HM;eMiMyAYmOypyhxGdxIupYYnxTpxQMDDvEAVyxkIaUxINoEvtXk<lY\\<xYerTDrcMrVhwIEQ_aLtxM><KYlUQAnSujYXVHepKDJSdMWdTi\\qrQVbIo;IV<LLVPWn]SHHqqYmHqvBupg=YaPULYUnajLaod@Q<YUxTwt<pHalePWdMWd<XX<KxqQuhVEDYxyTuQYNqokISLambArcHwAeMw]odplu]T[XYHqYJ\\wMarlivEite@O=ULmQMjQwmLwF]MmtqQmpiAxReyJPmSpmppQMXtJTPqlKV\\vlaTDeRt<l@yOIAsbdjRXtGqRJyWbtnsMwvLxilLEPoyxtGtRDHKHpXpDjt@NImNEDSLirOIOQhM^Tqp=oyasm\\T@]qkmpn=PrMkoLw@DVEaxQ@R>=nXquXLLPqUSqQVUVeEkl\\wnMwYEXtYnJ=OrYq\\yOsTVTaM]XUqpWOuOw@xvdUIMMcAW^urpUwoyuwtxfdkImMAlqZevKTtQuXthxNiy[@xlARw=w^Gm;vng^utVw^Y]KGpJxg`PuAOuYNusAxTYycynX`xqOwkw[N?qbY\\UYkBfw<Wxh?fZ>`xpjq_wnpnOYuJxvcNtTQuUFd;OcHoqRIj;YpGqa`Iht`rcy`WVq`n^cfqSyrvnp`^mYigIYvt_xpwvoHpp^]TphSX`pppuffRqxuy\\B?`@YxZOy@pxTpnsFdnI[lalMqy]Vq`>w^Aiw^eiNs>pq;Yh=qv=paHHblnb@wre?[=ApQo^Nh\\iy]yqyWhpiYstwvgOln>^@gnSImJIiEPhaqxVOwqIlgxcgWxpHlxf]dyw_vrJOnApsvh[UXpUwetGdgQ[SwgfXgTqoWOcZ>\\Fy_Z^my_xRhndIocHZo_bk_d_whx@opteMxyuycIhxiHvWduyXGSDC=ryIytyWxyeuGbkOhEiSIGYyQsZIrnYESmsbEy\\ywDqgKehCIdM_W:MEbEGXwuruedsEr]eYmdGUeX]Tu[equCDAclOwIyy_yGX?xiLxxHYaQmUpj^ImauPsIyfTUTxKfMO<Qn;tv:@rdujqdjkqy=QY<PXyTpsylPQP<QOBDWJuSweK:hrJtuuhvqtqPUUFXyZhu:yJrErKHRjIKEyyEpSX<YiTnV=OM\\VQyrYTYfdTYPRxyrc`w=TJ=dsa<NJljZ<V[inIDnAaL>hXutxVppelV@mq[@w<lsY=KDpn]dN>HjSQkMElx@njLrapuP\\qW\\UwlkvDK[YMqLomhM@qlCivOuWYewhhMtlKELQDAsa@V]Er@QvGhJEuOAlSQumddlWLXK=TwPok`qHmQcaNqLp:uWYdw\\mLgTmm`vj\\ThPTXeUsQjMxSgqobAt:uM_YjpXsPUs;DNNdv;Yp[APWYmi<yuXjrpTBIMaPKipUguMrlkJhlgQOrix;uuPLXwdP`aVbTOBDNaXwp]JJaYPqUalSQlTaloq\\tw]n;IsGaJ>TQviq^QvEhupHRwhqk<roURShXleju?qpWbg?uOXnkit]GkkikeAc=XhM>m:@fvVw<V_MxbTvvHYpFyu\\v^MhvSXspQeHOrtwp`AoF_jTIwMIwSH]dv`Hw_oVrKW`[>sufgRYuQYo@^kb`eU_]\\ii<X`[InGNvxFbuw[nqZUY]i^\\NIZkoqEGqLgsr@nknvB>is_xap`iXlnHfVOeNIZ]anUg\\Nah>w]aYx;w^hqoVaodi_^YgtA]wIjvQqVPaAsBiX?ydGiSUiwNGTcwfoSUT]siwXWgYpceFSeMqSZqG\\AfEQVk[XxmbGyBFgTvwtJuRtcgVCYOcuqmbg_SHuFdow\\uhPqbpescsh?MesUcnqhpURTkgiSGhKraiWKOwLytMGeQoI?ayByXqAy]iCmqHhms\\gGveWRAtLOEM[ilwVtkhIquuufLQeC[B<or;qt>YWFYw@iHwyye]WsabVUHiIXwYEducj;u]ihi=Temxn]vGYRQib`iEoayTOHY_XR]XwGdpAi]QtqwdqyD;oRLquM_gykCh=gyCtx?uROb<OBiAVUwiD=E\\eXf;tv=bv]GYYWiKUF[SlID?Sx?yIkcwhQywKicUVZQI>kgCIUQaHEsxbyxk]ermUbucrKvB?rw?V??DbAVhIVucsKsi=?HZGdVUyrQhTOekeBk;dQce>cdvsVpMFvCCmQeRoe[Cr=asEScVwWHEdj[fegsQ=bQ;S>IW@EyJqTF;CG=Ypac];s\\aW<GuSIEokIocSKcCXkycyS=cv;Ue<=H:?RdwwtOi^Kg\\ihEaGOiCceW;KBFAewivJSEj]fUceV_x\\;R?uCkKHWEXDYSK?Fn;XsyRAyFWQXssEvuHogB^;sVCX^CCJESFAVZMt[mcEqVCCF[MgHIckICTIw?yVaAwROukWWNOvuUfXYi`kfNicq[uR;SIKRWMx\\wV[gGs]SdiYIyBrmSKHND]x[xwOdLr\\uMTQtAL:Un\\aYIAW`ARtayETwYmW=AqBYVfUYDpY;yxjpQXDMUtnkXkIlrGpyU=nIXs_tQiTumxVL=y?\\TdlW>dQ^ipdetVamZMXItQoLmMMUUQV=<J^xuVxvVqNmHL`=TbXNGisRPPciY:iX^PPTTxPTxXlvj]TptWXQvwALQ<u]`TddjyXwWppIPO]LsM`nIEtHesdYtLxpK\\TmpORmvfTWO`jN=K>Ljshs]`MS`W;Uu;dkDly\\YTIIWaQJuUy<XM:XN:XOfausXPkxsc]o>qrfpnS<jtyMdmxahKu<VbePZ\\qcQRypqZARBTV[yLElQPlYW=VbQxpuLgMJBlYyXvHYQcEr@@L;Lr:hJlUx`is;tjL=Kq=tl\\vvdWH]UXULHQRGTl@<uUInxlVX=L>DNrlTvtMOPTB=wR]UaAX<IVK]UR=M?Emj=TGpkiQQIiwLeTTiSY@mR@jN\\S<eOVpm<dvkqLaeQtPLpUN[MM@Dn>dX;mMZlVYuy@yPdMR\\Tnf`Lv<rK\\OR=vd@UvYMJxLTaJY<K?mptDwoqNgDUhtSgiJoPN=lxH`VhLvBDwJltwEjWIN>QYWAOl]jm<ykXjD`q\\ajaanbxr`pu`HJ;Am@qWgtYjyYv=LYYMH]sBpn^xpo\\mGAtP<oITuKyLtPX>=toYTLEtq=Mq=Wa]k?]YjiMdLWwulSTv?prImPV=smHLm@PldVgYsSQT^UY]xUJuM^HpoIP`YN@qOx<MiDXw]m^`SC=kNTJdXVWtXwuxu`PPAWHEYgUklewVTmbhmaqsrDruUnNesRUnG@xvXRWDpK=JlISwITGDNiqrvEpK<YXxpBUklHnV@YadYeqnU`o[`sktNsmu`QXsTWuExVhRTIKiUL]\\lbDYmqLwIVUxpRAW<eyZmX?xS]hYTHoPyQQXrnxM<DjZExZal=ulMyvIySt\\syqq^xpbdKMaV:XOv`xlYsXYqpPLE]R\\eSj@VaTK`UlN<Y;YuPDQW=omtXcqTW\\ytLL\\=WAytB@L=YKBdOr]LK<oN<x=DJJLvfesUxkIdtHARb=rhHNAEu<qO`pOB=pSiJPlSR@j[Im?