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2007-05-26, 20:32   #8

"Richard B. Woods"
Aug 2002
Wisconsin USA

22·3·599 Posts

Quote:
Originally Posted by axn1
Quote:
 Originally Posted by cheesehead The efficiency of each choice is proportional to the ratio (chance of finding a factor)/(time to find a factor), so that ratio calculation is the one I use in the following: Prime95 will prefer combination X because 1.0%/10 (.010/10) is greater than 1.3%/15 (.013/15) or 1.5%/16 (.015/16).
No
You know, as I was writing that, my subconscious indicated that something was wrong, but I couldn't figure out what. I should have obeyed my impulse to add a note that I was uncertain.

Quote:
 You cannot define efficiency of P-1 without considering the cost of an LL test.

I was treating the cost of an LL test as an implicit multiplication constant (constant for a specific exponent, that is -- so that it would multiply each of the calculations in my example by exactly the same number and thus need not be explicitly included -- hence my "proportional" remark).

How would you rewrite my example, or at least part of it?

(It's quite possible that when I see your explanation, I'll think, "Oh, how could I have forgotten?" or "There it is, right in the middle of my earlier posting in this thread, but I got mixed-up!" I eagerly await your explanation.)

- - -

Added: Possible source of problem: I have used the term "efficiency" privately in certain calculations for a certain concept. It's possible that:

(a) "Efficiency" has a formal meaning in the context of real, public P-1 discussion that conflicts with my private definition, or

(b) I may have a "fuzzy" private definition of "efficiency" and have gone-wrong in using it here, or

(c) I may have two separate private definitions of "efficiency" for two different contexts and mixed them up here.

My private usage: One of my private definitions of "efficiency" in this context is:

(total L-L time saved by finding a factor)
/
(time spent in P-1 effort to find that factor)

Another (apparently equivalent, to me) is:

(Total L-L time expected to be saved by finding factors of a given set of Mnumbers with P-1, on average given fixed B1/B2/"Available Memory" for all Mnumbers)
/
(Total time spent in P-1 effort to find factors of a given set of Mnumbers with P-1, on average given fixed B1/B2/"Available Memory" for all Mnumbers)

Last fiddled with by cheesehead on 2007-05-26 at 21:02