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Primes

Primes. Ali Salman Soutcho Toure Prof. Geoffrey Exoo Prof. J eff K inne. Computer Power. SETI@home run 225,534 cores. 15 computers, 4 cores each. Each core can do around 1billion operations/s. 60 cores running 24/7. Goals. Goal 1  Find large primes composed of 2digits.

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Primes

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  1. Primes Ali Salman Soutcho Toure Prof. Geoffrey Exoo Prof. Jeff Kinne

  2. Computer Power SETI@home run 225,534 cores. 15 computers, 4 cores each. Each core can do around 1billion operations/s. 60 cores running 24/7.

  3. Goals Goal 1  Find large primes composed of 2digits. Like « 1616161661666111 » or « 15515151515511 » Goal 2 Find large primes. Goal 3 Find large Sophie Germain primes.

  4. Is 8,876,044,532,898,802,067 (19 digit) a prime ? PrimesExample : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … How can we check if a number is prime ? Trial Division Lucas Theorem

  5. Trial Division Checks if n can be divided by any number that’s greater than 1 and less than n. Example, 49 49 Can be divided by {1, 7, 49} Example, 47 47 can only be divided by {1, 47} 8,876,044,532,898,802,067 { 1500450271, 5915587277 }

  6. Lucas theorem Checks if n is prime by taking the factors of n-1 and doing a sequence of tests on them. Example N = 47 N-1 = 46 Factors of 46 {2 , 23}

  7. Results n = 5,551,151,151,151,111,151 (19 Digits). 1. Finding primes that are made out of 1’s and 5’s.

  8. I was able to get 30-40-70 digit primes. n = 5111511115111115151151155551511551555115151515151551511515111111511551511151511111515151115555151111 ( 100 digit ) factors for (n-1):  1: 2 2: 5 3: 29 4: 755861 5: 42189106789 6: 43634772601903617:126670745376096399606480420313915707172298481447007567082016637811

  9. 2. Finding the biggest prime Lucas Theorem Example N = 47 N-1 = 46 Factors of 46 {2 , 23} What if we took random primes and multiplied them together ? (2*5)+1 = 11 (prime) (2*7)+1 = 15 (not a prime)

  10. 79792619445519451854981072123004932740684819032839119995820245735751191645669415589929393784276152837429898558449344174921676323618407418297026765598463344686367985219310529198013379987097852576317670382994110601958951745033098701630832317164761722997727544420392246547634746693218326700435323028366736100996782089511568712840499723616082146608922345532352777754257828367883342114795244544063517441637108288480463898983615836271225130768819316954565101764309042772035833215248538312057421042242430318383198885281046884152972736313656674399107234630718553615963124436877650522122021408257165402399159719519893784970640324522659487709135405331771569948004987816945863532815263926861200333567140560636857568555655473178156192685356886746949579038770471542180032767900616037648464187840238873108411946904661414018758824132583208798306829441487762461558972779624303765184337958918688463007826949389157676457103889599122721858478773724516207359738907503813430141690574919531360239969694754522680661320617680090413187041617385711411543268393184387890457034054593124336527455758123707380885848252461269689708325116117730780455887916975741757334417460590832271785709936567467374450080545171025198945283288990228294131267080250902192873016844067836103510070053824306773850045822543448969686697079634816872403600560224000686157751073766932456657699653789078144068150750385343302934838251842527681826240812899863863644529261314199054630811776128354132919576231652379966850017154117794893863790392835128200724808911138033550279235734671514673463459208630058473689522869808895209639024175480822397610665439461138191198742135284411285730465352227045596365967789090540803874257005913251106873623174277834867357457048244454837313738399567633864183772008927077542994212916197517141195313563731701556405031138992694366966575749819366011781710708075240359847459136686036157334200981319079469969934872697966614154946462075976420433243296580020823039203921625036514118964714854279012522096954882021263052527609962452665160596343003528704283943634284508689873585047637508155104255558916771384709653633254836245650988249671510186971131486518612985552728202496428631253833849514900986490822026883048789127822884406482031370304822563886528136975986005154652732300655211409488000627527184837755273681414538349091768749023608268169105825048350344964583154927967933017366514959763607077069142002823059789680034153895344253555642528004372902789263555239022209282865692403727200974719584193943961560560811855333939606890984447169804386156016485786105496564242095285747989484440094302229103110975743589280002935350953271691358908896866508295247157106865223710799579781497090875834321695048591057261453899040649267065902365302739609422287048614561279158745778226321664796009804402176326517798467079674188926231911176633256456566911240099075843704438718439460442569871790059903001674573871986655091650092597654821446796201890201422245132904969774917541890478572721378943033936433216537394575414815043027072140024726213115014180423184768460612876493733668237856047901773841962766583245915315282113552041297786610004663836113987599153462106139844462699303473320330866916140536544483897852540343797038276898191295338115883226564676245818541997889074547209884329944617369615647256744267962868719463304346335584038815923558171992382654540720314551151490831075673556578456357295035645737662008223165709608068521579151434815324124031689011558531985816587947256530931235404639730082714694194468224377694776508061934307647830443618818681398315915472585125792469866476828277651109523741444054708909176864374153558693144270529971643045306779647003129429205428118674182919774621263513084999535659020936707021655874110340385781708615382604363488967068437714354973242746153877094541756184144524551352100662457617413926998159452699751135090198635357161235233151512551172279927992828756773932329679237631517723369399002027994665602737207256326624405062343763160373149520433089113910664214966539931926371130474598870077181632737432628557282419981839737316361499632966663594544890344355903811550436970711235086829371336224639064703644617393879869074498299422555188768498230936724312777615183803077321459646665219254184482251661096300487944934739207254770686859087566632772654825123495254909556106520478218015146899 ( around 4,200 digits ).

  11. p = 5 2p+1 = 11 5 and 11 are primes. Therefore, 5 is a Sophie Germain prime. Currently working on p = 2981625476911166341900898692545033822173452735465017273841874360846727618978016091529967311332707048954384883904760278503 (121 digits) 2p+1 = 5963250953822332683801797385090067644346905470930034547683748721693455237956032183059934622665414097908769767809520557006 Sophie Germain prime p and 2p+1 are both prime.

  12. Future Goal Records 5000th largest known prime (as of now) is 287,407 digits. 20th largest Sophie Germain prime (as of now) is 29,628 digits. Reaching the lists of the largest prime Or Sophie Germain prime.

  13. Professors : Jeff Kinne Geoffrey Exoo The End Students : Ali Salman Soutcho Toure Po-Ching Liu Troy Schotter KarthikTottempudi

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