Hi, could you tell me how can i prove that 2011 is a prime number, Generally how do i prove such number is prime

Question

kc_kennylau · Answer

You check if every prime smaller than or equal to $\sqrt{2011}$ can divide 2011.

kc_kennylau · Answer

That is, you check if any number in 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 divides 2011.

kc_kennylau · Answer

The reason for not checking primes greater than $\sqrt{2011}$ is that it is redundant. If one factor is greater than $\sqrt{2011}$, the other factor must be smaller than $\sqrt{2011}$.

anonymous · Answer

Good, do you have another way ?

kc_kennylau · Answer

search it in wolfram alpha: http://www.wolframalpha.com/input/?i=Is+2011+a+prime+number%3F

anonymous · Answer

Yup i see.

wolf1728 · Answer

Or you can use a prime factor calculator: http://www.1728.org/prime.htm and this says 2011 is prime.

raden · Answer

@wolf1728 and @kc_kennylau 

2014! + 1, is it a prime number or not ?

! = factorial

anonymous · Answer

http://www.wolframalpha.com/input/?i=++2011

kc_kennylau · Answer

This is 2014!+1 expanded:

kc_kennylau · Answer

57255346355781325106422581770832989762510298366455291815359180145294601669961310202840516211855765436548360053196824283749279879773455998919164870522708484952035978565283573705289777011436905549164670648632355266229701724292030848296422283185745261085401231672324244354655992975275056877520358294476659939850449151624768316777711431323970960016801708905452626565212327165871856448417823432331011994617638757698403799263166803728903310355566269638279768023431545341997049590753035545554564262465710939980978217976229793072642708596885158330618379089415267183320459874331171356197817510428652246103730907205167328357425284490221146092538826172353791746432387362980268483660688776873432949998796616433218610436152794773215835940182711248925749715436323470593281045389451424593877624077402007142781435397541394674033535114722015955390746316891336342767770523467158614229624269612207186137105751942531495511340780426435201375998775220117103905500377261851493972232145468782899765887394025083648056763895040092749879644308259670003671777882257333019999549953721410884676408184984542995051783443370550531221194238457194113182834410454884388606963312303563806700317955978891577439063263932768388072242287668589879978893051086220559629581014658205699769817370501683698258288850969174546960990223520326969365154476411433668671938870287815641924631484819120330681138479172762819641855587167110858554530209866834997166072248885392903623449016231004999106207416971824260475893617565597235826110941196558458593492591458373509416588972512220993278291196555459600136547479843075439614605417625538880145885935960352437151652417182460415737735437021644193991225657433699417248439746517201133494571749532882362892217349223593804155256951360711310774050441653938497684778238410705146594610516034908693068779094340885697921007741808170634807961255538293377545028592601580783351297669428010574584193888819072321903901400572418394050754891942407918305438100152865049867193661481896928332223938898437847422673633810150826193933781425399771011870563676325257562707292322397830643682340690002090542993628620158342707850635802218423788691145060969816601348249525054638474321539692610035613994328820376272953956145447006386872851333545891204214064072561802882861326708341683281630367262748689768603177285958305299209311628615287257102047750653737904981025226059795323114150866995464657919746926280413225772519754455422082098429526982364706930513389885086319030518754998694095372437483387975460347955395671186852141046519312038166415726092875582144245656783018060418771632585564121447235106025798956659666813695470300778672857410841868070776832228688236597604608297779349863660947652221907681489550914711871165370514399590145775445889161853921473584026002845381803722383425739847529430521353139817774366933901396581213330219362585777201795293355130291147345524343039584921121022818063667354590579834475933141845498536948403786986250595699018679148679637434084296501251777288890968300054336635802915470105834948775045491475187079118789799967242569696199490545780353424228422185838200045784314089545988301056266523184060122354997674303532714592357032764429651832193277341333383646118055725369196909971016985070697001283057370129276836423160112174716139388162760282454062057117257303388827683925830795661674869857099969547427107678651600864411673297576261350362212987988041163045444881268035811115029600836691355558899817203676321994018624156026922674349275358314983539465349221822877731246518511377869136469930622476496118124170399019745455323656039976927059499326651540056927540258106757161697917736984771533295827647213315024831652026714047271619267730580351385236088829422794117777692779632575470434571118246080486086480551848651041997857021557772768580149692941560517100314403880519741718044630849820928621556181583498541479812743172736963440419389532408038902492704574315487925292303754457501682858167305929678552950326081296360813775005501962433853186786387304153373223601186677393564391422284969108716471891982171474004911376616459178648864471569056732760234818423546867082877773063469639914032062818365165227301844741189073711496798858236011365325268376822823807389105058664600997977924351667522350312466961996188806854076175852615279941200475722688554873294273988731837945495539910416432572138904810769085529829918645747752966951475114737436723823633155155147675062612256923615739051560112493111770755729159234960916181086371877354819288001019783333241902883048524753853208883035434461627922795061285587693688968469205295511093971425477850500021527969863214581311974139601461386238983354080307284149785762744176477228766650702710172515258245724205767616246484934509901380720917479393573230505885784797870373475981962626785115973946754915466515663727992559887012279216571643972973989972846016364226623478984469125770591390796955240948426179334711143338552975629433416240739999455100295605071584248370909814958353625417861903280493206942471885604325123253399811442419675368533808451486362884927345510325302255101636107119449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raden · Answer

so, prime or composite ?

kc_kennylau · Answer

well, eh...

raden · Answer

i tried by using wolfram, but it is not working (-_-)''

raden · Answer

btw, i got this question from : https://www.facebook.com/groups/pencintamatematika/

anonymous · Answer

I use Mathematica
PrimeQ[2014! + 1]
the answer was false. It is not a prime.

raden · Answer

waw, Mathematica is bravo :)