@La\\SHYK`YJ:hOi\\wZURZ]wglnFHUgEUnIqxAL@EpRuOYyVyLUvHUBarmHnSHVuuQphLNYuAXs]`M;yrnDVupxdysKUY<aj;uqQuY@lyIdo=\\wGtKxey[]pEMu_EWX\\nuPwdxqlyyI@WIDSNYYbytkHpkLQyERQlmKdy;hWWDJB\\u`INe=KX=jWMt\\XlAxq]]KlTWkdm<ixLuXKpJweN_qWsxOJlR>htodjp]lods[@Xjmy<PkPLJdAt:uYGuu=anCuwQ\\R;AtUyrVTkriK]ijlAkCdVDDJtDkwlnXqjC=vLTmfxtAYTkhYfmt[\\oIXnnXPtqqD=wR=RxmSTqOIIoJamMMyVtKUTYxaQIIqxLW`ay?aY:=wVeYx\\wyPx:MNdppWMYNHoEQRZuN`eUGUjxay^XxPLUAlmq@tnMmKTYKpvDXOh`KNHLiYv^dyU`XXqPTyntAuFXmqvhDFasNqJ?^J>[`Y]JHrY?hrVZfNGawRaba?fBEFP?Hgsc<gb?iRYIe@WTZGwyIHQ?uGSRCYcFGS>=hM[IocI?UitOy<oB[ABE[hgkdkkXNGhesD_[C\\Et?myWmeyGBFUETCsEKRC[BU[dYOwYKh=wb?sD<KDaGGS]yH]x?EEWWI`ACyAUjIR\\aXa]YwKR<oCV;UA_IR=tt[vJWR<kY^[YrOeH[yhmI=Cy]QytyixaEgQdP[EleTlMkfYKwtOJhqOELoMvkDTf\\XcHOA=O=@V@DNVusiLogHlP\\vr`v_IlB`S:Um@QRF\\p`mKclklTO>@nRlVLIl^akI`P^YvWtwvTknLJ=pR:uJnX\\CYrkvywxipyf;piCVgYnw=?[^gyHwesQmDV[kproQc[Pd]^u?htu>t@H\\cghlPrw_kppcUyrjYnKOeYv^[>mCOs``mpGbsoHWvNCS^CSuOwmQcocTBoBO=T_epSTwkUx;\\J^lmjqswxyJ<V:Tx<\\nZHMmqL]INxmsd@tqELyxoTdmqHWtatVTmkUXPauvHpwXS?LJ;@RJQMrPk>tviPmmDNqPsJUxK=Mf\\JMpuhAphYO;<rpHME`kimq<LL\\ImUEnLLy<Yr>`rnDmZekDhsVEJHAvR=xf=r<aK;MJudXJlNtaPGhjgtOV<LMtlQtwryxeMww\\wZirS`p>en[iRYXnWDrFhWwQyyPKRpQ>hlALjE\\Sq@TX\\tCtuKTPt\\wX]uAxu[pm>DmdHMj<ND]VLYvpiJ>DkjpPC`oiHTQ]R<Mro\\M`XjluJBHWBeuJpL>EL<lPIhLXtOKpXZQuRTT[LrPdUAHmRHlITLLdyMuOJuKnhuoyUwHtgXk=mQZatFTmrUT:yro<QRQREujJPsKeYIxuJyjwpUnEoh`YElX>hkp\\S<=yJyrbyonhYFHXKytMYmD`MSxwH@pstjpHjMxQ:DNwLoWEqV=wi\\smMNq]McTsMQy`DmI\\RN`lW@KdqnT`UA<lV\\y@pQGTWm`Nmql;LtXdT@MOAMRM\\qtuvgMmxdKFxPi]sO`T`dLsAKUaUJ<K>LJ;Ux_YJfhUmMugUyupPMeksUT]\\jS]mSdkguNRaP=Qj:xKu<VP<no=VAUWb=WJeLuPRpepvlJ?DnQlSv`lAXxWtsZiUglUF=LTpTQqJZAxjlK[Yy>YvIPlp`Jx=LjdR\\Mv;aj;hWKHO<Et^AYGmUqtuvUPwtKp@vBdXDqqf<tx@l:MvgLkR]lS=N[ENBXRoQwutXfhVSMQn<waHJKTjIujc\\M=aNAHjp<VLqjn@OapwQUjlAxHUOAHQ_Qxjiq:\\M@@RBDuSdMqIjj@w:=YF]tO@s\\QoOmY^HMnxLHyQ:qovlmK=xI\\QFLKpQYsdseaUimJvAVr\\yhlw;=YslKIPSgavoYmxXkFDjwTmeQKF\\YHdJdeWeUSRuUM\\Wd<qaAtL`Rmoryqci^pdGrUIPoCdkR:kTm]fMsx:?S?Kw\\ErhGxkuiGEtx;ukovxwrrmb]uWiwFNKTYyxGirPscVSb[cwLadnOuH;C<SDZggTCw]qfOYRUsYjYY:YI\\[WHEXUQR:yhGYXQ=XYgxeqrKMenIy:ys_AdBQyv?vBMFPyxZWtxMYyWry=sVwhruyJ]hvsWfIemqD>AC>mboCWkUPQXXxpvgeQwMWUXpEqJgIVZdWTyK[<N<Dj:Gq:I\\;>[PfZs@[eY^UPfSasjpvG@j:>t<@f[_oSibmnsZ>[ofgkaZSneFH]n@d\\wlJI\\h?\\[Ws^f[fhi;QfThtV`sWWxC`g:WxKvb:o^whu;oeVXZ<opMx]>VxThmQwssX\\khxowv`oksysknwsfcGWyZfkKntL`]dyraN^uirN>bSWg;vbv?a>qZnvcXqsavt=NZNvrhykDY\\<f^FQr<qhFGyFglJQaSohKigIipPisrva<ygUPdSPu@age_wnWw<i]>>\\BFaF_kGI`cW[EN]Go[`VdsvomFecnhQVdwV[T?\\UIiHNabpoF_xswtr^fFNmgQl`tb_htAuhmVYsH]oEpOhkMur;TrmvJsyhGEasCRGcleu<qeEixayukYUV=uaAixuvuYr`iGiMV:?G?isSmEIQi:wuhcYDsrxiw]kxsSWEcbVKEgwSB;c:=Fb=BB;y=sh<_HxMtCEbjay:UGlqWoCB;IhI[hH=IlSI^qSDCxhEFZcSkIB[WDveCLAVmmRA]Ixqe;IBe]tMcYk;tmYC^YwCKTf;BeqI\\[hbOU\\cSkQv=WYZ[Gm]XeoIA=s`AhgoFASclyrZiE:=CT;UnCsxgE<[VQ=T]IVDktbac_WbKybn_R`GHlYr\\_UnQt<=HKiSq;Xhaby?WmiYTwWG[BMMIQArmiX[YY=KReshmKfSedDqI;Wf;eTGKI_ubKCB@MttCyIixlYRuQRuer_YBkKb:GdIGHcKtUqrVSV`GuN[ByAGGubGweAgRgIX?sHqaeRoVtybNAdEsG\\odggY:]vwyVa?E=ofjkRKQi@KyvqIpsvaoIAEdp?IRow:Kf@MyrCsVMcUSCkEWGIIOstpOyrMG>asAcixisbyXymiuUEnkvvgRyAX:wc^WXpKXXqsmuelAu]yiRwYpGIeUeeORx[B<CRe?b=SD[ebJQCL?h[Ur@KtvWXXyuywxXps<DUb=qlLJxhjuYwo`tCdQfLNPpMSQOd@xtDMkHLKPS?UkpUL]YR;LpLhs`Yl?MyCHxSARX=XX`oRpnLdtDeUW`nETxoQK^pslqMW@sLmPvtoqXQU\\qQQlh\\tnlo?AjJMvhmp`YLqHNyuvp`oQ=tBPTFLwyhjKHWUDOIPwYUUsdWs=wsaNgum^dwO`PwMtpuKYXQSQqtAQCEY]pYEPOQhwq`RmMoHqPIUl@qpKTLTqVPhSDpRXiSgpmqHW@yTwTxO]mHiJ<DjHdUe@L`HV:qKxlSpqpKPKvqLaELNpPYAOgLkx=X[HYBaWTxVAEWMMlnHSm=y:eWn\\oPxR;Qv?