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| dan73... |
 Posted: Mon Nov 02, 2009 7:52 am |
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On Nov 2, 5:25 am, dan73 <fasttrac... at (no spam) att.net> wrote:
[quote]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
More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.1415926535897932384626433832795028841971693993751058209749445923078164062Â86208998628034825342117067982148086513e+111.
Dan- Hide quoted text -
- Show quoted text -
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.
[/quote]
You are probably right, I have only run it on ECM
for a few hours and at (no spam) curve 750 it appears this
composite has at most three factors but maybe
only two. |
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| master1729... |
| Posted: Mon Nov 02, 2009 10:21 am |
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Virgil wrote :
[quote]In article
968439331.150126.1257112893522.JavaMail.root at (no spam) gallium.
mathforum.org>,
master1729 <tommy1729 at (no spam) gmail.com> wrote:
Virgil wrote :
In article
1699063352.149909.1257108152590.JavaMail.root at (no spam) gallium
.mathforum.org>,
master1729 <tommy1729 at (no spam) 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))
thank you.
regards
tommy1729
I said PLZ.
(46^46 - 1) /( (46+1)*(46-1)) factors into
[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46^23 +
3 + 1)]
And similarly for the others.
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)]
My poor proof reading, sorry.
Should have been
[(46^46 - 1) / (46-1)] * [(46^23 + 1) / (46+ 1)]
Which is a factorization.
[/quote]
still wrong !!
lol
regards
tommy1729 |
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| master1729... |
| Posted: Mon Nov 02, 2009 10:26 am |
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dan73 wrote :
[quote]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
More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.1415926535897932384626433832795028841971693993751058
209749445923078164062862089986280348253421170679821480
86513e+111.
Dan
[/quote]
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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| dan73... |
| Posted: Mon Nov 02, 2009 3:30 pm |
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[quote]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
More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.1415926535897932384626433832795028841971693993751058
209749445923078164062862089986280348253421170679821480
86513e+111.
Dan
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
[/quote]
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... |
| Posted: Fri Nov 06, 2009 2:58 am |
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tommy1729 wrote:
[quote]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
[/quote]
[quote]More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e+111.
Dan
[/quote]
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... |
| Posted: Fri Nov 06, 2009 3:03 am |
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On Nov 6, 7:58 am, dan73 <fasttrac... at (no spam) att.net> wrote:
[quote]tommy1729 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))
thank you.
regards
tommy1729
More of a challenge --
The 3 + the first 111 decimal digits of pi changed
to an integer.
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e+111.
Dan
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.
[/quote]
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... |
| Posted: Fri Nov 06, 2009 5:23 am |
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Pubkeybreaker wrote:
Pubkeybreaker wrote:
[quote]Sigh. People simply do not read.
As I said:
It will take only a few days on any modern PC using >GNFS.
[/quote]
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... |
| Posted: Sat Nov 07, 2009 10:26 am |
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dan73 wrote :
[quote]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
[/quote]
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... |
| Posted: Sat Nov 07, 2009 2:16 pm |
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[quote]Dan , which part of
"It will take only a few days on any modern PC using
GNFS."
didn't you understand ? x)
lol
tommy1729
[/quote]
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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| factorboy13... |
| Posted: Sun Nov 29, 2009 12:42 am |
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[quote]I had it wrong also, even with GNFS it is going
to take more than just a few days!
Dan
[/quote]
I don't think it will take more than a couple of hours to factor it with ggnfs (only 112 decimal digits).
I will do try it now and will post the factors here |
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| factorboy13... |
| Posted: Sun Nov 29, 2009 4:03 am |
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Factored
3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513 (112 digits)
prp43 factor: 1215666422974078739455530964256912318288897
prp70 factor: 2584255511395974781222544726762221278238062155282351848420786629580529
elapsed time 00:03:10 |
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| dan73... |
| Posted: Sun Nov 29, 2009 4:38 am |
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[quote]Factored
31415926535897932384626433832795028841971693993751058209>74944592307816406286208998628034825342117067982148086513 (112 digits)
prp43 factor: >1215666422974078739455530964256912318288897
prp70 factor: >25842555113959747812225447267622212782380621552823518484>20786629580529
elapsed time 00:03:10
[/quote]
This was allready factored ---
See "more on factoring floor(pi*(10^111))
posted on 16th nov.
Dan |
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| factorboy13... |
| Posted: Sun Nov 29, 2009 7:51 am |
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[quote]This was allready factored ---
See "more on factoring floor(pi*(10^111))
posted on 16th nov.
Dan
[/quote]
Ah ok. You took a significant time but is normal with ECM when a factor is of this size. |
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| dan73... |
| Posted: Sun Nov 29, 2009 9:13 am |
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[quote]This was already factored ---
See "more on factoring floor(pi*(10^111))
posted on 16th nov.
Dan
Ah ok. You took a significant time but is normal with >ECM when a factor is of this size.
[/quote]
I guess so, 3.10 sec. against 14 days.
I must live in the dinosaur age.
It would probably be much faster with ECM if
my cp was a duo core processor and I downloaded
the ECM software instead of doing it online!
Probably more like 10 days.
Even at that, 3.10 sec. really makes that look sick.
What are the bench-marks with 60-80 digit composites
with GGNFS and ECM when the two factors are of equal
length in these composites.
Dan
Dan |
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| factorboy13... |
| Posted: Tue Dec 01, 2009 2:11 am |
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[quote]
I guess so, 3.10 sec. against 14 days.
I must live in the dinosaur age.
[/quote]
Well, not 3.10 sec, actually 3 hours and 10 minutes 
And I did it with a i7 860 working with 8 threads!
[quote]What are the bench-marks with 60-80 digit composites
with GGNFS and ECM when the two factors are of equal
length in these composites.
[/quote]
GGNFS is not the best for factors up to 100 digits, probably SIQS is better when factors are about equal size and ECM can not find fast a factor up to 30 digits |
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