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master1729  
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 More options Nov 2, 3:26 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 11:26:31 EST
Local: Mon, Nov 2 2009 3:26 am
Subject: factoring request
Plz factor the following 4 numbers :

(46^46 - 1) /( (46+1)*(46-1))

(58^58 - 1) /( (58+1)*(58-1))

(82^82 - 1) /( (82+1)*(82-1))

(106^106 - 1) /( (106+1)*(106-1))

thank you.

regards

tommy1729


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master1729  
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 More options Nov 2, 7:42 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 15:42:02 EST
Local: Mon, Nov 2 2009 7:42 am
Subject: Re: factoring request

I said PLZ.

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Virgil  
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 More options Nov 2, 7:04 am
Newsgroups: sci.math
From: Virgil <Vir...@home.esc>
Date: Sun, 01 Nov 2009 14:04:46 -0600
Local: Mon, Nov 2 2009 7:04 am
Subject: Re: factoring request
In article
<1699063352.149909.1257108152590.JavaMail.r...@gallium.mathforum.org>,

(46^46 - 1) /( (46+1)*(46-1)) factors into

   [(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46^23 + 1)]

And similarly for the others.


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master1729  
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 More options Nov 2, 9:01 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 17:01:03 EST
Local: Mon, Nov 2 2009 9:01 am
Subject: Re: factoring request
Virgil wrote :

sigh.

im tired of these jokes.

you people know darn well that

1) i was aware of the above trivial factorization

or should i say : " what is intended " since the above is actually wrong :

quote :

(46^46 - 1) /( (46+1)*(46-1)) factors into

[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46^23 + 1)]

/

wow a number factors into a smaller number !!??!!

yes smaller because (46^23 + 1) / (46^23 + 1) = 1

so that joke is even wrong and pathetic.

2) im not a beginner at factoring , otherwise i could not have known that (46^46 - 1) /( (46+1)*(46-1)) is actually an integer.

3) thus i wanted - as you darn well know - a full factorization. and a correct one !

4) if you will reply with jokes , mistakes , nonsense and irrelevant stuff , i will too and say here : axiom of choice is wrong.

regards - assuming and hoping you will give a better reply now -

tommy1729

since this reply of virgil was rediculous ( didnt say virgil is ) , i feel the urge to quote an idiot :)

" sd354fq35f13e4f115fsd  search the people " musatov.


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master1729  
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 More options Nov 2, 9:28 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 17:28:09 EST
Local: Mon, Nov 2 2009 9:28 am
Subject: Re: factoring request
in the meanwhile i computed that
(46^23 + 1) / 47 = prime.

tommy1729


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Pubkeybreaker  
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 More options Nov 2, 9:35 am
Newsgroups: sci.math
From: Pubkeybreaker <pubkeybrea...@aol.com>
Date: Sun, 1 Nov 2009 14:35:44 -0800 (PST)
Local: Mon, Nov 2 2009 9:35 am
Subject: Re: factoring request
On Nov 1, 11:26 am, master1729 <tommy1...@gmail.com> wrote:

> Plz factor the following 4 numbers :

> (46^46 - 1) /( (46+1)*(46-1))

> (58^58 - 1) /( (58+1)*(58-1))

> (82^82 - 1) /( (82+1)*(82-1))

> (106^106 - 1) /( (106+1)*(106-1))

(1) Each of the numerators is the difference of two
    squares.
    Their factorization is trivial.

(2) You can find the full facorizations at Richard
    Brent's website.


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Martin M. Musatov  
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 More options Nov 2, 9:36 am
Newsgroups: sci.math
From: "Martin M. Musatov" <m...@yummy.con>
Date: Sun, 1 Nov 2009 14:36:27 -0800
Local: Mon, Nov 2 2009 9:36 am
Subject: Re: factoring request
Blow me, you impotent puke.

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master1729  
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 More options Nov 2, 10:17 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 18:17:07 EST
Local: Mon, Nov 2 2009 10:17 am
Subject: Re: factoring request

> Blow me, you impotent puke.

shut up musatov , you retarded son of a german whore who married a bad smelling pokemon.

go ' search the people '


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master1729  
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 More options Nov 2, 10:19 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 18:19:25 EST
Local: Mon, Nov 2 2009 10:19 am
Subject: Re: factoring request
pubkeybreaker wrote :

thanks.

i will look at R Brents website.

i already factored 3 out of 4.

but that last one is tricky , better use his website.

maybe it will lead to a nice conjecture.

regards

tommy1729


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master1729  
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 More options Nov 2, 10:48 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 18:48:00 EST
Subject: Re: factoring request

i have trouble with .gz files for some reason.

didnt find an online program to factor , did i overlook ?