=ND@kR@P?PQW=nmHLKdvWxpKAw\\lv`xo@qvO<PkPo@YK>ESEAL_<j^HLdqLLHxpPNgUoEQLA=QL`uQtnOYoqps[]r^hmqeQLayXplNhp\\`UcMsNQwk=MqqKCP^UHe@qbEi]Pon`oxc_tVhk\\v]\\hyJ>[Pn[RIsAxcR^Zs_m?hrx^grqkbni:iuqouhp_TwpH`jp_];>rYIvUoZg>ZLQvT>jJwvBNs=>wQic[y]sArYfk=_o]^arv]IAr^PZqYvq^novomI]d_e@V]ZopYnlipyfc?[Bx=Wt;qVxOLYNrPLeeQJxOxyMPuQhuT`LOtYpSymKts:=upmYpMtpDWcqVOUPQLubhjjLkB`Rg\\Ot@VQdR>MO_AQ;ynTaltMlGPXolUBQWPQNQAsHdX]LjDqwt@SQYSnLwWTpW`uplpt]nkDSeatkmtc]JiLk:eONeUThyVaPmqTntM<DRuQJ<=PFqlZlu<=y_yw:HYr<NxUV[aMYyTuuVEDvT\\Jb=JaINkyXwAn_ULriK<aqH]VjiUymQMXj_mRs@J>xOApV:\\N:\\r;QoG=X><Y^YKgpr=tQxxQZ\\rmDq:DNjIKEqrG`X`LlSxOBmJxysqAnF=NKDV^YJIYva=rfpyAxxwArympxuMlatoPOCMu^XNB<SLLLLplB@wEtSLLNLlv:\\m>`P>LwKlX\\DqDaP?>kT_cUG_vP[c@cIVmjV\\qnhM@mRn`Twk@wrCOlag^gvcLahGQ]Uisdyw?@^DhxPhaGGeuFhXx`]xcM@\\IFtx?[>V[E^bM^j@XZKIyrA^O?[XQas?f<HjYA_GXxu^ZcotJ@jB`gqacL@mJAxqA_\\Yfuqo=NrsVgF^x=@gcq]I@hZQiRIZWAaJn`FadDh`ynnSgdL`i]AZY_\\hX\\vg\\MPyD`^cWlHH^ZFcC?cVQfKnfhh\\_Om?ItI?rVgxRoyZWj?`laA^:Ilnwl=OeFaqbApf`ij^q`_u<plpGfgxf[nebi]qqdL>jsqbLF^@wcMfb@OeSq_W@u`iwPovHOg=qdhOenOyvicdHxJNx[>\\f^aRWskhfEq\\LHp:O`jiiop^jYw^PZc?xupiiqeuqwiYmIFbRqfmYnoxnVPuJGuRaZEn^BWuM>yV?m:Iqpo`gfjhoc@`ioO\\l@mKQ\\aIj@wenAeJ?y]o_Npp?Q\\IYv??]=V\\fFyvXxi^nIfmTXefNeiI[uA`;Pvv@y=Ii[NsE_l@YjEIaYW[upyvhjrahT@pLfxcotRguWHtbWmCNueoyqOyvhclp]CFyJ>[TyZEga\\IZmF^PQj:ou\\?bEOrTy[^Hrqge=Or>_rVipqfcrPw;?]s>fAfgbwb\\uB;e>EbFAH:=djuCB?cxmiNch=wdiGu@CW:svp]uiUYpUI]gVH=wCUf\\aFS=YFiU`AHuUY>oV^YRAcy;CwWwv:KtJoBp_i:mI<qse=Sl?dacDPQdTwfCKtoWwvmd]oex[SMuc@mrBUhUYWxOsWaslwGNaEewhvYimYI[gTmyTBub:=tX?UgIItUHZMc^WdA[YYktvmIRIHTuBucSAGFDIVuKCfASHSXdceF?rYUFH;GMSCyqVsER<]st=fx]w>oWpGRVeeJmSbubB_rcEftesa=w_MHGQsPKEGEIB?HcKE_SFKUcjUITYXqWbZ]ufEr?mXvgB<ox>Mtsoiuws[EFXKB;?fX;Ru=ByMCMmv_Erymi=Ax`gRN=EXqexiFGEtJcr;wC\\[VYcWVobHWbBcuoKWXWrjTqj\\tUDSeLO<xsvUmS\\pMQJi\\j[Hy]epWMrXTK>LPQijr=K>Lj`AJ<LyL@K<Hl^UPx\\kB]jWYSIaWLDPBTYpUqXpnXitheJDMXjtUL@STUkS`XBLUe<nNYYXUSahpGhoHEVg=uhxVKAKS]lsUOJ<K>dk:DnleJE@j:@mEtcTFlrN`l@t>XnOY[bWqCFeEHdZ?uWVwVqcAVch^by@mmQoWPwRQksv_<pq:?>chbuTGKbJ;dsMDZKdXwGl?E?OTK[E>Kb?iHi_VHYC>KB;?RB;SUCDKCDF[B<Cj:=NJ<K>dMF=RZipIXrvAXtPVuHKriwduXh<LB\\J<ZR__:vd:vfBOkRG[xwmwxxPW^unpqhf_gx=YZQVtmhZ<Fj:C>NjpGZrPrZq]EQ\\axkOAjFf[GFoWXfMniVFv<oaYq`TA\\M@\\B^Z<:NjPYZTwkSHuSOaEaZVFnqXaigcaom;NlB@j:vZfYpqP]WfwOw_w`ylPupXgQ`pr@bZ><D:[Gl=rfQCTwc;ou\\wY@sEs?S^MfG_gLSI[wxoyxeWbHKIBeTDiv:GwKaYYwh[;DB[:>^bw]>>sAfyGaZHfZiXm:`fWn>Wg_MVn[wuiCLKDOGi:=FJ<;>fqyZByjhhyBqbbGbLF\\J>uhglEq_SAbxhlDXc<?xJFxw@\\B^:<>TkU`YJ<SKEPahyjHyy]N`<NxmvHmnOdTkaPZDQA`YNeTUxMEINJ<K>L:<\\nP\\XFxZxoJ?enVsA^jo@^NHnMxi_PaA_b>NZ;\\BjZELm=L=@Y>HWyLTK<LwTNW@kB\\J<Dj:;?FH?YNiR:MrlkB[CDB[B<D:RrKU<=RTGxZE:B;@VkIRRXj:=NJZ;L<LNJJ;JBF:K:J<DRWAyyAJstJ`uRH_`iAZ:>Z:Fc?oc>oo<?f<6<\"\{\} Sn1b Primes \302\251 Czeslaw Koscielny 2007 Academy of Management in Legnica, Poland, Faculty of Computer Science, Wroclaw University of Applied Informatics, Poland e mail: c.koscielny@wsm.edu.pl Abstract The worksheet concerns particular primes numbers which can be written down by means of the sequences of ones using positional representation with an arbitrary base.

