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Old 2022-07-10, 23:15   #67
retina
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Originally Posted by storm5510 View Post
CADO? That's a new one on me. A Google search is not revealing in this context.

As I wrote, a long time.
And as has been stated in the past, Google doesn't have all the answers.

There is literally a forum on this board.

https://mersenneforum.org/forumdisplay.php?f=170

Last fiddled with by retina on 2022-07-10 at 23:16
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Old 2022-07-10, 23:41   #68
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FWIW. Several years ago, someone mentioned the best shot at M1277 would be with NFS, (Number Field Sieve). These are used with YAFU as add-ons. M1277 is 385 digits in length. Could YAFU handle a number of this size? I do not know. There is YAFU 2.0. It might be able to. Even if it could, there would be a lot of time involved.

Try reading.

https://www.mersenneforum.org/showpo...0&postcount=10
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Old 2022-07-11, 09:41   #69
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Quote:
Originally Posted by storm5510 View Post
CADO? That's a new one on me. A Google search is not revealing in this context.

As I wrote, a long time.
https://www.google.com/search?q=cado+nfs

Revealing to me.
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Old 2022-07-11, 14:38   #70
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Originally Posted by retina View Post
And as has been stated in the past, Google doesn't have all the answers.

There is literally a forum on this board.

https://mersenneforum.org/forumdisplay.php?f=170
I will have to check this out.

When I searched, I didn't add "-NFS." I did not know to add it. Mentions were simply "CADO."
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Old 2022-07-11, 17:34   #71
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When I searched, I didn't add "-NFS." I did not know to add it. Mentions were simply "CADO."
Then you didn't try hard enough, Google is an advertising engine, not a mathematics tool.

If you gave it some more context, by supply more keywords, then it might have a chance to find what you want. Or if you were more diligent and went beyond page 1 perhaps it is there. Don't blame the tools, they only do what they are programmed to do.
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Old 2022-07-11, 18:45   #72
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Then you didn't try hard enough, Google is an advertising engine, not a mathematics tool.

If you gave it some more context, by supply more keywords, then it might have a chance to find what you want. Or if you were more diligent and went beyond page 1 perhaps it is there. Don't blame the tools, they only do what they are programmed to do.
How I hate this damned machine!
I wish that they would sell it.
It never does just what I want
But only what I tell it.

That poem is about 60 years old by now.
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Old 2022-07-11, 18:58   #73
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Quote:
Originally Posted by storm5510 View Post
Mentions were simply "CADO."
Try to find soap (the genome alignment tool).
Is it Google's fault that if you search for soap you will not find it? Too much soap in the world!

Hint: search, obviously, for soap genome alignment tool . It is easy. Use specific queries.

On the other hand, if you wanted to find soap protocol, then search, obviously, for soap protocol
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Old 2022-07-30, 15:51   #74
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You can't write 2^1277-1 as a^2+3b^2 so it means than all factors of M1277 are == 2 (mod 3) ? And I have seen on this link https://oeis.org/A215799 than prime factors of 2^p-1 which are == 2 (mod 3) come in pairs.

So it means than 2^1277-1 is a semiprime or has 4 factors ?

Oops sorry for the report Balatov and admins my bad misscliking.

Last fiddled with by kijinSeija on 2022-07-30 at 15:53
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Old 2022-07-30, 16:05   #75
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Originally Posted by kijinSeija View Post
You can't write 2^1277-1 as a^2+3b^2 so it means than all factors of M1277 are == 2 (mod 3) ? And I have seen on this link https://oeis.org/A215799 than prime factors of 2^p-1 which are == 2 (mod 3) come in pairs.

So it means than 2^1277-1 is a semiprime or has 4 factors ?


What makes you believe that 2^1277-1 can't be written as a^2+3b^2? We won't know if it can be until we know at least one prime factor. N can be represented in the form a^2+3b^2 if and only if every prime factor of the form 2 mod 3 divides it an even number of times.

So even if you did somehow know that 2^1277-1 couldn't be written as a^2+3b^2, all it would tell you is that there is some prime of the form 2 mod 3 that divides it an odd number of times. (And since 2^1277-1 == 1 mod 3, that would mean it must have a second prime factor of the form 2 mod 3 - this is the "factors of the form 2 mod 3 come in pairs" observation.) Not that all its prime factors are 2 mod 3.
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Old 2022-07-30, 16:17   #76
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Quote:
Originally Posted by charybdis View Post


What makes you believe that 2^1277-1 can't be written as a^2+3b^2? We won't know if it can be until we know at least one prime factor. N can be represented in the form a^2+3b^2 if and only if every prime factor of the form 2 mod 3 divides it an even number of times.

So even if you did somehow know that 2^1277-1 couldn't be written as a^2+3b^2, all it would tell you is that there is some prime of the form 2 mod 3 that divides it an odd number of times. (And since 2^1277-1 == 1 mod 3, that would mean it must have a second prime factor of the form 2 mod 3 - this is the "factors of the form 2 mod 3 come in pairs" observation.) Not that all its prime factors are 2 mod 3.
Ok I thought than M1277 can't be write as a^2+3b^2 because I checked that with WolframAlpha but I didn't know than you need at least one known prime factor for that. Thanks for your answer !
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Old 2022-07-30, 22:00   #77
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I won't be running M1277 myself. Others with much newer hardware can run it. What I have is long-in-the-tooth and there may not ever be anything newer.

Off-topic: I've been experimenting with M4363. I might as well stop with the experiments and set it up and let it run.
I've done quite a bit on M4363.
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