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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1111.0. "Largest Known Twin Prime Pairs" by AITG::DERAMO (Daniel V. {AITG,ZFC}:: D'Eramo) Tue Aug 15 1989 21:06

        The next three replies are from the USENET sci.math
        newsgroup, and present what are claimed to be the three
        largest known pairs of twin primes.
        
        Twin primes are positive integers n and n+2 such that
        both are prime.  I believe it is as yet unsolved whether
        there are infinitely many such pairs.
        
        For the record, the largest known pair is given as
        
        		   11235		    11235
        	1706595 * 2      - 1 and 1706595 * 2      + 1
        
        Proth's theorem is the subject of at least one reply to
        an earlier note on primes, but I don't have the exact
        topic.reply number at hand.
        
        Dan
T.RTitleUserPersonal
Name		DateLines
1111.13rd largest known twin primeAITG::DERAMODaniel V. {AITG,ZFC}:: D'EramoTue Aug 15 1989 21:08105
Article 6622 of sci.math
Path: ryn.esg.dec.com!shlump.nac.dec.com!decuac!haven!ncifcrf!nlm-mcs!adm!husc6!ginosko!uunet!tut.cis.ohio-state.edu!ucbvax!hoptoad!chongo
From: [email protected] (Landon C. Noll)
Newsgroups: sci.math
Subject: 3rd largest known twin prime
Keywords: twin,prime
Message-ID: <[email protected]>
Date: 12 Aug 89 07:53:44 GMT
Organization: Nebula Consultants in San Francisco
Lines: 92


	                                7650
                              663777 * 2     - 1

                                    is prime

                                                                       50290
    856185054079777688313032752753820486925181396669154354391009545635357813
    244080841086995247160048914879451222899911533413534318280820285618806143
    021525740263558852018759097409108893736675504343782762844550785566686116
    804039127130158846580023548299149894188316315103594074400837332310252659
    520206355986889842792991115213918486296135295222353354057572133188881286
    694590208297088685222797526131189944576117867704447450028506922657825467
    767944563549562869590715978043585326201075031655158841159256116488978932
    111760834305779684229623729277931781479645240993957714092429511353901144
    208906364897998602910778482235194483487271104193802943327023496366601867
    730499234165657519778834959726073043070878774483821323900241425049237735
    444051726146836477781189864405800141771130091393019437362571976537238927
    048825567096953122828158680706422919350382949160211920420648516720863127
    989711834706943512159935104586453887055810147484211013614121161626099413
    184469064050225920019101510236928264946350920914363449365622708635784116
    269375830170433357028465484994450648709849991879419927564750650199775661
    346520219682442150836932258247590599181613664303093525934118615594672908
    226953003568197407436703585747270008352970826544875503216543219402241975
    824388549132982641528820388687618058136857790769911474288309225679457645
    851495759315209137675572803258059723154929662687675063683801283255517892
    035692542501064602771917134962909374880794569102337953642021488579784072
    620854900106693403516187609037681674740970834819303902688837820567595064
    084742481783994258548363819407547674102615442686264310586036779994196755
    486515661557728626820384479732521424921213866824853841342418701526153300
    449967087767994341019107912273207338619698474085858695117135142501229377
    914098175156292446681260165812804029924349242810501962967138103070240564
    239308052980006642888391297385215393288056854223324137122671349217321522
    478389939889697786536024516474189222906318712279295319671798715371101199
    161320545028386270051391977199647567009208364218563882209967336322313653
    905830637034438198790254488819369739389666151514705359963755408188347014
    924733202033315325477371372314726376464989618309373272241240793429446112
    801935164461910767200316579614670095941713069807376956653023907639907870
    138892560739916360601042770134197540043548761919510604724691918911438847





