Octoproths

[smh]

Originally Posted by R.D. Silverman

May I ask:

With so many other established computational projects already available,
why do this one?

This one is as good as any other.

But i choose this one because i can't use that pc for anything else (except maybe ecm) and it's only available to me for a few days. PRP-ing takes only 15 minutes on my P4. The pc will be gone tomorrow morning and i didn't want to let it run idle.

For the last year or two, i spent most of my cpu time factoring for a few projects (including Paul's). Unfortunately, Cunningham numbers are a bit to hard for my limited resources. I might be able to do a < c140 with GNFS, but my P4 has only 256MB RAM. I have a laptop with 2GB, but that one is used for work, and part of that memory is often needed. Besides, i'm not sure GGNFS is upto the job yet. Sieving on multiple pc's requires to much book keeping for the time i've currentely got.

I'm open for any number you want to have factored, as long as it can be done in a reasonable amount of time.

[smh]

Below the results for N=157 and K<2*10^13

All are prp, not tested for primality

541364899635*2^157+1 
541364899635*2^157-1 
541364899635*2^(157+1)+1 
541364899635*2^(157+1)-1 
2^157+541364899635 
2^157-541364899635 
2^(157+1)+541364899635 
2^(157+1)-541364899635

5375998941495*2^157+1 
5375998941495*2^157-1 
5375998941495*2^(157+1)+1 
5375998941495*2^(157+1)-1 
2^157+5375998941495 
2^157-5375998941495 
2^(157+1)+5375998941495 
2^(157+1)-5375998941495

7137839620995*2^157+1 
7137839620995*2^157-1 
7137839620995*2^(157+1)+1 
7137839620995*2^(157+1)-1 
2^157+7137839620995 
2^157-7137839620995 
2^(157+1)+7137839620995 
2^(157+1)-7137839620995

16986089468655*2^157+1 
16986089468655*2^157-1 
16986089468655*2^(157+1)+1 
16986089468655*2^(157+1)-1 
2^157+16986089468655 
2^157-16986089468655 
2^(157+1)+16986089468655 
2^(157+1)-16986089468655

May I ask:
With so many other established computational projects already available,
why do this one?
I accuse noone. However, I suspect that the answer is:
"Because this project is new, it is relatively easy to get results".
Let me quote John Kennedy:
"We choose to go to the moon and do the other thing... Not because they
are easy, but because they are hard."
There is little reward in using other people's software to do easy computations. Rewards come from succeeding at something that is hard.
The satisfaction one derives from solving a problem is commensurate with the
level of effort.

I would appreciate if you respectfully ask questions elsewhere. (buzz off)
This project has been around for awhile, and now has a new spin on the fundamental property that started it.

[robert44444uk]

We would still be computing the number of angels on the head of a pin unless we had adapted and explored.

The facts are:

This is original thinking, adaptation and exploration in virgin territory
It is simple, but not so simple, there are pitfalls for the unwary
There is interesting mathematics if anyone wants to look at it
Axn1's program is a masterpiece
This is true 1+1=3, as I like to define human co-operation
This is the shitzit right now

Mr Silverman, have pity on us poor humans, nattering together and taking up your valuable bandwidth. Consider yourself flamed, or at least singed, as I am a pacific sort.

Regards

Robert Smith (aged 53 1/4)

[Dougy]

Silverman? Hmmm... sounds familiar. Are you related to Joseph H. Silverman who published (among others) the paper "Wieferich's Criterion and the abc-Conjecture" in the Journal of Number Theory?

[Dougy]

I've been looking at the "weights" of certain bases again. Working as I defined it previously, W(157) = 62. Is the heaviest W(n) for n <= 200.

The next three heaviest are
W(175) = 60
W(187) = 56
W(112) = 54

So the bases n = 112, 175, 187 should be good for finding octos.

[Dougy]

Newies:

4358737887315 87 (a monster!)
2232065722095 88
2148136610235 88

for n=89-96 there are no known octoproths.

Searched n=89 to k=780321515295.

Okay, i have a few hours sieving time available

Is'nt it faster to verify bitwin primality first?
With RMA 1.75 in 2 minutes I was able to find no octoproth's for n=5000, with k<200000000.


TTn

[smh]

Originally Posted by TTn

Is'nt it faster to verify bitwin primality first?

No, the remaining 4 possibilities often have small factors.

Originally Posted by TTn

With RMA 1.75 in 2 minutes I was able to find no octoproth's for n=5000, with k<200000000.

With octo_fast it took less then 1 second to 'sieve' this range, with only 4 possible candidates left.

1297905 5000
111183135 5000
116381265 5000
176976555 5000

No, the remaining 4 possibilities often have small factors.

Right on, I will include this in my script.

Although not all those look like the same candidates I came up with.
hmmm... Ill double check.

Ah, newpgen has caused some errors due to the large file size.
Or machine/Os cannot handle correctly.

I am surprised that you are getting so much speed without errors.
If this is true, then congradulations!
I will tri-check thouroughly, with a belts and braces technique.


TTn