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.
I found one:
369366330749038867897893668393805612642918680582292937308971545479760347907109341323708805106695369434736906150693548436354696716399668361638628209577922355836809350348899072604211196205482919692572775939925073317741838900329553660209639337573685710018914791551502621373105181342221559743697674019791012920717577725121024919299650622178992054600681748676346821270668379499465796023738626242419051194984224293900285919203045184517936519093748643446528623496712716578384297033988631154388239130666962809691029535377270020206015697625712257964942024932740952525677167870503619104856762236116860761063425798781120602435613629493886056109602930547227493286854893750754871365051460454366239421269284354955350268510380695060772790690080354134278750287944343371853700373843273638579739839241023303368155047375709443960754168422715114495221242899257039685970326723325433836758668512857627571153611198453888697044216607490031440321569967669266020499870573008138382896719028169027619852267272397904138510566548213076514721875909951879257138291624274435357624259885746102747952023580533072115647968112119022974392980326532524602506628795480838429850751755454154562101981267418673572972900166475192779503316405443421443500176588908774383733588579638392620333054982915621352940208650979081659740564464270181436799520346902018868959076946712586605076377175280343150853641822367905214795932396360495289346614450450186361183164439089362705775198256971378663341429756900153461329705119001099341546093502561789939270883418250160640253265508912014096520495463938450520941631887346075583437417708876419335167693095077017364252156639342989255305592483827505169496517234218673720969238184960982485956202203178883943838216383062956150050153720581283324334003986513802894061500149452818444924649857887086583998421695928339209572883569449081295285362517140910639792269085262370173686482918847777037910643727721888482545497895656810233683873862919707909596114470065792710680288017595230891164723058632001177940188998913880509985637974168010312413225074591083336813493166565339587335901953170853385254698980311913077332591668914166086229694369761763835821442219538915244844169093433529926036487730081668026085901372148414365462467382380192215252286579660072182905632658907771081979347133628282811035072754599394363774998851621969142440231214678516063460071734504917478461471933769670691922751846637610766970770676694154686334121890625663745627560281793964966256239608884338118084265503173177124224656291325489260295167846841604072671192938675131058242907738729566406177367999639514627096758520925993992781212349069332916007590853205538257339498175031546640216824920647719967748243619368282693318881669531386142382924117495356751189996957397183562263713803985166156027038331808076767247341690818518690761017687265579383603675914035131572815974667444610629238225339409479430
>>10-kun, you know little of math other than your consternation when presented with its formalities. I have not failed. You have failed instead. You are a failsome failer. You fail so badly, that you totally avoid success successfully.
At any rate, the problem attested to by the OP is based upon prime numbers. Primes disturb us since they are only discoverable, but not generative. We cannot answer the assertion until we find out why primes continue to exist in the integers. Why is it that no matter how large the number we calculate up to, we continue finding another prime? Why don't primes disappear once the number gets large enough? That implies a patterning throughout the integers, but such a patterning should be generative, meaning we can generate a prime when needed, and predict them as we go along. This seeming contradiction is behind the reason why primes disturb us.
Name:
Anonymous2011-07-04 10:28
>>13 Primes [...] are [...] not generative we can generate a prime when needed
wat
Why don't primes disappear once the number gets large enough?
LOL. Why should they, 'Cheese?
>>14-kun, please understand that I wrote that in a language with which you are not familiar.
The fact is that primes should be generative by their very nature, yet we find ourselves unable to generate them. There is a generator, but we can not find it.
And it should stand as intuitively obvious that when a number gets large enough, it contains factors. If not, then we are back to the generator again. Where is the generator? Why can not we find it?