	                                7650
                              663777 * 2     + 1

                                    is prime

                                                                      50290
   856185054079777688313032752753820486925181396669154354391009545635357813
   244080841086995247160048914879451222899911533413534318280820285618806143
   021525740263558852018759097409108893736675504343782762844550785566686116
   804039127130158846580023548299149894188316315103594074400837332310252659
   520206355986889842792991115213918486296135295222353354057572133188881286
   694590208297088685222797526131189944576117867704447450028506922657825467
   767944563549562869590715978043585326201075031655158841159256116488978932
   111760834305779684229623729277931781479645240993957714092429511353901144
   208906364897998602910778482235194483487271104193802943327023496366601867
   730499234165657519778834959726073043070878774483821323900241425049237735
   444051726146836477781189864405800141771130091393019437362571976537238927
   048825567096953122828158680706422919350382949160211920420648516720863127
   989711834706943512159935104586453887055810147484211013614121161626099413
   184469064050225920019101510236928264946350920914363449365622708635784116
   269375830170433357028465484994450648709849991879419927564750650199775661
   346520219682442150836932258247590599181613664303093525934118615594672908
   226953003568197407436703585747270008352970826544875503216543219402241975
   824388549132982641528820388687618058136857790769911474288309225679457645
   851495759315209137675572803258059723154929662687675063683801283255517892
   035692542501064602771917134962909374880794569102337953642021488579784072
   620854900106693403516187609037681674740970834819303902688837820567595064
   084742481783994258548363819407547674102615442686264310586036779994196755
   486515661557728626820384479732521424921213866824853841342418701526153300
   449967087767994341019107912273207338619698474085858695117135142501229377
   914098175156292446681260165812804029924349242810501962967138103070240564
   239308052980006642888391297385215393288056854223324137122671349217321522
   478389939889697786536024516474189222906318712279295319671798715371101199
   161320545028386270051391977199647567009208364218563882209967336322313653
   905830637034438198790254488819369739389666151514705359963755408188347014
   924733202033315325477371372314726376464989618309373272241240793429446112
   801935164461910767200316579614670095941713069807376956653023907639907870
   138892560739916360601042770134197540043548761919510604724691918911438849

These two numbers represent the 3rd largest known twin prime pair.  They were
discovered on 30 May 1989 at 18:24 PDT by a team consisting of Joel Smith,
John Brown, Landon Curt Noll, Bodo Parady, Gene Smith and Sergio Zarantonello.

Primality was demonstrated by a program implementing the Lacasian h=3A test 
and Proth's theorem.  An Amdahl 1200 takes 6.3 seconds to confirm each twin.
Independent confirmation was kindly provided by Prof. Atkin.

chongo <m23290> /\pp/\
1111.22nd largest known twin primeAITG::DERAMODaniel V. {AITG,ZFC}:: D&#039;EramoTue Aug 15 1989 21:08106
Article 6623 of sci.math
Path: ryn.esg.dec.com!shlump.nac.dec.com!decuac!haven!ncifcrf!nlm-mcs!adm!husc6!ginosko!uunet!tut.cis.ohio-state.edu!ucbvax!hoptoad!chongo
From: [email protected] (Landon C. Noll)
Newsgroups: sci.math
Subject: 2nd largest known twin prime
Keywords: twin,prime
Message-ID: <[email protected]>
Date: 12 Aug 89 07:56:33 GMT
References: <[email protected]>
Organization: Nebula Consultants in San Francisco
Lines: 92


	                                7701
                              571305 * 2     - 1

                                    is prime

                                                       97468578728074825013
   696427871717032674522675940856636457244386056504010105704493764321049096
   889746820678772691668735787913881516597886386820605509225365338931554729
   370264054844908914802263228515537620509821509582690999236941473058499877
   159759915328395858612340770538832959874972504236379670564426449720089070
   762909732375360661685331787449876423790329670408026685925819525787747532
   719459533234490986961509575907420609582889798493211982186190255748989620
   780898653703080121366337926437629957128960067422638915646074333600725122
   069192295573784916912571596308100065391076761892402045572569491639318201
   246701051127387230404576957625786535959758811135967647255245829442602318
   577782837512903200025006111221309069264475501625387025852585884891899772
   125584412088123021267524390291116367514783465664544765938025849166030853
   863996990610823340213308900808925242156993587202153332294159595744273536
   347537084704595721657977451692165103316344581174923435194607570052535593
   235427945887410282093703408820471621114022103734079117274295094214194364
   831548687028175119178620194623111543170530984710869823837903114826802642
   395418740506149712965575365337628858140508672125948266070673666494434228
   784976797383934967056455295176597946073241946250450735808053974666905965
   583093749470847973005431362161718924779763525574241913359301996275364486
   376084447202235891512798731491846533846374133826525088571966503120943520
   339037483521663630535229117310104235234931773102809516903934060155976693
   376202860215050126267261195086424447386969905624753340822880489472389318
   895596697732526679130995944762299777600063149378439816821143545709492463
   133589430740264813675339894798904394072235021627814033523597477669753473
   218750059383149626557796671977993369554037107852190230818956034597774598
   071944091158115614025443357744949237949814711259805697611799377586169530
   768234207861853105644749317665663997102708547499652521994554970065751390
   169030195780895814609051760689120192190150415514122188407532724918080346
   357065172861003300885147713368524917478031041600994228397404582490645702
   586518825229054069134719866750281989342390183300158547559661677039449456
   752085638601103394215319587586341665981029844295895635776101247055028946
   983210922020658067313013448835399573771193493467917641122990658271915579
   154268894291171143650065840860794030501860283243639992558366825497231359





