Re: [Cfrg] Prime 630*(427!+1)+1 for classic DH?

Travis Finkenauer <tmfink@juniper.net> Thu, 06 April 2017 01:54 UTC

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From: Travis Finkenauer <tmfink@juniper.net>
To: Greg Rose <ggr@seer-grog.net>
CC: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: [Cfrg] Prime 630*(427!+1)+1 for classic DH?
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Date: Thu, 6 Apr 2017 01:54:18 +0000
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Subject: Re: [Cfrg] Prime 630*(427!+1)+1 for classic DH?
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I just realized the '>>>' of the python shell might be rendered as a triple blockquote; here is the python session with '>>>' replaced with '%':

% import math, sympy
% q = math.factorial(427) + 1
% q
2906347176960734841102915400715931684676738386917551293602548940017089151563020096075793145507544909799419325859795323626093294797601295362066222447438952667031315410724883975028255045041250967003021649815634917672723512152046317329813204370731220675839985347995496026203846545595056245788546987335750260208358284546291147473293252515791139722473131884086360496749320657551127839785289082610236625397838417994044140052064528157551457620578232391435991791325758463549417841949376589453031999388696831078873411074599909633778369511252614215116845902011637486786496344033030211520607498474074348716583103427724802387789604245206457732417620741922128269046960386975413294794633781512968490642838333805952796503387711844405306514987765843460355064766744241388139564882514479660485760706796398091343123973467734371818224366218814091320885248000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001L
% p = 630 * q + 1
% p
1830998721485262949894836702451036961346345183758057314969605832210766165484702660527749681669753293173634175291671053884438775722488816078101720141886540180229728708756676904267800678375988109211903639383849998133815812655789179917782318753560669025779190769237162496508423323724885434846784602021522663931265719264163422908174749084948418025158073086974407112952072014257210539064732122044449074000638203336247808232800652739257418300964286406604674828535227832036133240428107251355410159614879003579690248976997943069280372792089146955523612918267331616675492696740809033257982724038666839691447355159466625504307450674480068371423101067410940809499585043794510375720619282353170149104988150297750261797134258461975343104442292481380023690803048872074527925875984122186106029245281730797546168103284672654245481350717852877532157706240000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000631L
% sympy.ntheory.isprime(q)
True
% sympy.ntheory.isprime(p)
True

-Travis


On 4/5/17, 6:33 PM, "Cfrg on behalf of Travis Finkenauer" <cfrg-bounces@irtf.org on behalf of tmfink@juniper.net> wrote:

    I verified the primality of q = 427!+1 and p = 630*(427!+1)+1 in a python shell:
    
    >>> import math, sympy
    >>> q = math.factorial(427) + 1
    >>> q
    2906347176960734841102915400715931684676738386917551293602548940017089151563020096075793145507544909799419325859795323626093294797601295362066222447438952667031315410724883975028255045041250967003021649815634917672723512152046317329813204370731220675839985347995496026203846545595056245788546987335750260208358284546291147473293252515791139722473131884086360496749320657551127839785289082610236625397838417994044140052064528157551457620578232391435991791325758463549417841949376589453031999388696831078873411074599909633778369511252614215116845902011637486786496344033030211520607498474074348716583103427724802387789604245206457732417620741922128269046960386975413294794633781512968490642838333805952796503387711844405306514987765843460355064766744241388139564882514479660485760706796398091343123973467734371818224366218814091320885248000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001L
    >>> p = 630 * q + 1
    >>> p
    1830998721485262949894836702451036961346345183758057314969605832210766165484702660527749681669753293173634175291671053884438775722488816078101720141886540180229728708756676904267800678375988109211903639383849998133815812655789179917782318753560669025779190769237162496508423323724885434846784602021522663931265719264163422908174749084948418025158073086974407112952072014257210539064732122044449074000638203336247808232800652739257418300964286406604674828535227832036133240428107251355410159614879003579690248976997943069280372792089146955523612918267331616675492696740809033257982724038666839691447355159466625504307450674480068371423101067410940809499585043794510375720619282353170149104988150297750261797134258461975343104442292481380023690803048872074527925875984122186106029245281730797546168103284672654245481350717852877532157706240000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000631L
    >>> sympy.ntheory.isprime(q)
    True
    >>> sympy.ntheory.isprime(p)
    True
    
    -Travis
    
    > On Apr 5, 2017, at 4:20 PM, Greg Rose <ggr@seer-grog.net> wrote:
    > 
    > 
    > Somewhat to my dismay, it did NOT immediately pronounce the number to be prime. 20 minutes later it's still trying to factor it. I don't have anything to hand that will just check primality... perhaps someone else should check it. (Or I will try harder when I have something better than my laptop, which will be a while). It's also possible I made some sort of transcription error, and if so I apologize. Someone who has Mathematica or Maple lying around?
    > 
    > Greg.
    > _______________________________________________
    > Cfrg mailing list
    > Cfrg@irtf.org
    > https://www.irtf.org/mailman/listinfo/cfrg
    
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