2,776+ Status

R.D. Silverman · 2008-03-11, 12:28

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.

fivemack · 2008-03-11, 18:47

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) ?

R.D. Silverman · 2008-03-12, 00:46

Quote:

Originally Posted by fivemack

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) ?

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).

R.D. Silverman · 2008-03-12, 12:21

Quote:

Originally Posted by fivemack

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) ?

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

JHansen · 2008-03-12, 13:45

Quote:

Originally Posted by fivemack

Is this a consequence of the disgusting polynomial ... ?

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

R.D. Silverman · 2008-03-12, 14:01

Quote:

Originally Posted by JHansen

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

No. I used 4x^6 + 1

fivemack · 2008-03-12, 15:49

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).

R.D. Silverman · 2008-03-18, 11:56

Quote:

Originally Posted by R.D. Silverman

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.

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+.

R.D. Silverman · 2008-03-23, 21:49

Quote:

Originally Posted by R.D. Silverman

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+.

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.

R.D. Silverman · 2008-04-06, 23:51

Quote:

Originally Posted by R.D. Silverman

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.

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

xilman · 2008-04-07, 00:16

Quote:

Originally Posted by R.D. Silverman

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

I can do it. I'll contact you by email to arrange details.

Paul

2008-03-11, 12:28	#1
R.D. Silverman Nov 2003 2²×5×373 Posts	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.

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2008-03-11, 18:47	#2
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2×13²×19 Posts	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) ?

2008-03-12, 15:49	#7
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1916₁₆ Posts	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).