	                                7701
                              571305 * 2     + 1

                                    is prime

                                                       97468578728074825013
   696427871717032674522675940856636457244386056504010105704493764321049096
   889746820678772691668735787913881516597886386820605509225365338931554729
   370264054844908914802263228515537620509821509582690999236941473058499877
   159759915328395858612340770538832959874972504236379670564426449720089070
   762909732375360661685331787449876423790329670408026685925819525787747532
   719459533234490986961509575907420609582889798493211982186190255748989620
   780898653703080121366337926437629957128960067422638915646074333600725122
   069192295573784916912571596308100065391076761892402045572569491639318201
   246701051127387230404576957625786535959758811135967647255245829442602318
   577782837512903200025006111221309069264475501625387025852585884891899772
   125584412088123021267524390291116367514783465664544765938025849166030853
   863996990610823340213308900808925242156993587202153332294159595744273536
   347537084704595721657977451692165103316344581174923435194607570052535593
   235427945887410282093703408820471621114022103734079117274295094214194364
   831548687028175119178620194623111543170530984710869823837903114826802642
   395418740506149712965575365337628858140508672125948266070673666494434228
   784976797383934967056455295176597946073241946250450735808053974666905965
   583093749470847973005431362161718924779763525574241913359301996275364486
   376084447202235891512798731491846533846374133826525088571966503120943520
   339037483521663630535229117310104235234931773102809516903934060155976693
   376202860215050126267261195086424447386969905624753340822880489472389318
   895596697732526679130995944762299777600063149378439816821143545709492463
   133589430740264813675339894798904394072235021627814033523597477669753473
   218750059383149626557796671977993369554037107852190230818956034597774598
   071944091158115614025443357744949237949814711259805697611799377586169530
   768234207861853105644749317665663997102708547499652521994554970065751390
   169030195780895814609051760689120192190150415514122188407532724918080346
   357065172861003300885147713368524917478031041600994228397404582490645702
   586518825229054069134719866750281989342390183300158547559661677039449456
   752085638601103394215319587586341665981029844295895635776101247055028946
   983210922020658067313013448835399573771193493467917641122990658271915579
   154268894291171143650065840860794030501860283243639992558366825497231361

These two numbers represent the 2nd largest known twin prime pair.  They were 
discovered on 30 May 1989 at 18:29 PDT by a team consisting of Joel Smith,
John Brown, Landon Curt Noll, Bodo Parady, Gene Smith and Sergio Zarantonello.

Primality was demonstrated by a program implementing the Lacasian h=3A test 
and Proth's theorem.  An Amdahl 1200 takes 6.3 seconds to confirm each twin.
Independent confirmation was kindly provided by Prof. Atkin.

chongo <Landon Curt Noll> /\mp/\
1111.3Largest known twin primeAITG::DERAMODaniel V. {AITG,ZFC}:: D&#039;EramoTue Aug 15 1989 21:09135
Article 6624 of sci.math
Path: ryn.esg.dec.com!shlump.nac.dec.com!decuac!haven!ncifcrf!nlm-mcs!adm!husc6!ginosko!uunet!tut.cis.ohio-state.edu!ucbvax!hoptoad!chongo
From: [email protected] (Landon C. Noll)
Newsgroups: sci.math
Subject: Largest known twin prime
Keywords: twin,prime
Message-ID: <[email protected]>
Date: 12 Aug 89 07:57:50 GMT
References: <[email protected]>
Organization: Nebula Consultants in San Francisco
Lines: 121


	                                11235
                             1706595 * 2      - 1

                                    is prime

                                                                       20143
    352544560125323858255923099520074091940294248370427871157129560968807632
    451543311255400317919904059798723084940887081441002584729480178275775785
    361968690664881197033784783646381050042587086223690993061420529014939634
    750549375246637789196101072703984362960663207317122267452754370331704981
    123180537346617495667913370134162175105185085469182284674830684411144628
    496336356251105788172667889895614185407273741737317338179043293812607448
    187643185242527535987971554161361538902765991487249068666185121393939820
    869663410690401822192552522060374001016609805524237103655060189725522501
    868371770385891263396728896252436115313959713384925834829096549281092500
    530007719670288548414264665230145749935069001126312045662681273766540573
    660875172862800094440437138196599852035480271764210296992468486579942777
    429257727229560441953856297764936195032643988504534378941212378729771224
    876063289348367607290273390161235789361106552906137055542632360746688873
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    156152027554720101086538954922899258624764999126000282075079949783371260
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    676517248286290152569524954536018776602562612077311370825963120191666889
    051222959995000829753342597748646682605282775224428487015676567128185895
    580231699632903997870939567834524926618064114724778931329338262273176474
    673336820177815427788422632395111836631374503047634010282660759592802488
    244612693844619475110896142213347152050763895189428229620542233381517059
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    197208219906923943773580667662994541608406830299761515641098727715949909
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    603768424081434415527783265357116526062098920647036689026029864454282804
    513724012504411999228371918773691882204786525104794942962800687048044237
    042808480590228372225298061189494715290001599478682415818725846912302659
    129645227900144440576509593371529176211592238765893711704331037412472218
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    938489198831092233503268722784895203384183925605950366443447732911829166
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    258114679219555500656408220402941704564285660205204204971179341698345473
    512386870560961227887976098637804022768489912075714143947861913178479536
    475383087546514167953115035158520832032373867017329917164479500672689411
    795588991824278954475147823610627747948635452554450097818274164786456934
    669570918462062866071317849723214279486615105862821052791399518902056967
    628069544115473086064218164034971774021915203344768886618039502531265609
    068932340917929610548974433533473530886013565205635511200482989352481074
    822962780254824415879578436041191378136302377420707757289636353756190735
    177475209689787565379442727812461433229280123512834635462273227511025370
    223107133001854332757451830019176298188502305741116961025721813092252266
    288385045136789857897721174872482448028513123250508166749467836374056959




