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Prime gap of L = 112194

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  • Jose Luis Gomez Pardo
    I have found a gap of length L = 112194 and D = 14.0273 between prp3474-112194 and prp3474, where prp3474 is given below. The limiting numbers have passed the
    Message 1 of 1 , Dec 3, 2001
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      I have found a gap of length L = 112194 and D =
      14.0273 between prp3474-112194 and
      prp3474, where prp3474 is given below.

      The limiting numbers have passed the Miller-Rabin test
      with 10 randomly chosen bases and also other
      pseudoprime tests. They are within Primo's
      reach but I will have to find help and their
      certification will take some time. The method used to
      find the gap is based on the use of the Chinese
      Remainder Theorem and so it has much in
      common with the one recently described by Henry Dubner
      in this list. In fact, I was led to this
      method by a remark of David Broadhurst saying that
      Dubner had used the CRT to find a large
      run of consecutive composite numbers, so I should
      thank Henry and David for the inspiration.

      Thanks also to J.M.F. Vilaboa, who allowed me to use
      his Pentium III 800 computer to find the gap, and to
      Manolo Ladra for checking the gap in his computer.

      I take the opportunity to mention that Manolo Ladra
      also certified with Primo the top prime (with
      2978 digits) of the gap of length 72196 previously
      reported by me. The bottom prime of this gap
      was certified with Primo by Manuel Seijas and both
      certificates have been validated with Cert_val,
      so that this one can now be considered a proper prime
      gap.

      PRP3474 =

      40304802323693974861441201822989771461417124557622297227625154826275765206954\
      10862247144758040320534903879042674706879283833621906160570559479333497675512\
      37697462189058830992726614952857661231587300795953187157486804931105746746715\
      77877077715574251543966963912246890727785117363273685407147382603590401877967\
      64355356692135780669484439032868685316760532233237869141392670618514144352805\
      46856269171899590616140124766386257586812782976563425265843882955739099132018\
      40567889002894824173724790311854676184916264930647265575411119495453228685489\
      34995529288945503046276180314304362356229705339950443111191951587896990873038\
      11001357910094722541305451337708723751064018160607760619675996380810660254751\
      33776143585990474858127280391919190710579157025943309727691122863516873611325\
      59163866647124579499965357629333551108813787861225532427312415211404219663993\
      75342222045273874821960701322488083265821809020123981290334615917292227004685\
      09991745353562560593789066839172206577449058895497565837049228757346279334430\
      62827825310547957352512378259646563338026981708381288715787131943656476678821\
      46484770132701789650659839016599171214165114754093395213179539577513631756944\
      92561351168629182286245640960870690831134950361765218411442607130889553818964\
      60494247088394881847391339635247213233043900701906979130836485104449030629361\
      39847772055031819417280981463025130913444148846472075510176939328358047764130\
      75958279087671660506986847137468134041795568354065209994607807702159586400312\
      66385032103006787645929879636786497572696339278402360877957077444109761017182\
      83354705408049003430718238729122759671670429072289355439169800479901431358417\
      66624799152283965115066473518425527517794421118793943022169358937231189687622\
      90855666324577748662184388663297504188142331952532845456039821323082890409424\
      29247845728669942865907260050431554277687090058900641071208020092473557723939\
      98579851243779168269764483365350514643879669403197122606823244623038596115800\
      79835463276176908016926727256786464078379364160659989700031652502336595547799\
      25657500470694420539083716983858785398324603331861815017718324138856569265823\
      39369697910661494686358309109565130944196661053454038162081537019957094141352\
      72512449592082122215377162126889565073204790228406705392003999185320850105688\
      76125598571293264975276191220464752626737665282102132950250705707453230912157\
      13769437452333425811375305357180367526669730338225964912113623084181809453360\
      03524805804286433445457810596530083804392333340798665258598706634705981609527\
      07783342175569463341026427049140518606924188045795552680520995418284613859095\
      15069129639586898638743801208880053427674549896858598430102628681118509782124\
      54924299602107179092268773015886651287859041284973019418289996938270865544684\
      57203558493261971152530811300748347160218127255749500501534638979860445166022\
      03717976219606966702619786257327973568615829308218106893099263412951761406091\
      99640466252726209638006707603062657001382619774570082084512626017429773732561\
      70475186204782094246972994845903276042426690480688988520023801085816147970132\
      21095359562519035473292828744187535516272066430428453905926818163001462578043\
      43145422041381101253120754890415117117494098912652293170053890897092198870721\
      96021767234768860846017788603438449584708102451942513917350216619207978861212\
      93145819528544222635854024051777422904677016586609163390856270536363959355671\
      72531247153781006122148462418513328846816508921160542979807289856287702492015\
      35207871510051943113181018670622393861642932270533574707401536974300852864198\
      460077081

      Jose Luis.



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