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Old 2008-03-10, 18:19   #1
ET_
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Default New Fermat factor!

I just received this email from Maximilian Pacher:

Code:
Hello!

My name is Maximilian Pacher, I am from austria and I have interesting news.
After 7 years of searching, I am very happy to find my second Fermat-factor. Now I proudly present my second Fermat-Factor:

351276975*2^1719+1 is a Factor of F1710!!!!

This is the first factor this year if I remember correctly. I have found
him on March 9th, 2008 with the three programs "NewPGen", "PRP" and "WinPFGW". The last program wrote this:

351276975*2^1719+1 is a Factor of F1710!!!! (0.032000 seconds)

If you have questions, please mail me!

With regards,

PACHER MAXIMILIAN
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Old 2008-03-10, 18:49   #2
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Congratulations to Maximilian!!
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Old 2008-03-10, 18:53   #3
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Quote:
Originally Posted by Andi47 View Post
Congratulations to Maximilian!!
Indeed. Very nice.

The next thing to do is test the cofactor.
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Old 2008-03-10, 18:59   #4
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Quote:
Originally Posted by R.D. Silverman View Post
The next thing to do is test the cofactor.
Any chance to finish this before the end of the century?

Last fiddled with by Andi47 on 2008-03-10 at 18:59
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Old 2008-03-11, 01:08   #5
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Quote:
Originally Posted by Andi47 View Post
Any chance to finish this before the end of the century?
Sure........ The same chance as being able to find storage for 2^1710
bits.........
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Old 2008-03-11, 07:25   #6
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Quote:
Originally Posted by R.D. Silverman View Post
Sure........ The same chance as being able to find storage for 2^1710
bits.........
i think u mean 2^2^1710 bits
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Old 2008-03-11, 11:51   #7
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Quote:
Originally Posted by henryzz View Post
i think u mean 2^2^1710 bits
Henry. I suggest that you stop posting here. Everytime you
open your mouth, you put your foot in it.

If N = 2^x, then N has x (+1) bits.
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Old 2008-03-11, 12:01   #8
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Quote:
Originally Posted by R.D. Silverman View Post
Sure........ The same chance as being able to find storage for 2^1710
bits.........
We could use storage stolen from another (few gozillion) parallel universe(s). I don't see the problem
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Old 2008-03-11, 12:56   #9
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Quote:
Originally Posted by R.D. Silverman View Post
Sure........ The same chance as being able to find storage for 2^1710
bits.........
Not necessarily. One test, which does not require a large amount of storage and could be completed before the end of the century is the same as the one which proved F_1710 composite. Finding a second factor would undoubtedly prove the cofactor composite.

Proving the cofactor to be prime, on the other hand, would appear to be a non-trivial task given known algorithms and technology.

Paul
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Old 2008-03-11, 13:07   #10
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Quote:
Originally Posted by xilman View Post
Not necessarily. One test, which does not require a large amount of storage and could be completed before the end of the century is the same as the one which proved F_1710 composite. Finding a second factor would undoubtedly prove the cofactor composite.

Proving the cofactor to be prime, on the other hand, would appear to be a non-trivial task given known algorithms and technology.

Paul
I would say that "non-trivial" is an understatement........

We can't even test F33, and even the status of the F25 cofactor is
unknown.
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Old 2008-03-11, 15:46   #11
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> even the status of the F25 cofactor is unknown.

This seems to be an entirely curable situation.

Alex
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