[QUOTE=Dubslow;277825]I think shortage of LL is about as subjective as whether or not DC is too slow. I personally don't see a shortage in LL, but rather think of the LL work being done as setting how important everything else is. The P-1 to LL ratio of work being completed is lower than is optimal, which is why we say there's a shortage of P-1. It really is each to his own here.[/QUOTE]

I think we are all singing from the same hymn-sheet.

If a CPU gets an LL assignment with inadequate P-1, it
is little trouble (even a refreshing change) to do it before the test.
But inadequate TF requires a GPU.
BTW I understand the interest in factoring low mersennes,
but the "effort" >100M seems to me to be completely pointless.

David

[QUOTE=davieddy;277826]BTW I understand the interest in factoring low mersennes,
but the "effort" >100M seems to me to be completely pointless.[/QUOTE]

Of course it is. But let us please be honest... At the end of the day the entire GIMPS project is pointless...

Except, of course, for the advances in algorithms, optimization of code, and distributed computing methodologies that this project requires.

And I have already explained (many times) why I have my cluster trial factoring above >100M. But to say again: as a sys-admin / network admin, it is useful to have the machines I am responsible for generate a small but regular amount of traffic which is a function of the CPU power available to them (as opposed to, say, a Worm or Virus).

This has helped me solve many issues over the years.

[QUOTE=chalsall;277789]Please forgive me for this "plug", but I'd like to bring to the attention of all P-1 Workers that the "GPU to 72" Tool is now making available low exponents (with no LL work yet done) which have been TFed to high levels (72 bits) by GPU's which need a P-1 run.

Please see [URL="http://gpu.mersenne.info/account/getassignments/p-1/"]http://gpu.mersenne.info/account/getassignments/p-1/[/URL]. (If you don't have an account at the site, you'll have to create one before being able to be assigned work.)[/QUOTE]
Great - nice work as usual, chalsall! I'll grab a little P-1 work in a few days when my supplies run low. Doing P-1 after GPU-TF makes so much sense!

[QUOTE=davieddy;277826]BTW I understand the interest in factoring low mersennes, but the "effort" >100M seems to me to be completely pointless.[/QUOTE]Is [URL="https://www.eff.org/awards/coop"]$150,000[/URL] pointless???:ouch:

[QUOTE=Uncwilly;277856]Is [URL="https://www.eff.org/awards/coop"]$150,000[/URL] pointless???:ouch:[/QUOTE]
It'll be worthless by the time a 100M digit prime is found

More to the point, how much use is TFing
the b*****s to say 68 bits?

Chocolate teapot IMO

I was looking at low level exponents checking the amount of P-1 done (similiar to what James H is doing but in the 7M range) and set up to run P-1's on the ones that had lower B1/B2 bounds. Since the bounds most often used seem to be 85000,1593750 I skipped all the exponents at or above these bounds. 90+% of these were TF'd to ^63. Since the GPU is fairly quick on these (8 min I believe), I set my worktodo with TF to ^64 inbetween the GPU to 72 exponents I am running so it cranks out 6-8 TF a day.

Now, I'm wondering if anyone could help me to understand this if possible:

7000163,63,85000,1593750 shows this exponent was TF'd to ^63 and the B1/B2 bounds were such that I did not send it to P-1, yet the GPU running ^63 to ^64 on this exponent came up with 12771553988326268647 as a factor.

I'll admit my math capability is no where near understanding P-1 and TF, but from what I have read on here so far it seemed to me that the P-1 should have found this factor that going another bit level found. Can anyone give me a low level explanation why this happened?

Never mind.

[QUOTE=bcp19;278329]I was looking at low level exponents checking the amount of P-1 done (similiar to what James H is doing but in the 7M range) and set up to run P-1's on the ones that had lower B1/B2 bounds. Since the bounds most often used seem to be 85000,1593750 I skipped all the exponents at or above these bounds. 90+% of these were TF'd to ^63. Since the GPU is fairly quick on these (8 min I believe), I set my worktodo with TF to ^64 inbetween the GPU to 72 exponents I am running so it cranks out 6-8 TF a day.

Now, I'm wondering if anyone could help me to understand this if possible:

7000163,63,85000,1593750 shows this exponent was TF'd to ^63 and the B1/B2 bounds were such that I did not send it to P-1, yet the GPU running ^63 to ^64 on this exponent came up with 12771553988326268647 as a factor.

I'll admit my math capability is no where near understanding P-1 and TF, but from what I have read on here so far it seemed to me that the P-1 should have found this factor that going another bit level found. Can anyone give me a low level explanation why this happened?[/QUOTE]

I am no expert on the guts of P-1, but according to James' page here, you would have had to have B2 be around 12M (the size of the biggest factor of k). 1.5M won't get the job done.

[URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=7000163"]http://mersenne-aries.sili.net/exponent.php?exponentdetails=7000163[/URL]

[QUOTE=bcp19;278329]it seemed to me that the P-1 should have found this factor that going another bit level found.[/QUOTE]TF and P-1 typically find different types of factors; the ones that are "easy" to find by one method are not necessarily "easy" for the other method.

TF is easy to understand: try each prime number between 2^63 and 2^64 and see if it divides into 2^exponent-1. If it does, it's a factor.

P-1 factors are only found when they meet certain criteria. The so-called "k-value" of any P-1 factor is the prime factorization of the discovered factor minus one, with 2 and the Mersenne exponent removed. Trying to clarify that with an example:[quote]M7000163 has a factor: 12771553988326268647
12771553988326268647 - 1 = 12771553988326268646
factorize(12771553988326268646) = [b]2[/b] × 3^4 × 7^2 × 19 × [b]7000163[/b] × 12096811
k = [color=blue]3^4[/color] × 7^2 × 19 × [color=blue]12096811[/color][/quote]For P-1 to find the factor, B2 and B2 need to be greater or equal to the largest and second-largest prime powers respectively, which means that the minimum bounds for P-1 to find the factor is B1=81 (that is, 3^4) and B2=12,096,811

You can see these numbers, plus some pretty graphs to try and help visualize that, on my site: [url]http://mersenne-aries.sili.net/7000163[/url]

The factor you found isn't very "smooth", which makes it more difficult (as in larger bounds are needed) to find with P-1 and therefore more likely to show up with TF. Compare with [url=http://mersenne-aries.sili.net/6877433]this relatively large factor[/url] I found yesterday which was easily found with P-1 but would take a current GPU a few billion years to TF.

[QUOTE=garo;278334]There was an error in the P-1 test?[/QUOTE]There was no error. You can clearly see on [url=http://mersenne-aries.sili.net/7000163]the P-1 graph[/url] that the factor lies outside the bounds used for the P-1 test.

[QUOTE=James Heinrich;278340]
The factor you found isn't very "smooth", which makes it more difficult (as in larger bounds are needed) to find with P-1 and therefore more likely to show up with TF. Compare with [url=http://mersenne-aries.sili.net/6877433]this relatively large factor[/url] I found yesterday which was easily found with P-1 but would take a current GPU a few billion years to TF.[/QUOTE]

[URL="http://mersenne-aries.sili.net/exponent.php?factordetails=16861341412139695521233727186051728863"]http://mersenne-aries.sili.net/exponent.php?factordetails=16861341412139695521233727186051728863[/URL] is by far my favorite example. All of the GPU's in the world would never find this, but it is almost trivial for P-1 to discover.