hey someone prove this, pronto

It might be that every even number from 4 up is the sum of two prime numbers.  So, can you prove it?  Or maybe you found an even number that can't be written as the sum of two prime numbers.

>>2-kun, re-check your results, for I found an error in your reported number, as given here:

369366330749038867897893668393805612642918680582292937308971545479760347907109341323708805106695369434736906150693548436354696716399668361638628209577922355836809350348899072604211196205482919692572775939925073317741838900329553660209639337573685710018914791551502621373105181342221559743697674019791012920717577725121024919299650622178992054600681748676346821270668379499465796023738626242419051194984224293900285919203045184517936519093748643446528623496712716578384297033988631154388239130666962809691029535377270020206015697625712257964942024932740952525677167870503619104856762236116860761063425798781120602435613629493886056109602930547227493286854893750754871365051460454366239421269284354955350268510380695060772790690080354134278750287944343371853700373843273638579739839241023303368155047375709443960754168422715114495221242899257039685970326723325433836758668512857627571153611198453888697044216607490031440321569967669266020499870573008138382896719028169027619852267272397904138510566548213076514721875909951879257138291624274435357624259885746102747952023580533072115647968112119022974392980326532524602506628795480838429850751755454154562101981267418673572972900166475192779503316405443421443500176588908774383733588579638392620333054982915621352940208650979081659740564464270181436799520346902018868959076946712586605076377175280343150853641822367905214795932396360495289346614450450186361183164439089362705775198256971378663341429756900253461329705119001099341546093502561789939270883418250160640253265508912014096520495463938450520941631887346075583437417708876419335167693095077017364252156639342989255305592483827505169496517234218673720969238184960982485956202203178883943838216383062956150050153720581283324334003986513802894061500149452818444924649857887086583998421695928339209572883569449081295285362517140910639792269085262370173686482918847777037910643727721888482545497895656810233683873862919707909596114470065792710680288017595230891164723058632001177940188998913880509985637974168010312413225074591083336813493166565339587335901953170853385254698980311913077332591668914166086229694369761763835821442219538915244844169093433529926036487730081668026085901372148414365462467382380192215252286579660072182905632658907771081979347133628282811035072754599394363774998851621969142440231214678516063460071734504917478461471933769670691922751846637610766970770676694154686334121890625663745627560281793964966256239608884338118084265503173177124224656291325489260295167846841604072671192938675131058242907738729566406177367999639514627096758520925993992781212349069332916007590853205538257339498175031546640216824920647719967748243619368282693318881669531386142382924117495356751189996957397183562263713803985166156027038331808076767247341690818518690761017687265579383603675914035131572815974667444610629238225339409479430