P-1 factoring anyone? - Page 101

kladner · 2012-01-31, 15:40

Quote:

Originally Posted by bcp19

Sorry, I hadn't ruled that out, it just seemed an awful big jump in bounds for just a few extra levels.

On the bright side, you caused some very informative discussion to take place, clearing up some misconceptions.

Dubslow · 2012-01-31, 17:57

Quote:

Originally Posted by bcp19

Sorry, I hadn't ruled that out, it just seemed an awful big jump in bounds for just a few extra levels.

Consider that the total number of candidates tested for the higher one was 8x greater than the other four. From that view, it's no wonder the P-1 bounds dropped.

Mini-Geek · 2012-02-01, 03:38

Quote:

Originally Posted by Prime95

The biggest source of deviation from 1000 is that prime95's initial estimate is not very accurate.

On a four core machine, is it expected to be around 1000 or around 4000? Mine is currently at 3707 (it was lingering around 2000 when I manually bumped it up to ~4000, as I mentioned), which is roughly accurate. The CPU is an i5-750@2.8GHz. If you want more info (e.g. for debugging, to make the estimate more accurate) let me know.

cheesehead · 2012-02-01, 09:36

Quote:

Originally Posted by bcp19

Sorry, I hadn't ruled that out, it just seemed an awful big jump in bounds for just a few extra levels.

Mr. Dickman's function ( http://en.wikipedia.org/wiki/Dickman_function , http://mathworld.wolfram.com/DickmanFunction.html ) leads to some broad maxima in the optimization function.

Mr. P-1 · 2012-02-02, 12:00

Quote:

Originally Posted by lorgix

(For that particular assignment you may want to adjust the memory settings so that 40 or 48 relative primes can be processed at once.)

44 relative primes is just fine, finishing stage 2 in eleven passes. 40 would need twelve passes, while 48 would do it in ten. The difference in performance would be miniscule.

cheesehead · 2012-02-02, 18:26

"Miniscule" (or, at least, "Detail Oriented") is some of our middle names around here.

LaurV · 2012-02-03, 03:06

Miniscule... that is like factoring, hard and odd.. :D

bcp19 · 2012-02-03, 07:30

I was looking for some easy numbers to get a better understanding of the P-1 process, and in looking at M2011, it lists bounds of 5 and 27 where K=2*2*3*3*3*5. As I was working through this, I got to thinking, couldn't this also be found with bounds of 5 and 9? In using 27, you'd have 2*2*5 from S1 and 27 from S2, but wouldn't 2*2*3*5 from S1 and 9 from S2 also work?

axn · 2012-02-03, 08:35

Quote:

Originally Posted by bcp19

I was looking for some easy numbers to get a better understanding of the P-1 process, and in looking at M2011, it lists bounds of 5 and 27 where K=2*2*3*3*3*5. As I was working through this, I got to thinking, couldn't this also be found with bounds of 5 and 9? In using 27, you'd have 2*2*5 from S1 and 27 from S2, but wouldn't 2*2*3*5 from S1 and 9 from S2 also work?

Where did you get this information? Neither 5,27 nor 5,9 will find this. A stage 1 bound of 27 is needed to find this.

With B1=27, you'd use an exponent of 2^4*3^3*5^2*7*11*13*17*19*23, which'd find the factor.

MrHappy · 2012-02-03, 10:24

29.8 percent chance of finding a factor!? Is that expectation correct? Until today I have only seen values from 4 to 7 percent...

axn · 2012-02-03, 10:31

Quote:

Originally Posted by MrHappy

29.8 percent chance of finding a factor!? Is that expectation correct? Until today I have only seen values from 4 to 7 percent...

>>>>> Assuming no factors below 2^-1 <<<<<

There is nothing wrong here. Nothing at all...

2012-02-03, 10:24	#1110
MrHappy Dec 2003 Paisley Park & Neverland 271₈ Posts	29.8 percent chance of finding a factor!? Is that expectation correct? Until today I have only seen values from 4 to 7 percent... Attached Thumbnails

2012-02-02, 18:26	#1106
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	"Miniscule" (or, at least, "Detail Oriented") is some of our middle names around here.

2012-02-03, 03:06	#1107
LaurV Romulan Interpreter Jun 2011 Thailand 2×3×1,609 Posts	Miniscule... that is like factoring, hard and odd.. :D

2012-02-03, 07:30	#1108
bcp19 Oct 2011 7·97 Posts	I was looking for some easy numbers to get a better understanding of the P-1 process, and in looking at M2011, it lists bounds of 5 and 27 where K=223335. As I was working through this, I got to thinking, couldn't this also be found with bounds of 5 and 9? In using 27, you'd have 225 from S1 and 27 from S2, but wouldn't 2235 from S1 and 9 from S2 also work?