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 2015-05-21, 13:58 #1 LaurV Romulan Interpreter     Jun 2011 Thailand 100010111001002 Posts Stupid question reloaded 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)
2015-05-21, 14:35   #2
axn

Jun 2003

22×5×239 Posts

Quote:
 Originally Posted by LaurV 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.

2015-05-21, 16:21   #3
R.D. Silverman

Nov 2003

26×113 Posts

Quote:
 Originally Posted by LaurV 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.

2015-05-21, 19:00   #4
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by R.D. Silverman 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.

2015-05-21, 22:59   #5
jyb

Aug 2005
Seattle, WA

5×11×29 Posts

Quote:
 Originally Posted by R.D. Silverman 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.

2015-05-22, 02:10   #6
LaurV
Romulan Interpreter

Jun 2011
Thailand

100010111001002 Posts

Quote:
 Originally Posted by R.D. Silverman 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..

2015-05-22, 04:28   #7
axn

Jun 2003

22×5×239 Posts

Quote:
 Originally Posted by LaurV 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 )

2015-05-22, 06:51   #8
LaurV
Romulan Interpreter

Jun 2011
Thailand

100010111001002 Posts

Quote:
 Originally Posted by axn 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

2015-05-22, 07:54   #9
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

5·2,039 Posts

Quote:
 Originally Posted by LaurV 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 )

2015-05-22, 11:19   #10
R.D. Silverman

Nov 2003

26×113 Posts

Quote:
 Originally Posted by LaurV 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.

2015-05-22, 15:05   #11
LaurV
Romulan Interpreter

Jun 2011
Thailand

22×7×11×29 Posts

Quote:
 Originally Posted by R.D. Silverman 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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