2,776+ Status
 

I have (barely) enough relations for 2,776+ to begin the linear algebra.
However, I can't cope with a matrix of 15million rows, so I will need to do
some extra sieving to reduce its size.

That seems really very large for a 'mere' 776-bit SNFS; it's rather larger than the matrix I got for 2,841-, and a lot larger than the matrices NFSnet report here for numbers around 800 bits. Is this a consequence of the disgusting polynomial (and presumably the large factor base needed) ?

[QUOTE=fivemack;128538]That seems really very large for a 'mere' 776-bit SNFS; it's rather larger than the matrix I got for 2,841-, and a lot larger than the matrices NFSnet report here for numbers around 800 bits. Is this a consequence of the disgusting polynomial (and presumably the large factor base needed) ?[/QUOTE]

This is a matrix created with only 2-way merges. There are no higher order
merges at all; I have no extra relations needed to conduct such a merge.
I expect the final matrix will be about 7M rows, once I get another 2 to
3 million relations (accumulating at 600K/day).

[QUOTE=fivemack;128538]That seems really very large for a 'mere' 776-bit SNFS; it's rather larger than the matrix I got for 2,841-, and a lot larger than the matrices NFSnet report here for numbers around 800 bits. Is this a consequence of the disgusting polynomial (and presumably the large factor base needed) ?[/QUOTE]

Actually, I did not use that large a factor base. The FB bound was
30M, the LP bound was 800M.

[QUOTE=fivemack;128538]Is this a consequence of the disgusting polynomial ... ?[/QUOTE]
I assume the polynomial is X^4+1. Which features makes this polynomial especially icky (besides the large norms on the rational side)?

--
Cheers,
Jes

[QUOTE=JHansen;128668]I assume the polynomial is X^4+1. Which features makes this polynomial especially icky (besides the large norms on the rational side)?

--
Cheers,
Jes[/QUOTE]

No. I used 4x^6 + 1

And the icky features of 4x^6+1 are that it has no real roots and very few roots modulo primes (two modulo any prime ==5 mod 12, six modulo any prime ==1 mod 12 for which 4 is a cubic residue, of which the smallest is 109).

[QUOTE=R.D. Silverman;128476]I have (barely) enough relations for 2,776+ to begin the linear algebra.
However, I can't cope with a matrix of 15million rows, so I will need to do
some extra sieving to reduce its size.[/QUOTE]

I have finished the sieving. Filtering is going slowly because I keep
running into Windows address space limits. At the moment I have
a matrix of 18.7M rows, but have not begun 3-way and higher merges.
The excess is currently 1.7M, so I have a lot of extra relations to play with.
I hope to get a final matrix of about 7M rows.

I have started sieving 2,1068+.

[QUOTE=R.D. Silverman;129048]I have finished the sieving. Filtering is going slowly because I keep
running into Windows address space limits. At the moment I have
a matrix of 18.7M rows, but have not begun 3-way and higher merges.
The excess is currently 1.7M, so I have a lot of extra relations to play with.
I hope to get a final matrix of about 7M rows.

I have started sieving 2,1068+.[/QUOTE]

I finished filtering the data. The final matrix was 8.8M rows, which
is too big for me to run (my biggest machine has only 2G memory),
so I must do some more sieving.

2,1068+ is in progress, so I have to switch back tomorrow.

[QUOTE=R.D. Silverman;129527]I finished filtering the data. The final matrix was 8.8M rows, which
is too big for me to run (my biggest machine has only 2G memory),
so I must do some more sieving.

2,1068+ is in progress, so I have to switch back tomorrow.[/QUOTE]

After more sieving I was only able to bring the matrix down to 8.4M rows.
Windows still refuses to allocate enough space to solve it.

Can anyone help? I can send the final matrix, or the final filtered
data, or the raw data with singletons & dups removed.

Bob

[QUOTE=R.D. Silverman;130930]After more sieving I was only able to bring the matrix down to 8.4M rows.
Windows still refuses to allocate enough space to solve it.

Can anyone help? I can send the final matrix, or the final filtered
data, or the raw data with singletons & dups removed.

Bob[/QUOTE]I can do it. I'll contact you by email to arrange details.


Paul

[QUOTE=R.D. Silverman;130930]After more sieving I was only able to bring the matrix down to 8.4M rows.
Windows still refuses to allocate enough space to solve it.

Can anyone help? I can send the final matrix, or the final filtered
data, or the raw data with singletons & dups removed.
[/QUOTE]
Can you make the filtering binary large-address-aware, using some kind of linker switch in Visual Studio? Doing that and rebooting in /3gb mode will give 3GB of VM space, though that still may not be sufficient for such a big job if you only have 2GB of physical memory.

[QUOTE=jasonp;130959]Can you make the filtering binary large-address-aware, using some kind of linker switch in Visual Studio? Doing that and rebooting in /3gb mode will give 3GB of VM space, though that still may not be sufficient for such a big job if you only have 2GB of physical memory.[/QUOTE]

I am using VC++ 6.0 and it does not seem to recognize the 3G switch.

And the machine only has 2GB anyway......

[QUOTE=xilman;130932]I can do it. I'll contact you by email to arrange details.


Paul[/QUOTE]The data arrived today but not the polynomial file. I've already sent email but if need be I can probably reverse engineer a compatible poly file. It's not that there aren't many plausible alternatives.

4*(2^129)^6+1 is the obvious one, with the reciprocal a close second.


Paul

[QUOTE=xilman;131692]The data arrived today but not the polynomial file. I've already sent email but if need be I can probably reverse engineer a compatible poly file. It's not that there are many plausible alternatives.

4*(2^129)^6+1 is the obvious one, with the reciprocal a close second.[/QUOTE]It was the obvious one. Filtering now started, and I hope the first pass will finish overnight.

Paul

[QUOTE=xilman;131692]The data arrived today but not the polynomial file. I've already sent email but if need be I can probably reverse engineer a compatible poly file. It's not that there aren't many plausible alternatives.

4*(2^129)^6+1 is the obvious one, with the reciprocal a close second.


Paul[/QUOTE]

I put a file called 'polyfile' on the disk. Didn't you see it?
The poly was indeed 4x^6 + 1. (yech!)

[QUOTE=R.D. Silverman;131739]I put a file called 'polyfile' on the disk. Didn't you see it?
The poly was indeed 4x^6 + 1. (yech!)[/QUOTE]nope, no such file on any of the disks. No matter, I've already built one [i]ab initio[/i] and the post-processing is well underway.

Paul