[quote]I suggest that ALL of you who continue these mundane calculations
change to doing something that will help push the state-of-the-art, or
change to something that has the potential to solve an open problem.[/quote]

The problem is that almost all of those calculations are profoundly unsatisfying in precisely the way that doing calculations which give an admittedly-small amount of new information after a moderate amount of time is satisfying; 'no factor found' causes less happiness than a factor.

Calculations that help push the state of the art require really substantial resources, [b]otherwise they'd already have been done[/b] - RDS is well-aware that the last numbers that I, who have devoted unreasonable resources to having local compute facility, could reasonably personally factor for the Cunningham project were done a couple of years ago.

Maybe I should instead be helping out Cremona and Elkies in finding new elliptic curves with interesting properties; but that's an area in which I spent quite a lot of time and resources finding curves (which formed part of my PhD thesis), and then Elkies or Cremona had a better idea and more resources and were able to push the boundaries out to places I couldn't look. I'm not sure I can usefully contribute to the work to check that 234446 is the smallest conductor of an elliptic curve with rank four - it's taken CPU-decades already, and the data tables themselves are becoming awkwardly large.

[QUOTE=fivemack;278291]The problem is that almost all of those calculations are profoundly unsatisfying in precisely the way that doing calculations which give an admittedly-small amount of new information after a moderate amount of time is satisfying; 'no factor found' causes less happiness than a factor.
[/QUOTE]

Ah. You seem to be saying that people want quick gratification. The
IGG strikes again. They are unwilling to participate in long term
projects unless it gives quick feedback or results.

[QUOTE]
Maybe I should instead be helping out Cremona and Elkies in finding new elliptic curves with interesting properties; but that's an area in which I spent quite a lot of time and resources finding curves (which formed part of my PhD thesis), and then Elkies or Cremona had a better idea and more resources and were able to push the boundaries out to places I couldn't look. I'm not sure I can usefully contribute to the work to check that 234446 is the smallest conductor of an elliptic curve with rank four - it's taken CPU-decades already, and the data tables themselves are becoming awkwardly large.[/QUOTE]

Actually, believe it or not, I am in the process of writing software that will
add to these kinds of efforts. But most people here would not recognize
what a conductor (or j-invariant) is, nor would they be bothered or
have the perserverence to find out. I don't blame them, I would not
expect anyone short of working on a math PhD to participate in such).
I'm currently working on some Heegner point code (and it is rough going, especially when working in fields other than Q).

But there are other elementary computational projects that CAN settle
some open questions (perhaps with a bit of luck). The Sierpinski and
prime-Sierpinski projects are such. So is the Euler-sum project.
We know examples of a 4th power as the sum of 3 4th powers, and of
a 5th power as the sum of 4 fifth powers, but have no examples for
higher powers. I can name others.

And I still fail to see the satisfaction (other than personal amusement) of
these mundane factorizations using code written by others. As I said,
it's like being a couch potato. We all enjoy TV without knowing how
it works (I understand a little of it but not all), but we don't announce what
we watched on TV last night as a source of pride or as if our TV watching
had outside value.

[QUOTE=R.D. Silverman;278275]Technical discussion of the worthiness of research projects is inherently[/QUOTE]

Since we've moved to soap box, I'll take the time to laugh in your face at your silliness. I'm personally not attracted to OPNs as a research project. I'm a hobbiest here. The appellation of "Wagstaff's stamp collection" is supposed to be a disincentive, but it catches the essence of why I do this and it encourages me that others share my motivations for factoring. It's an added bonus that a few mathematicians happen to be interested, but not the attraction. Continue droning about "technical research projects" to your hearts content - but it will continue be ineffective because it continues to ignore why we do this.

I am, however, grateful that there are non-hobbiest such as yourself that are advancing the state of the art. I look forward to using those advances for factoring even larger numbers for OPN projects.

[QUOTE=R.D. Silverman;278277]You keep trying to put words in my mouth. I said "pointless" within one particular post that was part of a SERIES OF POSTS.[/QUOTE]

If I had thought you only meant that OPN searches are pointless, I would have ignored or deleted the message. Your views on this are well known, and you haven't said anything new on the matter for several years.

You keep trying to weasel out of what you actually said. This was your first post here in a long time. Your usual approach is to entirely quote long posts and respond to a tiny part (a rudeness to the reader), but here you took to the trouble to quote ONLY the particular factorization. I've been careful to ask only about the particular factorization.

[QUOTE=wblipp;278307]Since we've moved to soap box, I'll take the time to laugh in your face at your silliness. I'm personally not attracted to OPNs as a research project. I'm a hobbiest here. The appellation of "Wagstaff's stamp collection" is supposed to be a disincentive, but it catches the essence of why I do this and it encourages me that others share my motivations for factoring. It's an added bonus that a few mathematicians happen to be interested, but not the attraction. Continue droning about "technical research projects" to your hearts content - but it will continue be ineffective because it continues to ignore why we do this.

