PrimeGrid's Giving Thanks Challenge

[bdodson]

Originally Posted by opyrt

I suspect you attached PrimeGrid and just ran it as is without turning off any projects? PrimeGrid has a lot of different sub-projects to choose from and the default setting is you run all. You can choose which to run from your account on the project pages.

However, if you did choose only "Prime Sierpinski Project (Sieve)", then you must have found 7 factors, not primes, as we do not find primes with sieving.

I'm not too familiar with the statistics on the PrimeGrid pages, but I know there are a lot of helpful people on their message boards... Maybe you can get more help there?

The main link over there refers to this thread (somewhere) on mersenneforum.
I spent some time on 17-or-bust, before it got bionc'd, and do recall that
sieving's supposed to clear away composites; and can't actually settle one
of the remaining how-ever-many are left (12? three being done on s-o-b;
the rest on boinc/primegrid). I'm inclined towards a guess that while sieving
can't settle one of the remaining main cases, if it is doing that by finding
factors (of something; candidates and some other numbers of the same
form) --- once-in-while one of the factors can be prime, yes?

In any case, the main link on the primegrid Challenge reports that there were
some 300 (prime?) factors found; one of my BOINCstats colleagues was
saying that he had one, and now my account reports

PrimeGrid  
PSP Sieve tasks 
Completed tasks 2396 
Credit 70,817.71 
Factors found 7

Ah. So I didn't hit the top20 in the challenge without having selected
"PSP Sieve" (as instructed), but the factors found aren't classified as
prime or composite.

The boinc projects don't appear to be heavy on the maths (we try not
to confuse our contributors on NFS@Home; Greg more successfuly than
me). I was just wondering whether I could fish-out one of these "factors";
perhaps as an example for my intro crypto course this spring. -bdodson

[Mini-Geek]

Originally Posted by bdodson

I'm inclined towards a guess that while sieving
can't settle one of the remaining main cases,

This is correct.

Originally Posted by bdodson

if it is doing that by finding
factors (of something; candidates and some other numbers of the same
form)

Yes, it's finding factors of candidates.

Originally Posted by bdodson

once-in-while one of the factors can be prime, yes?

Of course. In fact, in a case like this, since you'll always have already sieved above the square root of a factor you're looking for, the factor will always be prime.
But, we're not interested in whether the factors are prime or not. What we're interested in is what those factors (which'll be prime) divide. If they divide any of the numbers we're sieving, then when you run the sieve we'll know, and can eliminate that number from needing to be primality tested (e.g. LL test, LLR, Proth test, a PRP test, etc.).

Sieving helps reduce the number of candidates that need full primality (or PRP) testing by finding factors, (which due to the method of searching and progress in something like the PSPsieve will always be prime) thereby proving the numbers (the candidates, not the factors) composite without a lengthy primality test. It's quite similar to TF for GIMPS and Mersenne numbers, if you're familiar with that. (in end results, i.e. factors or certainty that numbers have no factor below a certain point, not in other ways like the mathematical algorithm or the number of candidates searched at once) Both make the time to process a range much faster by looking for factors. There is one major difference: due to the fact that you can run an efficient TF on a single Mersenne number, (details are at http://mersenne.org/various/math.php if you're interested) it's better to test them one at a time (TFing) instead of in a large group (sieving). (Or at least I'm assuming so, since that's how everybody does it. )

[opyrt]

Originally Posted by bdodson

I was just wondering whether I could fish-out one of these "factors";
perhaps as an example for my intro crypto course this spring. -bdodson

From what I know, there is no way to find out which factors you found and which candidates they proved to be composite through the PrimeGrid webpages. But I've asked on their chat, so maybe we'll get an answer there.

EDIT: Got an answer from PG now... This is currently not a feature.