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Re: really? (lame question about primes)

From bartekltg <bartek@gmail.com>
Newsgroups comp.programming
Subject Re: really? (lame question about primes)
Date 2015-09-03 13:58 +0200
Organization Aioe.org NNTP Server
Message-ID <ms9cku$fjg$1@speranza.aioe.org> (permalink)
References (12 earlier) <ms6uia$57r$1@dont-email.me> <ms710a$beb$1@speranza.aioe.org> <ms71gl$hho$1@dont-email.me> <ms7300$gk6$1@speranza.aioe.org> <ms91q8$d83$1@dont-email.me>

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On 03.09.2015 10:55, David Brown wrote:
> There have been a variety of silly ideas in this thread (some
> intentional, some accidental), as well as some good ones.
>
> But no one has come up with a working idea that actually has a chance of
> factoring a 600 digit number!

No one in this thread has also idea how to solve Goldbach conjecture,
whether P==NP or not, and how to solve world hunger.

Half of the cryptography systems is based on assumption a bunch
of programmers on usenet group cant solve it i a week.

;-)

BTW, I was hoping that Richard used two too similar prime numbers
and I ran very simple version of Fermat's factorization method,
but he was more clever;>

As we speak about security in cryptography, this would be a huge
mistake.

Look at this number:

N=6656306008655249164123957612534222424912000368941290054361681671810\
473358156447838705173390562626790029530951700110242362363665522412966\
725184603920088147004248502697963491242610310414234911578383282256458\
276766370874401860439165075488781472945530061660501484047480394326484\
617103517504379135200662278550486571819968410075879270762270920098859\
240729081188660838597729331149890859253931757548325818599364031204421\
156056681989351055481408743375643625566195491880462272863893726745649\
214127868608491830095813911837740111440280522968022277001255214954922\
415509187661120404292711047616795049622143667025617

a=ceil(sqrt(N)) is an integer

b2 = a*a-N = 2549038144 = 50488^2.

So
N = a^2 - b^2 = (a-b)(a+b)
We have factorization!

(a-b)
257998178455880753222629957810224903188635668669054943523104315214939\
729141587689643443680630721865791158466117549986755369945232060506699\
900127884744200089328505770486767278922047555842792645845125657099338\
127228378237306269322260898614453779605444120709703492181445013380135\
0709313944644504923750193
(a+b)
257998178455880753222629957810224903188635668669054943523104315214939\
729141587689643443680630721865791158466117549986755369945232060506699\
900127884744200089328505770486767278922047555842792645845125657099338\
127228378237306269322260898614453779605444120709703492181445013380135\
0709313944644504923851169

For
1167828229045445971662249118780447846520421784147226620494055391458180\
7601997478699930291352869903692219072218113241990374766447439973877729\
4941194722252835014243689673136787968254216972130137233976876436369535\
2457619346774027074180718388851030931546938988468043490672744425493977\
4094716263320750073186079507225495976235748036343558057410341532576049\
9174965884053070606699130271736508915807365053190141312702103604293220\
0884758543647787591759476041043940010480149898083866228838017408185691\
0653989137800961071176307478195531410877286659821988923600607842238369\
4669208917896312708803930694693988566589

a=ceil(sqrt(N))
b2 = a*a-N is not an perfect square, but if one check a couple bigger 
values - a=ceil(sqrt(N))+36 works.

p2-p1 was ~10^151, so only a half of booth numbers is the same

p1
34173501855172027009217658731049403512738189648854815841795142373676940621\
91652926400102176450757018262769049636027036800905264842784680568455612306\
69669953975946543695876440518626912368990108659170659267659700340363124255\
302847431247260784486932195413513794132970440858067868458027521763718757288441
p2
34173501855172027009217658731049403512738189648854815841795142373676940621\
91652926400102176450757018262769049636027036800905264842784680568455612306\
79669953975946543695876440518626912368990108659170659267659700340363124255\
302847431247260784486932195413513794132970440858067868458027521763718757289829



bartekltg

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Thread

really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-08-31 12:07 -0700
  Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-08-31 23:23 +0100
    Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 01:18 -0700
      Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-01 11:01 +0200
        Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 12:20 +0100
          Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-01 15:48 +0100
            Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:26 -0700
              Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-09-02 02:12 -0500
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 08:38 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:03 +0200
          Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:24 -0700
            Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 22:27 +0100
              Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 15:02 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 23:20 +0100
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:22 +0200
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 17:18 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:19 +0100
                Re: really? (lame question about primes) James Dow Allen <gmail@jamesdowallen.nospam> - 2015-09-02 12:42 +0000
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 14:21 +0100
                Re: really? (lame question about primes) Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-09-02 17:45 +0200
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 18:06 +0100
                Re: really? (lame question about primes) James Dow Allen <jdallen2000@yahoo.com> - 2015-09-03 17:05 -0700
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-04 02:18 +0200
                Re: really? (lame question about primes) Chad <cdalten@gmail.com> - 2015-09-03 22:37 -0700
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-03 23:49 -0700
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-04 00:18 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-04 08:25 +0100
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 14:36 +0100
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 16:49 +0100
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 17:32 +0100
            Re: really? (lame question about primes) Kaz Kylheku <kaz@kylheku.com> - 2015-09-01 22:55 +0000
              Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:15 +0200
          Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 03:19 +0200
            Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:37 +0100
              Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 11:24 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 10:42 +0100
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-02 03:01 -0700
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 12:28 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:12 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:19 +0100
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 14:56 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 15:47 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 16:27 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 16:37 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 17:01 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 10:55 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:05 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 11:49 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:54 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 13:22 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-03 13:58 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:34 +0100
  Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-08-31 23:10 -0500

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