	                                11235
                             1706595 * 2      + 1

                                    is prime

                                                                       20143
    352544560125323858255923099520074091940294248370427871157129560968807632
    451543311255400317919904059798723084940887081441002584729480178275775785
    361968690664881197033784783646381050042587086223690993061420529014939634
    750549375246637789196101072703984362960663207317122267452754370331704981
    123180537346617495667913370134162175105185085469182284674830684411144628
    496336356251105788172667889895614185407273741737317338179043293812607448
    187643185242527535987971554161361538902765991487249068666185121393939820
    869663410690401822192552522060374001016609805524237103655060189725522501
    868371770385891263396728896252436115313959713384925834829096549281092500
    530007719670288548414264665230145749935069001126312045662681273766540573
    660875172862800094440437138196599852035480271764210296992468486579942777
    429257727229560441953856297764936195032643988504534378941212378729771224
    876063289348367607290273390161235789361106552906137055542632360746688873
    186328232944279151864532332435941871169429547406606121217841352008831190
    156152027554720101086538954922899258624764999126000282075079949783371260
    975007516423014919600978745765760818910590508292838025502848931242417572
    321326051380563130393745123850025870082671061469286766177067293908409073
    681415041516450395760881293295804962195456087052991102945843196784288906
    485498070850440528566579334057279007785975681922028784869334808988433164
    676517248286290152569524954536018776602562612077311370825963120191666889
    051222959995000829753342597748646682605282775224428487015676567128185895
    580231699632903997870939567834524926618064114724778931329338262273176474
    673336820177815427788422632395111836631374503047634010282660759592802488
    244612693844619475110896142213347152050763895189428229620542233381517059
    411411717205553980450052909047156579927140833371461176227702138482917665
    197208219906923943773580667662994541608406830299761515641098727715949909
    443085776501623034606761558198932928501521045770942668329793765823381729
    568798409614351034445819170916117682014805769521714284446219827747582825
    838772140726792956296322434790972008922754950984491755791393520999750880
    603768424081434415527783265357116526062098920647036689026029864454282804
    513724012504411999228371918773691882204786525104794942962800687048044237
    042808480590228372225298061189494715290001599478682415818725846912302659
    129645227900144440576509593371529176211592238765893711704331037412472218
    528082314703337441602955959112116524526207874922394896876746427528063108
    938489198831092233503268722784895203384183925605950366443447732911829166
    996643870908402775234927478480275552143130606613776623857792293361663073
    258114679219555500656408220402941704564285660205204204971179341698345473
    512386870560961227887976098637804022768489912075714143947861913178479536
    475383087546514167953115035158520832032373867017329917164479500672689411
    795588991824278954475147823610627747948635452554450097818274164786456934
    669570918462062866071317849723214279486615105862821052791399518902056967
    628069544115473086064218164034971774021915203344768886618039502531265609
    068932340917929610548974433533473530886013565205635511200482989352481074
    822962780254824415879578436041191378136302377420707757289636353756190735
    177475209689787565379442727812461433229280123512834635462273227511025370
    223107133001854332757451830019176298188502305741116961025721813092252266
    288385045136789857897721174872482448028513123250508166749467836374056961

These two numbers represent the largest known twin prime pair.  They were 
discovered on 6 June 1989 at 11:55 PDT by a team consisting of Joel Smith,
John Brown, Landon Curt Noll, Bodo Parady, Gene Smith and Sergio Zarantonello.

Primality was demonstrated by a program implementing the Lacasian h=3A test 
and Proth's theorem.  An Amdahl 1200 takes 9.6 seconds to confirm each twin.
Independent confirmation was kindly provided by Prof. Atkin.

chongo <Landon Curt Noll> /\mp/\