Newbie advice

[R.D. Silverman]

Originally Posted by xilman

And if not here, likely somewhere else on the interweb thingy.

My advice to newbies is two-fold. Pay attention to Bob's advice (but don't necessarily follow it to the letter) and grow a thick skin,

Paul

My advice to newbies:

(1) Do your background reading/research FIRST.
(2) Engage brain before putting computer into gear. --> Compute first,
think later is a bad way to go.
(3) Ask questions.

[bsquared]

Originally Posted by R.D. Silverman

My advice to newbies:

(1) Do your background reading/research FIRST.
(2) Engage brain before putting computer into gear. --> Compute first,
think later is a bad way to go.
(3) Ask questions.

This is exactly what he did, IMO. Did you *read* his post? Or skim it and dismiss it?

[R.D. Silverman]

Originally Posted by bsquared

This is exactly what he did, IMO. Did you *read* his post? Or skim it and dismiss it?

Really? The content of his post strongly suggested that he thought
that a number near C160-170 was state-of-the-art.

Nor did he ask whether anyone else thought that doing that
number would be mathematically interesting.

Before I start doing work in an area new to me, I ask
those already working in that area:

(1) What problems are interesting?
(2) What do I need to learn? What do I need to read? What is the level
of effort needed to learn the basic background?
(3) What a newbie (such as I would be) might contribute?

[bsquared]

Originally Posted by R.D. Silverman

Nor did he ask whether anyone else thought that doing that
number would be mathematically interesting.

It was clear (at least to me) that he was doing this for the benefit of people who had already expressed interest in the result (OEIS). Leave alone for the moment whether it is *mathematically* interesting - the result itself is interesting to people for reasons of their own. He was doing the best he could to help, and was looking for advice as to how to be of more help. Perfectly fine, in my book.

[sean]

A factorization of 105!+2 (which I do not believe is complete) would help with extending the sequence A063684 in the OEIS.

I have previously run 4590 ECM curves with b1=11e6.

[Batalov]

Originally Posted by Belteshazzar

Wanting to satisfy curiosity about where the state of the art was in factorization and at the same time do something marginally mathematically useful (rather than, say, RSA factors etc), I saw the thread on factorizations needed for OEIS sequences and decided to try factoring 105!+2 on my laptop (1.86 GHz Core2 Duo).

... or just throw up my hands and leave this work to be done by somebody with a faster machine? If the smallest factor is much bigger than the current target of 45 digits then it's going to be semiprime and the smallest factor could be way out of my reach.

For 105!+2 cofactor, you'd rather want it to be semiprime and 105 will be the next term of that sequence. But your laptop will take more than a year to finish this number with GNFS. You could warm up by factoring the c136 cofactor of 108!+2 (which is the next candidate). Btw, 127 is the term of A063684 (out of order).

[xilman]

Originally Posted by R.D. Silverman

My advice to newbies:

(1) Do your background reading/research FIRST.
(2) Engage brain before putting computer into gear. --> Compute first,
think later is a bad way to go.
(3) Ask questions.

That, IMO, is some of Bob's advice which you should follow to the letter.

Paul

[Belteshazzar]

Really? The content of his post strongly suggested that he thought
that a number near C160-170 was state-of-the-art.

My "curiosity about where the state of the art was in factorization" had little to do with what the current records are- that has almost as much to do with where the state of the art is in computer hardware, clustering, etc as it does with the state of the art in factorization algorithms. GNFS and ECM are state-of-the-art, and I don't have to be factoring 240-digit numbers to get a better idea of how they perform and how one should use them.

Nor did he ask whether anyone else thought that doing that
number would be mathematically interesting.

Before I start doing work in an area new to me, I ask
those already working in that area:

(1) What problems are interesting?
(2) What do I need to learn? What do I need to read? What is the level
of effort needed to learn the basic background?
(3) What a newbie (such as I would be) might contribute?

I wanted to try these algorithms out, and the post about OEIS was sufficiently interesting to convince me to try them out on this rather than on random input. If there were numbers whose factorization would have extremely strong mathematical interest and whose factorization was within the reach of my laptop, I would anticipate they'd have already been done well before now.

I read enough to find the best known algorithms, download a couple of open-source implementations, and go through their documentation. Seemed like enough initial reading to me. Choosing to leave my laptop in one location to run these for a while isn't a career change.

As far as learning the background, I'm a math grad student but haven't ever taken a number theory course and don't really have time to go through a proof of ECM or GNFS. I've had plenty of algebra and a little algebraic geometry so I have a faint inkling of what's involved; though I'm sure there's lots of interesting math there, there are only so many hours in the day.

I have previously run 4590 ECM curves with b1=11e6.

Thanks for piping up. With my 6698 curves with the same b1, looks like it's time to move on.

[Belteshazzar]

Got 105!+2- yes, the c163 was semiprime. It was a stroke of luck to get it so quickly after bumping b1 up- expected # of curves for a 49-digit factor using b1=43e6 is probably >5000, I got it after roughly 200.

Batalov, what kind of ECM pretesting has already gone into the c136 cofactor of 108!+2?

[Batalov]

Report it to http://factordb.com/index.php?query=105%21%2B2
and OEIS.

The c136 should be ready for GNFS by now.

[Belteshazzar]

I figured it would be, so I got GNFS started, but since polynomial selection seems to only be using one core, I'd left the other core continuing with YAFU's factoring routine (which I'd started in order to find the c136 cofactor- I didn't know about factordb- and which was doing ECM w/b1=10M). So I'll just free up that core now.