Recall that Mersenne prime is the prime number of the form 2n-1, where n must itself be prime. A prime number is the natural number that has only two distinct natural number divisors: 1 and itself. But 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(111...1)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiRGKy1JJW1zdWJHRiQ2JS1GLDYnRi5GLy8lK2ZvcmVncm91bmRHUStbMCwxNjAsODBdRicvJSxwbGFjZWhvbGRlckdGMUYyLUYjNiMtSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGKw== i.e. Mersenne prime in binary notation is represented as sequence of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== ones, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRKiZFbGVtZW50O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRiw2JVEiTUYnRi9GMg==, where 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 since today only 44 Mersenne primes are known and it is unrecognized whether there are infinitely many of them.

My friend, MSc in electronics, Andrzej Teodorczuk, observed that in decimal notation the number 11 is prime, but numbers 111, 1111, 11111 are not. He wanted to find the nearest "all ones" prime, thus, by means of Maple we easily computed that a decimal number in form of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== ones, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRKiZFbGVtZW50O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5Ric={2, 19, 23, 317, 1031} is prime. I think that such primes deserves to be named Teodorczuk primes. It also can be easily verified that the next Teodorczuk prime, which probably exists, will be written down by means of more than 5000 digits.

Let the sequence of symbols 0, 1, 2, ..., LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRKiZ1bWludXMwO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRMG1lZGl1bW1hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUkjbW5HRiQ2JEZURjk= represent the successive units of the number written down in positional notation with base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIi5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGTy8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1GNjYwUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSFGJ0ZNRlBGUkZVThe LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== prime is the prime number of the form 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(111...1)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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== is prime. In other words LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSVmb3JtR0YuLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRk4vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRiw2JVElU24xYkYnRi9GMkY1prime is the prime number represented in base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjFRIn5GJ0YvRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUlZm9ybUdRIUYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRk0vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5Ric=positional notation by means of the sequence of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== ones (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== stands for "sequence of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MFEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSVmb3JtR1EhRicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGRi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JI21pR0YkNiVRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGKw== '1's representing a number in positional notation base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==") . Therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRIUYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRk8vJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5Ric=primes represent an ulimited class od prime numbers, containing both Mersenne and Teodorczuk primes.

