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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
Message 1 of 1 , Dec 3 1:42 AM
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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.

_______________________________________________________________
El Nokia 5510, un aspecto extraño, un sonido genial.
Visite http://es.promotions.yahoo.com/nokia/
descubra el Nokia 5510 y ¡lléveselo!
El concurso acaba el 16 de diciembre de 2001.
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