Who is adding all these N^a-1?

[chris2be8]

Sorting the results so all the known factors of a number get submitted at once would help. I've probably rediscovered quite a few factors. Also fully factoring the smaller composites with QS or SNFS before you submit them would help.

With hindsight submitting the results as you found them would have been better. That would have spread the load out over 6 months.

Chris

[ChristianB]

I stopped my yafu.pl and resumed my pandigit aliquot endeavor.

If you could somehow sort the cofactors before submitting would be a great help. Even if some are missing we could tackle them after your batch is complete.

[chris2be8]

After thinking it over I suggest submitting them in the following order:
1: Numbers where you have already submitted some but not all of the factors you know.
2: Numbers that are now fully factored.
3: Numbers where the remaining composite is small enough for you to finish with QS (or SNFS) before you submit it.
4: Remaining partly factored numbers (assuming you found something significant).

That should minimize wasted effort. Particularly case 1.

Chris

[henryzz]

@William
Are you planning to update the Smallest Known Roadblocks section of http://www.oddperfect.org/ at some point? The current listed number has be factorized according the factordb.
It would be interesting to see how far we can now reach with the "traditional" method.

[wblipp]

Originally Posted by chris2be8

After thinking it over I suggest submitting them in the following order:
1: Numbers where you have already submitted some but not all of the factors you know.
2: Numbers that are now fully factored.
3: Numbers where the remaining composite is small enough for you to finish with QS (or SNFS) before you submit it.
4: Remaining partly factored numbers (assuming you found something significant).

I arrived at similar priorities. I have made changes in how I interact with factordb both now and in the future. These new methods will greatly reduce the impact of OPN work on the unfactored composites list. I'm also taking steps to ensure that numbers that were fully factored as part of this exercise show up as FF in factordb for both (p^q-1) and (p^q-1)/(p-1).

[wblipp]

Originally Posted by henryzz

@William
Are you planning to update the Smallest Known Roadblocks section

It's on the todo list, but there's a serious shortage of tuits at present. Probably months away.

[henryzz]

Originally Posted by wblipp

It's on the todo list, but there's a serious shortage of tuits at present. Probably months away.

Understood. Know the feeling.

[R.D. Silverman]

Originally Posted by wblipp

II've previously reasoned that OPN researchers - some known to me now, others to come along in the future - will be interested in these factors,

A delusion.

[pinhodecarlos]

Originally Posted by R.D. Silverman

A delusion.

We, OPN researchers, don't care about your thoughts.
Also, "The Joy of Factoring" by Samuel S. Wagstaff, Jr. states, and I quote: "The Cunningham Project helps the investigation of odd perfect numbers." (page 9 line 15) This means you should not help the Cunningham Project because it would be a controversy saying publicly you are against OddPerfect Numbers but running it in the background.
On this same page there's two references, one for Ochem and Rao research and the other to Nielson research. Both about Odd perfect numbers.

[R.D. Silverman]

Originally Posted by pinhodecarlos

We, OPN researchers, don't care about your thoughts.
.

You??? A "researcher"???? It's laughable. It's also yet another delusion.

When you reach the point when you are no longer almost completely
ignorant about the algorithms and mathematics behind them you may
become qualified to have an opinion on this subject.

Until then, your "opinion" has almost no value.

[wblipp]

Originally Posted by R.D. Silverman

A delusion.

Maybe. But every few years somebody manages to come up with something new enough and interesting enough to say about Odd Perfect Numbers that they have a publishable paper - there have been three or four since I started co-ordinating the factorization efforts. Most OPN papers rely upon factor chains for part of the argument. So all in all, it doesn't strike me as particularly delusional to be thinking that in the next few years somebody will want OPN factors for another publishable paper. The older OPN publication record has instances of different people expending resources on the same difficult factorizations - I wouldn't want that to happen again.