New Fermat factor!

[ET_]

I just received this email from Maximilian Pacher:

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

[Andi47]

Congratulations to Maximilian!!

[R.D. Silverman]

Originally Posted by Andi47

Congratulations to Maximilian!!

Indeed. Very nice.

The next thing to do is test the cofactor.

[Andi47]

Originally Posted by R.D. Silverman

The next thing to do is test the cofactor.

Any chance to finish this before the end of the century?

[R.D. Silverman]

Originally Posted by Andi47

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.........

[henryzz]

Originally Posted by R.D. Silverman

Sure........ The same chance as being able to find storage for 2^1710
bits.........

i think u mean 2^2^1710 bits

[R.D. Silverman]

Originally Posted by henryzz

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.

[retina]

Originally Posted by R.D. Silverman

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

[xilman]

Originally Posted by R.D. Silverman

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

[R.D. Silverman]

Originally Posted by xilman

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.

[akruppa]

> even the status of the F25 cofactor is unknown.

This seems to be an entirely curable situation.

Alex