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Old 2015-05-21, 13:58   #1
LaurV
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Assuming I take out my magic hat and pull out of it a long list of Fermat factors candidates. They are all between few digits and few million digits. Not interesting how my magic hat produced them, by sieving, guessing, dreaming them in the night, or else.

My question is what is the best way (fast, existent program, win32/64) to check if they are indeed factors of some Fermat numbers?
(you know, squaring mod q, checking if it is -1, etc, but doing this fast and in somehow "organized" way, like pfgw or cllr are doing)
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Old 2015-05-21, 14:35   #2
axn
 
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Originally Posted by LaurV View Post
Assuming I take out my magic hat and pull out of it a long list of Fermat factors candidates. They are all between few digits and few million digits. Not interesting how my magic hat produced them, by sieving, guessing, dreaming them in the night, or else.

My question is what is the best way (fast, existent program, win32/64) to check if they are indeed factors of some Fermat numbers?
(you know, squaring mod q, checking if it is -1, etc, but doing this fast and in somehow "organized" way, like pfgw or cllr are doing)
PFGW.
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Old 2015-05-21, 16:21   #3
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Assuming I take out my magic hat and pull out of it a long list of Fermat factors candidates. They are all between few digits and few million digits.
If you would every bother to learn some of the mathematics (yes, I know, it is a futile hope on my part)
you would know that your last sentence is complete nonsense.

Hint: among the unfactored Fermat composites, the smallest possible factor has at least 4096 bits.
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Old 2015-05-21, 19:00   #4
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Originally Posted by R.D. Silverman View Post
If you would every bother to learn some of the mathematics (yes, I know, it is a futile hope on my part)
you would know that your last sentence is complete nonsense.

Hint: among the unfactored Fermat composites, the smallest possible factor has at least 4096 bits.
He never said new factors. There are known factors of 3-8 digits listed on Wikipedia, for example.
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Old 2015-05-21, 22:59   #5
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Originally Posted by R.D. Silverman View Post
If you would every bother to learn some of the mathematics (yes, I know, it is a futile hope on my part)
you would know that your last sentence is complete nonsense.

Hint: among the unfactored Fermat composites, the smallest possible factor has at least 4096 bits.
Huh??! Uh, no.
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Old 2015-05-22, 02:10   #6
LaurV
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Quote:
Originally Posted by R.D. Silverman View Post
If you would every bother to learn some of the mathematics (yes, I know, it is a futile hope on my part)
you would know that your last sentence is complete nonsense.

Hint: among the unfactored Fermat composites, the smallest possible factor has at least 4096 bits.
Who the fuck said anything about "unfactored" Fermat numbers?
641 is a factor of a Fermat number and only have 3 digits.
What NEW info YOUR comment brings, and how does it help me solve my problem?

@axn: thanks for the fast response, the icon was not necessary, I know about pfgw and how to use it, but think like that: if you would ask me 1 year ago, before I was crunching for crus, what program is the best to find R/S primes, I would answer the same as you answered me, including the icon, but meantime I found out about better/faster ways, (i.e srXsievers and cllr) of which I had no idea at the time. That is why I was asking. One never knows. I have a real life who couldn't care less about the factors of Fermat numbers, so you see, I couldn't know. Moreover, I don't have a magic hat, in spite of what Mr. Silverman thinks, I am trying to learn. But not all people a geniuses as his majesty..
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Old 2015-05-22, 04:28   #7
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Originally Posted by LaurV View Post
the icon was not necessary,
I actually meant: I don't know the exact command line option to do that, so you'll have to look it up. There aren't any other icon that does this (there is no polite-looking version of RTFM in the forum )
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Old 2015-05-22, 06:51   #8
LaurV
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Originally Posted by axn View Post
I actually meant: I don't know the exact command line option to do that, so you'll have to look it up. There aren't any other icon that does this (there is no polite-looking version of RTFM in the forum )
I am not upset with you, even a single bit! I really appreciate your valuable (every single time, here on the forum, and not only to my posts!) input and I am tankful for it. I was a bit upset with RDS's remark at the time of posting, sorry.

Which remark, by the way, is not only unproductive, but, if I am to nitpick, is totally on the weeds. The cofactors of F12 and F13, for example, are a C1133 and respective C2391, according with this site, and they are KNOWN composites, which means they have a factor smaller than their square root. Which square roots have 1133/2=567 and 2391/2=1196 digits, or respective (by multiplying with log2(10)), 1882 and respective 3972 bits. So, THERE ARE unknown Fermat factors smaller than 4096 bits, for sure... (gotcha )

Last fiddled with by LaurV on 2015-05-22 at 06:54
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Old 2015-05-22, 07:54   #9
xilman
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Quote:
Originally Posted by LaurV View Post
Which remark, by the way, is not only unproductive, but, if I am to nitpick, is totally on the weeds. The cofactors of F12 and F13, for example, are a C1133 and respective C2391, according with this site, and they are KNOWN composites, which means they have a factor smaller than their square root. Which square roots have 1133/2=567 and 2391/2=1196 digits, or respective (by multiplying with log2(10)), 1882 and respective 3972 bits. So, THERE ARE unknown Fermat factors smaller than 4096 bits, for sure... (gotcha )
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Old 2015-05-22, 11:19   #10
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Originally Posted by LaurV View Post
Who the fuck said anything about "unfactored" Fermat numbers?
641 is a factor of a Fermat number and only have 3 digits.
What NEW info YOUR comment brings, and how does it help me solve my problem?
Based upon WHAT YOU WROTE, it was clear that you did not intend "table lookup" to be part
of the problem/solution.
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Old 2015-05-22, 15:05   #11
LaurV
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Originally Posted by R.D. Silverman View Post
Based upon WHAT YOU WROTE, it was clear that you did not intend "table lookup" to be part
of the problem/solution.
Sure, you are right. I saw you wrote "among the unfactored composites" and I know you referred to the Fermats with no factors known yet, that is why I said (and underlined) "if I am to nitpick". But I just wanted to get back to you
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