[QUOTE=R.D. Silverman;98368]4239563023902513348819622724332183236332083668077140199504712814030159227742607854421301123833862589872079[/QUOTE]

How much ECM work has been done on this number?

[QUOTE=Andi47;98386]How much ECM work has been done on this number?[/QUOTE]

I have no idea. I did enough to make it quite probable that there are
no factors under 35 digits, but that doesn't say much.

Interesting......
 

The following interesting result turned up.

(5^241 - 2^241)/3 =

19763.11069831474198603.933088232224019489.9937464767133262547.10804377123378071864453.833624593429493753137729.98267814100362561246159385414187.525383037743383305420888402232747

A number this size should have, on average 6 factors by the Erdos-Kac theorem.

So this number is only about 1 std. dev. above the mean, which by itself is no big deal.

What is amazing is that it has one tiny factor then 7 other factors between
17 and 33 digits.

[QUOTE=R.D. Silverman;98394]The following interesting result turned up.

(5^241 - 2^241)/3 =

19763.11069831474198603.933088232224019489.9937464767133262547.10804377123378071864453.833624593429493753137729.98267814100362561246159385414187.525383037743383305420888402232747

A number this size should have, on average 6 factors by the Erdos-Kac theorem.

So this number is only about 1 std. dev. above the mean, which by itself is no big deal.

What is amazing is that it has one tiny factor then 7 other factors between
17 and 33 digits.[/QUOTE]Have you worked out how amazing it is? That is, how many integers of that size have factors with that distribution of digits?

I confess that I haven't, yet.

Paul

(5^241 - 2^241)/3 =

19763.11069831474198603.933088232224019489.9937464767133262547.10804377123378071864453.833624593429493753137729.98267814100362561246159385414187.525383037743383305420888402232747

A number this size should have, on average 6 factors by the Erdos-Kac theorem.

So this number is only about 1 std. dev. above the mean, which by itself is no big deal.

What is amazing is that it has one tiny factor then 7 other factors between
17 and 33 digits.



Have you worked out how amazing it is? That is, how many integers of that size have factors with that distribution of digits?

I confess that I haven't, yet.

It should be easy with Dickman's function. There are 7 factors between
(roughly) n^1/10 and n^1/5.

[QUOTE=R.D. Silverman;98374]Perhaps my expectation is faulty. I expect that those running msieve have
fewer CPU resources and I therefore leave the easier/smaller composites
for them to do.[/QUOTE]Those with few cpu resources should very well be able to run GGNFS. A c106 takes less than a single day on a not to old cpu. It takes about 18 hours on 1 3GHz P4 in a dual cpu server.

Once you figure out how to run GGNFS, it really is very easy.

[QUOTE=smh;98414]Those with few cpu resources should very well be able to run GGNFS. A c106 takes less than a single day on a not to old cpu. It takes about 18 hours on 1 3GHz P4 in a dual cpu server.

Once you figure out how to run GGNFS, it really is very easy.[/QUOTE]

Since ggnfs is quicker than msieve above about 98 digits, shortage of cpu resources clearly can't be the issue. My assumption was that 'I can't run GGNFS' means 'I don't have a Unix system'; I'm not sure how well the mesh of processes, with important parts written in AT&T assembler syntax, tied together with a perl script, that make up ggnfs, has been ported to Windows.

Indeed, 'echo "n: 106_digits" > c106.n; ~/ggnfs/tests/factLat.pl c106.n' could scarcely be easier.

It might also mean 'I have <= 256M memory'; I think the matrix step becomes problematic, or at least incompatible with doing anything else on the computer, on machines that small.

[QUOTE=xilman;98410]Have you worked out how amazing it is? That is, how many integers of that size have factors with that distribution of digits?
[/QUOTE]It would be sweet if two of the factors were the same -- would give us something to use against the abc conjecture. I'm not holding my breath.

[QUOTE=fivemack;98418]Since ggnfs is quicker than msieve above about 98 digits, shortage of cpu resources clearly can't be the issue. My assumption was that 'I can't run GGNFS' means 'I don't have a Unix system'; I'm not sure how well the mesh of processes, with important parts written in AT&T assembler syntax, tied together with a perl script, that make up ggnfs, has been ported to Windows.

Indeed, 'echo "n: 106_digits" > c106.n; ~/ggnfs/tests/factLat.pl c106.n' could scarcely be easier.

It might also mean 'I have <= 256M memory'; I think the matrix step becomes problematic, or at least incompatible with doing anything else on the computer, on machines that small.[/QUOTE]GGNFS runs fine on windows in the c100 - c110 range. I've done over 300 factorizations in the last 6 weeks with GGNFS on windows (c101 - c110) size.

I've done several in the c130 - c140 range (on multiple cpu's) without any problem.

All SNFS numbers upto difficulty ~200 ran fine to.

Two numbers i did get problems with where a c143 with GNFS and a difficulty 207 with SNFS.

Only 256 MB memory might be a problem though

[QUOTE=smh;98484]GGNFS runs fine on windows in the c100 - c110 range. I've done over 300 factorizations in the last 6 weeks with GGNFS on windows (c101 - c110) size.

I've done several in the c130 - c140 range (on multiple cpu's) without any problem.

All SNFS numbers upto difficulty ~200 ran fine to.

Two numbers i did get problems with where a c143 with GNFS and a difficulty 207 with SNFS.

Only 256 MB memory might be a problem though[/QUOTE]

Hi !

For GNFS :
256 MB isn't a problem with a cygwin built of ggnfs up to 108-110 digits in my experience (and maybe more).
I have done many composites up to c129 with 512 Megs of ram but I have carefully chosen (suboptimal) parameters to fit in ram for the larger ones. Note that you can do such composites on a single cpu if you have found a good poly (a crucial point IMHO) and a month to kill !
I'm now beginning a c131 and am confident if will fit in 768 Megs of ram with XP running...

Hope this helps.

[QUOTE=R.D. Silverman;98368]4239563023902513348819622724332183236332083668077140199504712814030159227742607854421301123833862589872079[/QUOTE]

A few ECM curves at the 45 digit level did the trick:

Run 57 out of 1000:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2448571626
Step 1 took 100328ms
Step 2 took 54516ms
********** Factor found in step 2: 1076768463221541221588996172658220297179427
Found probable prime factor of 43 digits: 1076768463221541221588996172658220297179427
Probable prime cofactor 3937302371596518955301979501006666039072382909280067817582200677 has 64 digits

Edit: Both factors are prime - (with Primo)