To begin the exploration of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== primes we can use the routine sn1b := proc(b, nmin, nmax::posint) local k, s, es; k := nmin; es := {}; while k < nmax do s := (b^k - 1)/(b - 1); if isprime(s) then es := es union {k} end if; k := nextprime(k); end do; es end proc: where the parameters b, nmin and nmx denote the base and the minimal and maximal values of the number of ones representing the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== prime, respectively. The procedure returns the set prime numbers, for which the number (1) , represented by means of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== ones, 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 is prime. For example, the statement sn1_3 := sn1b(3, 1, 2000);

PCsiIiQiIigiIzgiI3IiJC4iIiRUJiIlIjQiIiVuOCIlRjs=

computes the set sn1_3 allowing to determine first 9 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== primes for base 3. They are the following: for i to 9 do sum(3^k, k = 0 .. sn1_3[i]-1): isprime(%); end do;

IiM4

SSV0cnVlRyUqcHJvdGVjdGVkRw==

IiUkNCI=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

Iidocno=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

IkN0KEcienpOdD5TaSkqW2RLdGFQ

SSV0cnVlRyUqcHJvdGVjdGVkRw==

IlI4cWFeJXk5PSgpZSQ9RERBKipvSDojKSlIbGZkcA==

SSV0cnVlRyUqcHJvdGVjdGVkRw==

Il1bbCwjM1Ehej9LZURUNzRrNWZlSSopUmozIVwmZTVwZywwJ1J6bEZoNWEqXDFmKCkzR2xoMTs5IVxeI2VoUDllazkhMyUpUnAiW3ohSDUsLisrNUE+QCZvdFQlM0lZLiYpRzUwU1Eta1RqXkInNFV5bkQ8KHpTWiF6amxhTi5YdipcXj1wSm5WPT1aJlIlM2on

SSV0cnVlRyUqcHJvdGVjdGVkRw==

ImRbbXRAdEkrJypvXlAtay1AUEZybHBxXGw9Pil6cD8nKVxbPzVyQW1zKT47KycqeTwlUXE+PyIqUVZreG5hJnBVV15ucVFXP1ZwKXohZkgqR2ZfbkU6WTJwJil5ciV6T1x0I0guZkRUcUxVJSo0VzpwWD8ieVAjSCkqcCF5YixWKSlbJSpSQl5lKClbKVs4RShmPlhSUUVNIXkoNGR3JlxJdU9kWEhGUlZVME53dVFqNyRcUmUjeXNZVzk1Zyh6IVwrMiVbXClIMTVDaTMhW3l2Qi1EdD9GeUIkKVFhRSplIT5DVUNaPS48IlsqUWFwejt0KGVZbGIxdiJHeUklZiYzLy8kejM4VWknSGUnKXpaMVg9ZF0mPmIiMzk3Yz8wSD8qeSUzdCI=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

ImdjbSRIJypbYiJcRT4neUcoUik9IVw2KnpeJCl5L0BEImYoZjVIUjkmZmsmeWd1R2FWQVtGbjsqUiFbdTYlW1wuN1xwdmtoWlwjNCZIVCJcY3J0KXlsPD0xLGZfKjNUO18oUWZaRl5jUHp0NEc6OCxNazxHTmYhM2JxJ1shKTRhSD83QTEheUIza2VeO1R3R0RFKmYtdVJJIilbSUdCaGdmKGYqPmswYzJqXyxfeiUpNG5QWCc9U0ImUSFlM1tcZSFmeioqRyMqNHg0K0EzLj5hZDMhKVxPLDFLJlttQiVbVF5MOkQjR2clek9vZmpldE8vWm4kPiVlRShIUiRHUmwvJHksZFktLyIpcGt5Ozo8UlhlSkJCOFkiWyNbJ2ZxOFdQa1YxIylmbmlENyFRYTQjWzw1bVo1Z0AicGkxLkE+Iz0kKUdUJSk0dFZganBLO3ZoNlkvJ3o9TEBsLWgiPmZqSSteK2FqOngqKkcqUSk=

SSV0cnVlRyUqcHJvdGVjdGVkRw==

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

SSV0cnVlRyUqcHJvdGVjdGVkRw==

Next we compute several first LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== primes for bases from 2 to 100: t := time(): printf("The sets of lengths of sequences of ones, \n"); printf("shorter than 1000, representing Sn1b primes,\n"); printf("for bases from 2 to 100\n"); for i to 99 do x := sn1b(i+1, 1, 1000); printf("%s%d%s%s","sn1b_", i+1, " = ",cat(convert(x,string),"\n")) end do: printf("Computed in %7.2f%s", time() - t, " seconds"):

The sets of lengths of sequences of ones, shorter than 1000, representing Sn1b primes, for bases from 2 to 100 sn1b_2 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607} sn1b_3 = {3, 7, 13, 71, 103, 541} sn1b_4 = {2} sn1b_5 = {3, 7, 11, 13, 47, 127, 149, 181, 619, 929} sn1b_6 = {2, 3, 7, 29, 71, 127, 271, 509} sn1b_7 = {5, 13, 131, 149} sn1b_8 = {3} sn1b_9 = {} sn1b_10 = {2, 19, 23, 317} sn1b_11 = {17, 19, 73, 139, 907} sn1b_12 = {2, 3, 5, 19, 97, 109, 317, 353, 701} sn1b_13 = {5, 7, 137, 283, 883, 991} sn1b_14 = {3, 7, 19, 31, 41} sn1b_15 = {3, 43, 73, 487} sn1b_16 = {2} sn1b_17 = {3, 5, 7, 11, 47, 71, 419} sn1b_18 = {2} sn1b_19 = {19, 31, 47, 59, 61, 107, 337} sn1b_20 = {3, 11, 17} sn1b_21 = {3, 11, 17, 43, 271} sn1b_22 = {2, 5, 79, 101, 359, 857} sn1b_23 = {5} sn1b_24 = {3, 5, 19, 53, 71, 653, 661} sn1b_25 = {} sn1b_26 = {7, 43, 347} sn1b_27 = {3} sn1b_28 = {2, 5, 17, 457} sn1b_29 = {5, 151} sn1b_30 = {2, 5, 11, 163, 569} sn1b_31 = {7, 17, 31} sn1b_32 = {} sn1b_33 = {3, 197} sn1b_34 = {13} sn1b_35 = {313} sn1b_36 = {2} sn1b_37 = {13, 71, 181, 251, 463, 521} sn1b_38 = {3, 7, 401, 449} sn1b_39 = {349, 631} sn1b_40 = {2, 5, 7, 19, 23, 29, 541, 751} sn1b_41 = {3, 83, 269, 409} sn1b_42 = {2} sn1b_43 = {5, 13} sn1b_44 = {5, 31, 167} sn1b_45 = {19, 53, 167} sn1b_46 = {2, 7, 19, 67, 211, 433} sn1b_47 = {127} sn1b_48 = {19, 269, 349, 383} sn1b_49 = {} sn1b_50 = {3, 5, 127, 139, 347, 661} sn1b_51 = {} sn1b_52 = {2, 103, 257} sn1b_53 = {11, 31, 41} sn1b_54 = {3, 389} sn1b_55 = {17, 41, 47, 151, 839} sn1b_56 = {7, 157} sn1b_57 = {3, 17, 109, 151, 211, 661} sn1b_58 = {2, 41} sn1b_59 = {3, 13, 479} sn1b_60 = {2, 7, 11, 53, 173} sn1b_61 = {7, 37, 107, 769} sn1b_62 = {3, 5, 17, 47, 163, 173, 757} sn1b_63 = {5} sn1b_64 = {} sn1b_65 = {19, 29, 631} sn1b_66 = {2, 3, 7, 19} sn1b_67 = {19, 367} sn1b_68 = {5, 7, 107, 149} sn1b_69 = {3, 61} sn1b_70 = {2, 29, 59, 541, 761} sn1b_71 = {3, 31, 41, 157} sn1b_72 = {2, 7, 13, 109, 227} sn1b_73 = {5, 7} sn1b_74 = {5, 191} sn1b_75 = {3, 19, 47, 73, 739} sn1b_76 = {41, 157, 439, 593} sn1b_77 = {3, 5, 37} sn1b_78 = {2, 3, 101, 257} sn1b_79 = {5, 109, 149, 659} sn1b_80 = {3, 7} sn1b_81 = {} sn1b_82 = {2, 23, 31, 41} sn1b_83 = {5} sn1b_84 = {17} sn1b_85 = {5, 19} sn1b_86 = {11, 43, 113, 509} sn1b_87 = {7, 17} sn1b_88 = {2, 61, 577} sn1b_89 = {3, 7, 43, 47, 71, 109, 571} sn1b_90 = {3, 19, 97} sn1b_91 = {} sn1b_92 = {439} sn1b_93 = {7} sn1b_94 = {5, 13, 37} sn1b_95 = {7, 523} sn1b_96 = {2} sn1b_97 = {17, 37} sn1b_98 = {13, 47} sn1b_99 = {3, 5, 37, 47, 383} sn1b_100 = {2} Computed in 1897.25 seconds