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master1729  
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 More options Nov 2, 10:52 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 01 Nov 2009 18:52:29 EST
Local: Mon, Nov 2 2009 10:52 am
Subject: Re: factoring request
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Virgil  
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 More options Nov 2, 10:22 am
Newsgroups: sci.math
From: Virgil <Vir...@home.esc>
Date: Sun, 01 Nov 2009 17:22:03 -0600
Local: Mon, Nov 2 2009 10:22 am
Subject: Re: factoring request
In article
<968439331.150126.1257112893522.JavaMail.r...@gallium.mathforum.org>,

My poor proof reading, sorry.
Should have been
   [(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46+ 1)]

Which is a factorization. though apparently not the COMPLETE
factorization that OP did not actually specify he wanted.

> wow a number factors into a smaller number !!??!!

> yes smaller because (46^23 + 1) / (46^23 + 1) = 1

> so that joke is even wrong and pathetic.

> 2) im not a beginner at factoring , otherwise i could not have known that
> (46^46 - 1) /( (46+1)*(46-1)) is actually an integer.

> 3) thus i wanted - as you darn well know - a full factorization. and a
> correct one !

If you want a FULL (or more properly, a complete) factorization, it is
not that much more difficult to say so.


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Martin M. Musatov  
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 More options Nov 2, 6:01 pm
Newsgroups: sci.math
From: "Martin M. Musatov" <m...@yummy.con>
Date: Sun, 1 Nov 2009 23:01:22 -0800
Local: Mon, Nov 2 2009 6:01 pm
Subject: Re: factoring request
Blow me a second time, you impotent puke.

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dan73  
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 More options Nov 2, 9:25 pm
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Mon, 02 Nov 2009 05:25:17 EST
Local: Mon, Nov 2 2009 9:25 pm
Subject: Re: factoring request

More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.

3.1415926535897932384626433832795028841971693993751058209749445923078164062 86208998628034825342117067982148086513e+111.

Dan


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Pubkeybreaker  
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 More options Nov 3, 12:12 am
Newsgroups: sci.math
From: Pubkeybreaker <pubkeybrea...@aol.com>
Date: Mon, 2 Nov 2009 05:12:58 -0800 (PST)
Local: Tues, Nov 3 2009 12:12 am
Subject: Re: factoring request
On Nov 2, 5:25 am, dan73 <fasttrac...@att.net> wrote:

Not much of a challenge.  A few days computing on a single PC using
GNFS.  Even less if one can
pull out a small factor or two with ECM.

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dan73  
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 More options Nov 3, 4:52 am
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Mon, 02 Nov 2009 12:52:34 EST
Local: Tues, Nov 3 2009 4:52 am
Subject: Re: factoring request
On Nov 2, 5:25 am, dan73 <fasttrac...@att.net> wrote:

You are probably right, I have only run it on ECM
for a few hours and @ curve 750 it appears this
composite has at most three factors but maybe
only two.

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master1729  
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 More options Nov 3, 7:26 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Mon, 02 Nov 2009 15:26:59 EST
Local: Tues, Nov 3 2009 7:26 am
Subject: Re: factoring request
dan73 wrote :

nice problem.

i think its not so hard if you use a computerprogram.

but perhaps we can do without computers and use some math tricks !?

for instance the many formula's concerning sin , arcsin etc and products ?

maybe that is too optimistic. or not.

i bet on q-sine ...

regards

tommy1729


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master1729  
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 More options Nov 3, 7:21 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Mon, 02 Nov 2009 15:21:25 EST
Local: Tues, Nov 3 2009 7:21 am
Subject: Re: factoring request
Virgil wrote :

still wrong !!

lol

regards

tommy1729


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dan73  
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 More options Nov 3, 12:30 pm
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Mon, 02 Nov 2009 20:30:38 EST
Local: Tues, Nov 3 2009 12:30 pm
Subject: Re: factoring request

I was trying to use Darios' ECM and my python triangle
sum program simultaneously but the memory over head was
just to great.
So I opted to use only the ECM because it is much
faster, like probably 100 times faster!
Although in some limited instances of certain composites
my python triangle summing program beats the pants off
of the ECM.