[/QUOTE]

OK. You want to be a computer couch potato. That is certainly your
priviledge. But even couch potatos do not crow about every show
they watch.

[QUOTE=R.D. Silverman;278314]OK. You want to be a computer couch potato. That is certainly your priviledge. But even couch potatos do not crow about every show they watch.[/QUOTE]

Indeed. Today I'll probably factor 30,000 numbers for my OPN database. You won't see any of these. Only the ones of broader interest, like 811^71-1, get shown here.

Wow RDS: That's your second fight on this forum in a very short time. What's with you this month?

and yes: I'm hobbyist...might someday want to point to my contributions to the software. It'll take some real luck to actually do any new math.

[QUOTE=Christenson;278327]Wow RDS: That's your second fight on this forum in a very short time. What's with you this month?[/QUOTE]Perhaps it's the wrong time of the month?

Which reminds me: what's the difference between BSE and PMS?

[spoiler]One is mad cow disease. and the other is a serious agricultural problem.[/spoiler]

[QUOTE=R.D. Silverman;278295] I'm currently working on some Heegner point code (and it is rough going, especially when working in fields other than Q).[/QUOTE]

Excellent; I've done a bit of work on Heegner points, though I ended up passing the ball to Mark Watkins who ran with it and was able to find explicitly the generators of height a-few-thousand of some carefully-chosen algebraic-rank-1 Mordell curves ... I worked out the equations for four-descent, he did the Heeger calculations on the four-descendent curve and lifted them to the initial one. It's the only time that I've found [b]addition[/b] at high precision to be the limiting factor - I think Mark ended up having to write some code using the very deep internals of Magma.

I cannot recommend working with a workaholic genius as the path to inward happiness, though I wish Mark nothing but the best.

[quote]So is the Euler-sum project.
We know examples of a 4th power as the sum of 3 4th powers, and of
a 5th power as the sum of 4 fifth powers, but have no examples for
higher powers. I can name others.[/quote]

That's also something that I've done; for my MMath I found the smallest number which was the sum of two cubes in five distinct ways, and was other than entirely happy that I could google the number and find that it was the smallest number with that property - though Roger Heath-Brown was willing to accept the dissertation for MMath anyway.

[quote]And I still fail to see the satisfaction (other than personal amusement) of these mundane factorizations using code written by others.[/quote]
I think personal amusement is close to sufficient satisfaction.

Tom

[QUOTE=R.D. Silverman;278295]But there are other elementary computational projects that CAN settle
some open questions (perhaps with a bit of luck). The Sierpinski and
prime-Sierpinski projects are such.[/quote]

I find those significantly less pointful than the OPN work: there's a reasonable argument that the smallest number to satisfy the Sierpinski requirements will be a good deal larger than the largest numbers tested for Mersenne primality.

[QUOTE=fivemack;278367]I find those significantly less pointful than the OPN work: there's a reasonable argument that the smallest number to satisfy the Sierpinski requirements will be a good deal larger than the largest numbers tested for Mersenne primality.[/QUOTE]

The OPN factorizations have NO HOPE of ever yielding the desired result.
That result will have to come from new mathematics. All they can do
is keep raising the (lower) bound, a little bit at a time. Now, if at some
point in time a mathematical result (say) yields the result that if an
OPN exists, it must be less than 10^B for some reachable B, then yes
the computations will be worth pursuing.


The Sierpinski/17 or Bust project can (and eventually will) settle the
conjecture. It is bounded in scope and the computations themselves will settle the conjecture without any new mathematics.

So the choice is endless computation that can never achieve a result
versus computations that will.

[QUOTE=fivemack;278363]
That's also something that I've done; for my MMath I found the smallest number which was the sum of two cubes in five distinct ways, and was other than entirely happy that I could google the number and find that it was the smallest number with that property - though Roger Heath-Brown was willing to accept the dissertation for MMath anyway.
[/QUOTE]

You had Roger as your advisor? Wow. You were extraordinarily blessed.
He is an extraordinary analytic number theorist.

[QUOTE]
I think personal amusement is close to sufficient satisfaction.

Tom[/QUOTE]

I will express an opinion here: Only people with ego problems/low self esteem
should find it necessary to trumpet couch potato work to the Internet.
As I said before, I find some (but not much) TV to be personally amusing.
I don't trumpet the shows that I watch to the net.

I have some very minor new results on NFS that I could publish but won't.
I recognize that they are not important enough. They extend the optimal
sieve region stuff that I did for the line siever to the lattice sieve. I consider
it a trivial extension of what I did earlier, easily derived by anyone who
read my prior paper and of limited importance. Publishing would be a
pointless gesture on MY part. I am not someone who
publishes 'easy stuff' simply to publish another paper. Yet many people
here seem to just repeatedly trumpet their couch potato easy factorizations.

I also realize that you know that many academics do publish as much as
possible just to get published. The depth of the paper does not matter;
merely the total number of papers published. Yech.