It can be seen that there are not LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== primes represented by less than 1000 'ones' for bases 9, 25, 32, 49, 51, 64, 81, 91. Therefore, let us search the longer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElU24xYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== primes for these bases: t := time(): for k in [9, 25, 32, 49, 51, 64, 81, 91] do s := sn1b(k, 1001, 3000); printf("%s%d%s", "sn1b_", k, cat(" = ", convert(s, string),"\n")) end do: printf ("Computed in %7.2f%s", time() - t, " seconds"):

sn1b_9 = {} sn1b_25 = {} sn1b_32 = {} sn1b_49 = {} sn1b_51 = {} sn1b_64 = {} sn1b_81 = {} sn1b_91 = {} Computed in 4976.88 seconds

The patient reader may try to invoke the procedure sn1b once again with grater values of actual parameters nmin and nmax. Here are similar computations for bases from 1000 to 1100: t := time(): printf("The sets of lengths of sequences of ones, \n"); printf("shorter than 300, representing Sn1b primes,\n"); printf("for bases from 1000 to 1010\n"); for i to 11 do x := sn1b(i+999, 1, 300); printf("%s%d%s%s","sn1b_", i+999, " = ",cat(convert(x,string),"\n")) end do: printf ("Computed in %7.2f%s", time() - t, " seconds"):

The sets of lengths of sequences of ones, shorter than 300, representing Sn1b primes, for bases from 1000 to 1010 sn1b_1000 = {} sn1b_1001 = {3} sn1b_1002 = {3, 31} sn1b_1003 = {11, 47, 101, 109, 137} sn1b_1004 = {} sn1b_1005 = {} sn1b_1006 = {13} sn1b_1007 = {3, 5} sn1b_1008 = {2, 31, 89, 157} sn1b_1009 = {5} sn1b_1010 = {19} Computed in 12.89 seconds

t := time(): for k in [1000, 1004, 1005] do s := sn1b(k, 301, 1000); printf("%s%d%s", "sn1b_", k, cat(" = ", convert(s, string),"\n")) end do: printf ("Computed in %7.2f%s", time() - t, " seconds"):

sn1b_1000 = {} sn1b_1004 = {431, 727, 751} sn1b_1005 = {} Computed in 261.80 seconds

It has been shown how to begin the exploration of a new class of prime numbers, related to Mersenne primes. Considered problems may have some usefulness in the number theory and cryptography.