Here is where it stands now with no factors yet --

Factoring 3141 592653 589793 238462 643383 279502 884197
169399 375105 820974 944592 307816 406286 208998 628034
825342 117067 982148 086513 (112 digits)
Limit (B1=1000000; B2=100000000) Curve 1036
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability:----------100%  100%  100%   99%    34%   5%

About 10 hours worth.

It would be nice if someone could pickup on curve 1200.
After finishing my run of 1012 too 1199 I could jump
too 1400 and the other party could jump from 1399 to 1600
and so on!

Generally speaking, if there are just 2 factors that are
close to equal digit length then this may take about 5
or 6 days to factor on one computer.

If there are just 3 factors the factoring time
would be much less, more like what pubkeybreaker
is saying. Or 2 factors much different in length by
about 10 or more digits the factoring time would be
much less than the 5 of 6 day factoring time.

Dan


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dan73  
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 More options Nov 6, 11:58 pm
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Fri, 06 Nov 2009 07:58:10 EST
Local: Fri, Nov 6 2009 11:58 pm
Subject: Re: factoring request

The latest update on factoring  floor(10^111 * pi)

The ECM after 5 days factoring =

Factoring 3141 592653 589793 238462 643383 279502 884197 169399 375105 820974
944592 307816 406286 208998 628034 825342 117067 982148 086513 (112 digits)
Limit (B1=11000000; B2=1100000000)    Curve 2450
Digits in factor: >= 15 >= 20 >= 25 >= 30 >= 35 >= 40
Probability:------- 100% 100%  100%  100%   97%   33%

It now appears that there are just two factors.
I was wrong on this one. It is more of a challenge
than I first thought, on the high side it could
take years to factor.

Dan


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Pubkeybreaker  
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 More options Nov 7, 12:03 am
Newsgroups: sci.math
From: Pubkeybreaker <pubkeybrea...@aol.com>
Date: Fri, 6 Nov 2009 05:03:19 -0800 (PST)
Local: Sat, Nov 7 2009 12:03 am
Subject: Re: factoring request
On Nov 6, 7:58 am, dan73 <fasttrac...@att.net> wrote:

Sigh.  People simply do not read.
As I said:

It will take only a few days on any modern PC using GNFS.


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dan73  
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 More options Nov 7, 2:23 am
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Fri, 06 Nov 2009 10:23:29 EST
Local: Sat, Nov 7 2009 2:23 am
Subject: Re: factoring request

Pubkeybreaker wrote:
Pubkeybreaker wrote:
>Sigh. People simply do not read.
>As I said:
>It will take only a few days on any modern PC using >GNFS.

Yea I did read and used ECM, but it has chugged
for 5+days.
Will GNFS give quicker results?

Dan


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master1729  
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 More options Nov 8, 7:26 am
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sat, 07 Nov 2009 15:26:30 EST
Local: Sun, Nov 8 2009 7:26 am
Subject: Re: factoring request
dan73 wrote :

> Pubkeybreaker wrote:
> Pubkeybreaker wrote:

> >Sigh. People simply do not read.
> >As I said:

> >It will take only a few days on any modern PC using
> >GNFS.

> Yea I did read and used ECM, but it has chugged
> for 5+days.
> Will GNFS give quicker results?

> Dan

Dan , which part of

"It will take only a few days on any modern PC using
GNFS."

didnt you understand ? x)

lol

tommy1729


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dan73  
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 More options Nov 8, 11:16 am
Newsgroups: sci.math
From: dan73 <fasttrac...@att.net>
Date: Sat, 07 Nov 2009 19:16:59 EST
Local: Sun, Nov 8 2009 11:16 am
Subject: Re: factoring request

>Dan , which part of
>"It will take only a few days on any modern PC using
>GNFS."
>didn't you understand ? x)
>lol
>tommy1729

I had it wrong also, even with GNFS it is going
to take more than just a few days!

It is still chugging along on the ECM
after 6 + days but if GNFS is more than
twice as fast as ECM, it is possible GNFS could
factor it in a few days.
I never used that algorithm (GNFS) but it
is better to use on larger composites like this
one rather than ECM or so I have read!

Is there any free GNFS software for the Python
language out there?

Dan


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