The end of the prime number problem.docx

Theendoftheprimenumberprob1.emNote：A1.1.contentinthispaperisderivedfrommyownIndependentthinkingTEXTEng1.ishoverview:Thereasonwhythesievetheoryhasencounteredabott1.eneckandcannotso1.vethere1.ativeprob1.emisnotbecauseitisnotagoodmethod,butbecausetheabi1.ityofmathematiciansis1.imitedtofindingthemechanismforthegenerationofsuchprimenumbers,butcannotusetheexistingmethodsofana1.yticnumbertheorytofurtherImproveit.In-depthca1.cu1.ationsandrepresentations,andunab1.etodiscoverhowtomateria1.izethemintoanotherforminsomeprob1.emsituations,juststaringattheprimenumbercrvegeneratedbythecomputerbuthavenochoicebuttoknowwheretostart.Infact,whentheyseethef1.uctuationoftheprimenumberequation,theyshou1.dthinkthatthissievetheoryrequiresamorepowerfu1.equationtoexpresstheefficacytogeneratethefina1.trendandtheupperandIOWerboundsofthechange,whichcanbefittedwithinfinite1.yc1.oseequations.Forthisreason,Ispecia1.1.ySomenewsymbo1.sandanewfunctionareinvented.Forthetwo-primesumconjecture,duetothenon-smoothnessoftheintegerequation,thedensityequationcannotprovethatthepropositionissatisfiedforeveryevennumber,becausethereisa"dangerouspoint*'inthechange,thatisratone-ha1.fofanevennumberasThesituationwherethevacanciesonbothsidesofthenumber1.ineofthesymmetryaxisareoccupiedtothegreatestextentbythosenumbersthathavebeenscreened,thisisthe1.owerboundofthenatura1.variationofprimenumbers,so,tofu1.1.yprovethisconjecture,itisnecessarytoprovea1.1.dangerouspoints(primenonsmoothnon1.inearequationsThe1.owerendofthenatura1.numberequation)wi1.1.notpenetratethenatura1.1.inearequationorprovethatthenatura1.numberequationisabovethenatura1.numberequationinthedomainofdefinition.Thereisnoexpectationofbreakingthroughthenatura1.numberequation,andprovingthispropositionrequiresconstructingamaximumfitfora1.1.dangerouspoints.Functionequations,ortoprovethatthedangerouspointbreaksthe1.owerboundofthenatura1.numberequation,theinfinitederivativeconvergeswhentheindependentvariab1.ebeginstovary.Visua1.izationandMathematica1.Exp1.anation:1. Nomatterhowmanyactivenumbers(primenumbers)existinthedeathnumber,itssequenceisinacertaincyc1.eatitse1.f2. Theperiodistheproductofa1.1.primenumbers1.essthanthisdeathnumber.Periodicequation:T(X)=n11i=1Zn,na,aN+3. Eachnew1.ygeneratedprimenumberisaddedtothiscyc1.efromitssquare,wherethestartingpositionoftheprimenumberarrangementcyc1.einthenatura1.numbersetisdetermined,anditbeginstop1.ayaro1.e.Theforceisitse1.fandthesequenceofprimenumbersafterit.Theproductof,whichisa1.sothesievetheory,thatis,oneofthecoresoftheprimenumbergenerationmechanism.Itisexpressedasfo1.1.ows:F（三）effectstart-*Z2,T(nz)=T(X).Therefore,themechanismoftheestab1.ishmentof(1+1)isobvious:asthepointPmovesinthepositivedirectionofthenumberaxis,itexpandsby1/2ofthenatura1.growthwiththerightsideofthesymmetryaxis(theprimenumbersparseside)oftheoriginofthenumberaxis.increase,inwhichtherightborderexpandsat1timesthenatura1.growthrate,andthesymmetryaxisexpandsat1/2times.Therightboundarywi1.1.continuous1.yinc1.udetheprimenumbersontherightsideofpointPonthesparseside,andthesymmetryaxiswi1.1.a1.sofi1.terouttheprimenumbersthatwereorigina1.1.yonthesparseside,butthemovingspeedis1/2ofitsspeed.Eachprimenumberhastwoeffectsatagivenva1.ue.Thefirstperiodisaxisymmetricdistributionwiththegivenevennumberandtheaxisofsymmetryof0,Thiseffectisitse1.f.Theotheri$non-axisymmetric,andtheeffectofthisismu1.tip1.iedby2.Foragivenevennumber,inadditiontoitsownva1.ue,theeffectoftheprimenumbersinfrontofita1.sodependsontheforminwhichtheprimenumberssma1.1.erthanitssquarerootaredistributedonbothsidesofthesymmetryaxis.Itssquarerootisprimetomaximizethefi1.teringeffect.Therefore,theessenceoftheprob1.emisthecomparisonoftheiterativeefficacyequationZ(×)ofthemostdangerouspointofprimenumberswithf(x)=(1.2)x.Ifitcanbebrokenthrough,thenthisconjectureisfa1.sified.Ifitcannotbebrokenthrough,thenThestrongGo1.dbacbconjecture(1+1)ho1.ds.Mathematica1.form：Foranyevennumber,itsprimedensityinterva1.equation:RPg1.J-V?N屋®9二/-£空'/第EF(N,)二电涿，加川)m1.=c>N1.n,n*-RPJisthesymbo1.ofcyc1.esectionWiththisequation,a1.1.thepropertiescanbederived,andfromititcana1.sobederivedthatthe1.argerthenumber,thec1.osertheratioofprimenumbersistothefo1.1.owingequation:x1.nxWhyisit?Theproductofthereciproca1.ofnatura1.numbersandtheproductofthereciproca1.andthedifferenceofintegersnstant1.yinf1.uenceeachotherandmakeupforeachother.Whate1.secanbefittedattheInfinitedistanceoftheindependentvariab1.eexceptthe1.ogarithmicform?Whate1.secanabasebebesidesthenatura1.1.ogarithm?Iwon'twritearigorous1.ogica1.proof,it'sawasteoftime,whoeverisinterestedwi1.1.proveit,anyway,Imustberight.Dosomeana1.ysisonthedensityequationandthisequation,youwi1.1.findthatitsfina1.trendat(0r*(×>)isgradua1.1.yawayfromthenatura1.equation,thatis,the1.argerthenumber,the1.owerboundofthedangerouspointoftheprimeequation.Theregressionequationhasabreakthroughexpectationforthenatura1.equationThesma1.1.er,thatis,whenthenumberisre1.ative1.ysma1.1.,theevennumbersthatcann