GIMPS Home Page: http://www.mersenne.org/

Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities. MFNWtKUb<ob<R=MDLCdNVZZJ:@L>H:TKGxMkJ:<O`Lo\\lQxlQWdMWpsHqShmWhYoeXOPmTPmV`mvqyxq=Xj=xXquXaxnaXcEWc=UR=UweYwELKDLqtPq<R:=r^av^uRAurZ@nZtVauVb=WbMYtMyvayvYyuYYxmYxqyxqYyuYyEYsEYpmXpyyyyypqxp=J:>::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::dy<TypC>qULCTJcDXoXusT<aupkcfWMX@JCeU`dNuTmWxyyyppuPCDSSuLClu><xTpQmlsb]MihUO`qTeXSQO;@JxV]wOl:@syFv<w\\t@tsNnQn\\V?w<w\\?FqJijXynZVvnyHErmiB__tWit[MyxYRIIXvWgtSS=;gQMwAIC]IYrGXRogc[EpqYtsxn=BVSUGuEA[WxKrWaSHssoYBPkynKctqgmyUKAYQYUw_rs=wboYTWXI?IQKyo[X@wydqytYRGAy`ixs[SlyXaSyquy:mel=dXqydIfvgRIeSUkUmUBGwuZitS;eQ?S>AdMasnkySGbDSuimbSabjytNAyMuXlaTWaCp;y?at;_txaTwath?cj=GbgYVGCA[eAkh^ihyaIGoVdGxyWeQatamVHYx:SEIewyacmcSBAvgOyyssEyBVWCwQFtYWxYdMgcY_y^Uy?gce[WXQCDcwGuwHMw?qwx[gacscGrwOtuKFXKsc[FZIBOqIrII]kuICfRosM_yTSEWWcKQs_qGHeIiaWBsvaAXWoFsYTyuIYSdWCet[fZpOYtv[\\XSMvN=Xhluxel]ylvUn;PYsqvkmmCxSEQPsMOeUpQEKN`yVAqcqRQpYxHr[xU\\AtgPVexmHHQYDXptL;ey_\\XHxyTpLQ=qJhJklqA=wPxqOtpPmwQ=kWdSSYjxhQt=li<X=Pr\\HoxMKxppdUPGxl`<RadWsEMUhnMinaqvy\\t]pJw\\Pttt:lw_hy;PxuElWpfypiQyg<IbgHqQ?wRwvFgcQnmtI]lXZoauvw\\]Vi\\?yuIjGqyA_]j^cia\\^vaYfmXYvV_foyd_wZa?yIPfNXpOimbInwiieQyZ@[jf[p_`s?\\N@qaw[<a_=qpdIu]>gnHpUi\\^a[AGcS_y]pnHg_oIi=XkM`bK^yUWjFhhCpif?llhelhkKqk=qgCqqIokJadZ@]IOspHjgQgUv^Mp^[akXNokxcFaxMX>Efx=GJyY]=uKWXuefcYCV_DO;X]oeDwI]UrhIXhKdtYgv=sYMxyMhEAbdKdFED;MBimUYgvNsfBuDgqw^sRZoieyiYEfEAsYOcU;uf_C^;g>EIUmWy]xZ[H?UTiwhayb<EWUAhmghUee]ODLyfkYdOQDNMsleg]mHGkynUrrUhjgbvstrICsOiU?upUhtME_cVUeywWrSeSvIwHqsEUvwaS`mv_kCEgDEEVOoyfSFYGXh[xe;wfsya?Hbcu_SiHUfrStqsgICUKmR;IEGGiEUxSSewkBRcic?f[GHs]WBCeFSXMec@qwQYiOCFi;bd_epghCcrSIbrUFfKXpOE>CdGUVH_ss=GaEF\\Mh_uDJcXeWGSkIA=T`[uhOiKOy;Ido_sBQgPGbiMxZIx[=RNQHCUwlIhVAs>Mxv=t;Iekec[iToeB]YSVsI]UGkMgC=xM_cv]rCkGlOyE=wVsymoRPERGUWoKs>?dNGcqOvL=DcgUUid=SdBYtacBcyT;sC??sXsBFEIPKdwUibUUuowtCxLERxGUPOc=eeWWDJ_tBIFj[RMWXoaIniFDYyvIfFYH;EifaWAAdkQgSuIoYHS?s\\aYnkYcCRXAy;=urSsUEGXovmkdU?bIkuvIhf;hHKRmsIqkGkCIEGSQiUy?r[chy]DW?UJweo_HI;I[iRPuYCce]yIQGSR=SFcY@IHNabEyhT;H\\gC[iiEubXIY[?FhkfAaRyccQ;D<MBLksUGvM]FOSWZaFnmUVOB]Mh`gu]ew:CSX[VU[d^iWCITMkingVmcY;EuIkFZgetaSlkeD_SlUd?SU[Wh`_IHkuNaIBEY@KhQ[IbSfl_CpgV]IBgcf:CrOWWliVPSDMuEkwBYQbgKxGiWfcdg_cCoXDyFoAF<CYd_fZSUKOXmUErmvpWgaQIeWGyMiuOfheFY[UWgdGwe[;X@Yh<owskTwUgjYdvEhnTP`LJatUmyo]xlkUpgPSHmSOiSXtM?HsHhWglnu=ypMosmPWQtXmlLDR^erappAPq@Twu\\mf<ytMo_tNQDmwuUBal[TKM]UZ\\VsUPg\\OhXU]iw>lT>TtolYUeM\\`q:iNFQkMeuB<Y^yq[TqwLxyYk^mPDhUTEL[mxdYTrUwHYpp`R]tsyhm<\\rdhN\\]VGejEyTBLlXhUidSklVcImkuJA\\OFAJxXTJ\\oRpUr\\qnEUf<POaocioXxYUTRxhmKHnoUuBavvxt]@ordyqIl`tycEyg=St<V;LY`DoDElChWYdkpIkSMophnhqkeMW<QX^dogEmM<kxAYM=mpPKmTTMmXeQLnuK?HMeIU``TqMSdeNqmxHeLK=OUpx^@kiYp`xXVdoU@L=PprAPIuR[Qp@YlvPWwQToMpG`jOXyFhxAETieRADKgioVPOyXUlXT:Iwc<NgeMNup\\XWrdQFPQvlP=Toseo>qXbiWO\\yE=PUiPAASgLtxXLG=STASAxj=@WixwX`XOAtHloIeoHiLvyuouMtLtTyJsAxBXr@TqWXOsEKopuAEU<uyO\\LTyPAXm=tOUQneaND]KOYyLyXbtxuhmcYrXMkh\\ylLo_eq`tSeAOH]lqUwiPnkPwlHPgHrehY^pKhPwGPJ;<O<`qU=tMxUUEPW@RdITfYjjaowTqMQjXHJS\\M<EvappT@mWMJ@iOVhyLQKq]T=Eyc=UhqNa]PJ\\X\\Lu[DsQ@O[XRw<Rb`P`tSuejceYX@UN=rFexuHmDmk]XRLaYElRmIP]Pech`rxma?araaCxvWQ[\\aZ`yiFAj?gvVVd^@mGy[hhjxQvjIwMVwPGyXW_EpjDNnsy^EhvE_d:PnkOaDA^CnxEAoCh_ewc;pb[I[ZwcU?kpGwxvcVV\\OWaYGZWqbGG^jVkAQ]mXckfwTVfovZVnZLwfoIeS>e@HtcvsgPn<YqDOxcqbdNmPxtqwhsfag>myOedhqCFkNWqspy]@_VQrIIu]ncLIb>_xdQ^[yw^`^YqbSxeyga>OkV@fpVfeNhmxeSwn^?