The worth or futility of gratituous factorizations

[R.D. Silverman]

Originally Posted by schickel

3^345-2 = 505027 * 25631055313 * 620565502016389534342436351929 * c119

c119:

prp60 factor: 212176376860378077776315019478089127085008105128842176485863
prp60 factor: 237283278978015820127013108788399507515644303307564184722133

So the 3 largest factors are p30 * p60 * p60!

I realize that I will get flamed for this, but I am going to ask anyway.

What is the point of doing all of these mundane factorizations that do
not seem to be related to anything? Why is doing these mundane
computations more statisfying than being able to say, for example,
"I contributed to the record factorization of M1061"? (or any other
leading edge result?

The reward that comes from participation should be proportional
to the effort put forth. Isn't it more satisfying to put forth a large
effort toward (say) a record factorization, than a tiny effort toward
some mundane and unimportant result? Isn't it more satisfying to
participate in a computation that has a long history behind it and which
has at least some relevence to mathematics than to perform some
arbitrary factorization??? Yes, I recognize that larger projects are
collaborative efforts. But I then ask, why are such efforts relatively
unnatractive? NFSNET could certainly use help on M1061. It is
taking a long time. This forum could use help on M929. It is, after all,
the Mersenne forum! There are other projects that
have a long history behind them. The Sierpinski (17 or bust) project.
Factorization of Fibonacci/Lucas numbers. [many of these are well within
the reach of single contributors]. Helping the XY project. Helping
Xilman's tables.

With so many established projects, why do people find it
necessary to invent their own set of numbers which only require
minimal or modest effort??

There is no end to the (forms of) numbers one might create. Why is
3^x - 7 important? Why not 3^x-5, or 3^x - 11, etc. etc. ???

I could understand a response to my questions such as "I am doing this
because I am writing my own code and need some modest unfactored
numbers to test it". Can anyone provide an alternative rational reason?

Yes, people do it for fun. But people can have fun working on established
projects just as easily, can't they? Are collaborative efforts not fun?

[BigBrother]

Last fiddled with by schickel on 09 Jan 12 at 08:06 Reason: Just 'cause

[R.D. Silverman]

Originally Posted by BigBrother

Last fiddled with by schickel on 09 Jan 12 at 08:06 Reason: Just 'cause

I asked some (what I thought were) reasonable questions. This is not
a very satisfying answer.

[BigBrother]

Originally Posted by R.D. Silverman

I asked some (what I thought were) reasonable questions. This is not
a very satisfying answer.

That's because there is no satisfying answer, at least not for you. People do this stuff "just because" or "because they can". No rational reasons. A lot of people are not as rational as you want them or might expect them to be.

[R.D. Silverman]

Originally Posted by BigBrother

That's because there is no satisfying answer, at least not for you. People do this stuff "just because" or "because they can". No rational reasons. A lot of people are not as rational as you want them or might expect them to be.

I can accept this. However, it leaves one question still unanswered:

What satisfaction is derived from doing it????

I might choose to (say) nail two things together that have never been
nailed before. But what satisfaction might be derived is a mystery.

[wblipp]

Originally Posted by R.D. Silverman

What is the point of doing all of these mundane factorizations that do not seem to be related to anything?

The very act of posting to the Gratiuitous Factors thread is a statement that there is no good reason for this particular factorization. Seeking a good explanation for such activities is like teaching a pig a sing - it wastes your time and annoys the pig.

[fivemack]

I think it's more like picking up a pretty pebble at a beach, and marvelling that the two holes the sea has made in it meet at a surprisingly exact ninety-degree angle; it's pointing out a curiosity of nature.

I've often wondered whether I do aliquot-sequence factorisations mostly because it seems a pity to stop having done them for some years; I realise that I'm waiting for a {some small constant}/log N probability, and spending three dollars a day on electricity to do so, but I've got three dollars a day ... the aliquot-sequence jobs are sitting there at nice 19 and getting preempted by trying to see if quintics or sextics are better for the 204-digit GNFS job, but I'm not sure that's any more satisfying.

[R.D. Silverman]

Originally Posted by wblipp

The very act of posting to the Gratiuitous Factors thread is a statement that there is no good reason for this particular factorization. Seeking a good explanation for such activities is like teaching a pig a sing - it wastes your time and annoys the pig.

I'm not flaming here, I am asking!

[fivemack]

Originally Posted by R.D. Silverman

I'm not flaming here, I am asking!

I realise that, and I hope my answer is OK; on the other hand I think you might have got better answers by asking people to describe the satisfaction that they get out of it, rather than something that could be read as disbelief that there's satisfaction there.

[akruppa]

Posts moved to separate thread.

fivemack thanks, sorry for getting in the way

[fivemack]

Originally Posted by R.D. Silverman

Yes, I recognize that larger projects are
collaborative efforts. But I then ask, why are such efforts relatively
unattractive?

Yes, people do it for fun. But people can have fun working on established
projects just as easily, can't they? Are collaborative efforts not fun?

It's difficult to get much of a feeling of achievement from a collaborative effort when you're a tiny player and there are enormous ones - it was about all I could manage with my large-for-private-ownership resources to do 10% of the sieving for 7^374+1, if Bruce were doing it on his own it would have taken just as long and the matrix would just have been a bit larger at the end, my main role was to do some of the preliminary work and convince Bruce that that specific problem was worth several months on ~400 of his CPUs.

For some of the sequence-4788 work I found that it was easier for me to do the whole job (type 'make -j 48', come back in four days and issue an msieve command) than to collect tens of little batches of relations from rapidshare.