_GOklf`QqgK_yK?yj@pxvwbHtI`yYai?HvJ^wvQvYngAVo=XhwcReBIMflKTU_b`qrFQC<UGRWY=kVWAiv]X<CSyMycyweoE>?ttksVgBTmtGIXvKDT;D`atpaGQEVA=efoH@]TgswsCfWGEbCCLIYtSwG;tRaC?]hi[TfwSPUcSQYZCuloE[KTnOSTuDPqfpQU_Yx[?UZ=b`yCuETUectcrsaWIGhPUVdCXo[Dn;GTof=AVBcYRGgaaYbsvt=UBuVIOeZKgGmhHQr]]umsifyTPWtneyZKydmHjoWRAsSQHewDS=Hj]C>qdH[XHIgkwTGuvI_sgYDgabSsiLYrb]Ic[uZUuCeGN]InyyjiVnMuJibq]E>=sH[thQDXgT\\qhNwTVmGdoSiKsD]DD]UOksO=fX;XvIdbUwRiisCEv?tEAS?eH[EHiOy[mcE?hY;ewKCr[x;ECpUEaItRMUeMI@wF=GuqIdriXmAiHouB]UEkvboD`]bDeu^UHOsxwKSogVE_GNQbBAduMYQ;Y_]XbqBe[FFYGF=tXgxryYpAFDoidIRHgUf?uXGg]WguGig]URQrp;u=MHYIXxcIamsqEl<uR<PMwtwNMqNYMB?\\aIiqvboxhknwDOv]^r:a\\[WhExsn_cdQo@Ng]orLPnCptE?wJqi:ad`?gjX\\Bol:@dJis[vel^pK>]TpcIHhoSZoXJOhw[WgsesuBfEg]=uuUY=qXZWVYMSZECHWHqeX<Su^EuvYX;AFQQC]]Fl]SNqIO=ILQwhIwZoeqEoOqVY@TTprWANqYsuxNA@WjlpuaXytmXMRkdpI]K\\LT@=Pd\\SxHJSXNhulFYQmtwJhWI<QsuRUpwm\\rQDLyuMgMv>@pS@pftRiUniTV:uRRil<lRY<wltSViLhHKD@vViS`DOfaTvAsyMuKmQUhvqlQuLW@qlr`RddRKIm^QYAaXxdP\\TuVlktMYmyPA`xRivRUoLxKmANalL`qV`eTDIO;MY\\HoQiYnMkHLNqhylUJ\\tS^uKJIMKAY[qufMrxAXfxJyXxe`RPqxOiorlJW]XEHXw\\lJqr=XwN<T>`nFPklHv^LTd]kviu:YwlhWkTyDpLSUVUqQCAuTTliPopuoTHNSQyRts>IqKYKhTNQMseAjoalrQvbIslMp=\\ojLUMDuDQymaoiQulmPMELwhpuplnIvypP`XlCDM>LY@`rdqtoyn@MLFTUUPo\\UWR\\WMetOAoEewLIUctRw@t]ERG@XtqKuHQWqjWLqZ`LTUOTusmHPcYk?DN=uT\\aXSeLNuKrttf@kIunUTXCMtYyRUQplXw`Xv=iXppuLmRUqwTMm[]qxhLElt>lNi@qQ=Q_lRL<NgerhhXwAryAL=iw]IxYTUyhj;poqXPmUgHG\\ganfWfF>hrAwtwy[Ys<VuGXhSGxePjM^exn\\vabHNjTffFYwDNre@qoheHWmoW`]P\\gfq]Ikxx\\?vknnc\\giupovIhMaZOIkjIdVqtv?efnhe`i=OixVueVopxjJOuNY`[W\\jX\\SNkeqrQ_pUghjNiNQtpG\\CIe_IabYs@wwBw\\L`xO?r`qZi?c@WsW`^@fjogeppjkIpnXkKPndGadGidocE>m?Fjf_bYf\\\\?p]HieNqWggeIuCAnhiZwaepYnkgeFyjvOhu_[GQkpioSNa?ndiprUFjcV\\pQngw]R?]WFeWx`>i_H@tAwdbny<x__O`FyggqujAtJhaiAnSAs=xwtp^aYnloln?eYQtA^mJvwD?k\\Ql]xqMPc`_sjV]gvreOsIOkpP^Vy^[Vw`O[gwmLqi]NmZ@hBAriP]O>[@HdmYZyir[Nn<YpeNfonso^]dnfIYuXwkEAcUyn^A`]VeyYulPogAn;?\\K?mt^gp^jXGxf>ysfZsgu=`seb_aIESSJcWewtmCrECfgERaqENChB;f^IvxYL=PS]=yKXmGeMYLmrTSBpL_`UAlmXmXlUTXEn^EsSmmfyREXsDEwelvQqlQaX@@tj<pkTYkDSNqxPQjlusiTJELXQ\\Rw`sPaSUYJwPjdes_QsK`j@Ij_DuFmJmPLmllh<SSPKV<W[eOaaTN@wLltv=qd@OOHrc<K>huhPP=ApSURP]mbIVSurlDLqpKuaVliV>IoOxJxLyGXOhqt=QPBQVItRjdV?]PFPPCyvs]YB]RXAsPLysQT^MuLUODMueDP=UPpHsFUx:XJ`hNlEYKykqQLQHSEur^aX_XJH]UyxtgMRCXtjuo?EQWML[aRSikidoeLsUduWEMthYZyQ[qwxHT[tOu<VGxqb`qp<OQAWOeYIIw^Tv`HrNyP;EKhDLiTqcXLq<NXejsEKseT;MYA<osmuf@U@txUMJYaMFuvVajUelv]xX`ncuThTxB\\wxtvCiu@HsQUQ:msJyUVXLOeUALmdaY]TMouqEExW`xK=QQLyGAyiHP\\xOf]tG>cJw`gxw^f]mIdJwgXiybX]_^\\]x]wXoovfJ`vgQklWrhq`sxqThd_AuXHotauxqvVPs>fXQEG_YGyujGWqaCOyE>WX[wuEwysMHsACawYfsIiqvWiWpWGoGYmqwAeh;_XqGSy[YQUW<kFaUGmuhqeYE;xdwbDUDdWV<OYjmwc]rL?TpuwF_snWumiiaAInyB[aUbyx\\yy`cSLmHxsInwYLwf=ob_ktxgUJWTB]TtIvKkDDMICMVZCH<WWF;vXeuOGe^QeLwik]HkCfrUXu_DgoC[OIyuh_Iyb[eEhqryQ?MwTexIuNbumv<sOiwy]uO>ie?oNXpnFb]iykyv@pnM?^bQbcOp]@pM_wOIZ\\i]tVpGIu=PdbHfMxcxXat?aWPZsww>xaDvv<wqQvyk^piAr_@fdYyfoxsactW_uvgBPmqvmK_ZMArZWZyAvCPmuYd\\AbZp]ZNgXwryXaxva>wfYpcZgem>uxiu[GiYnuwQu<aiJns?\\UNpqHgjfwhq[bahb@xCGbHVkk_nTPeiobfycUf`XnaxidlwiTHjmheF?sw>qWXxTWygQbupZtYpgqpkwwfWvcHZcAw[iuMiyb^mEfyh_yyXsIIosXdJfxvq]>yaR_ZVxy\\bS?EbAws]w]wvcOFoMhwSURagyCYdiTwABuAEGWFuSIGoEkKYIGFYUY]uw`uwXoGuAFVWkGwqyfb@qrrifj?sYpu=@_]on=g[Q@ltQbQNZDf\\FWe\\yquw[<pu^>lvQx\\Yw<w\\<VxRPn=yxiN[CNgB^irOpwGnEfyyWntqw:gwEfZSpi_G\\<?`QnxV?wygm<NZ^qyaGpxxiMpk_OhqYrWx\\t@t?@vAA\\eq_rQqv>uy@tya`Wyy:xvmysXwyYf[MWxoWmIgvoE:;B:MTKWDKWgJ;eZ6:\"\{\}