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Old 2006-10-13, 23:08   #2
cheesehead
 
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"Richard B. Woods"
Aug 2002
Wisconsin USA

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Quote:
Originally Posted by Jacob Visser
With the current version Prime95 does allocating the maximum amount of memory constitute the optimal setting ?
YES!

When reading about P-1 stage 2 memory allocations, it's sometimes important to distinguish between two different cases because the behavior differs between the two. But this is often difficult because most users aren't even aware that more than one case exists!

First case (the one to which most users, including wackeyh in your linked quote as far as I can tell, refer in their posts): the worktodo.ini line command is Test=nnnnnnnn... or Pfactor=nnnnnnnn...

In this case, prime95 calculates an optimum combination of B1 and B2 bounds, taking into account several factors including the Available Memory setting.

Example (where I'm guessing at roughly realistic values -- don't quote these as authoritative): For a given exponent such as 33500153, if Available Memory is the 8M default or other small value < 30M, prime95 may assign B1 = B2 = 505000, so that only Stage 1 is run. If Avail. Mem. = 60M, prime95 may decide on B1 = 380000, B2 = 9500000. For Avail. Mem. > 150M, prime95 may choose B1 = 325000, B2 = 21775000. The first choice (<30M) will take the shortest time, and has the smallest probability of finding a factor. The second choice (60M) will take longer, but has a noticeably higher chance of finding a factor. The third case (>150M) will take the longest time, but also has the highest chance of finding a factor.

Thus we can see why wackeyh writes that increasing the Available Memory will increase the time. What wackeyh leaves out, however, is that prime95 has calculated that the increased time is justified by the increased chance of finding a factor. (Perhaps wackeyh is even unaware that increasing the memory allows prime95 to have a greater chance of finding a factor in P-1.) My advice is to trust prime95's algorithm for choosing B1/B2 limits -- the more memory you give it, the better your result will be. Prime95's B1/B2 choosing algorithm takes more factors into account than you know of (unless you read the source code or my past posting where I list them :), and its choice will optimize GIMPS throughput!

Second case: The worktodo.ini command line is Pminus1=nnnnnnnn...

Here, the user explicitly specifies the B1 and B2 bounds. Then the only effect of the Available Memory figure is to limit the number of auxiliary work areas that prime95 can allocate during Stage 2 to speed up execution. Here, increasing Available Memory will decrease running time, the opposite of the effect it had in the first case! And if you give it a whole lot of memory (like a GB or more), it may even shift into a "higher gear" (The Brent-Suyama Extension) that increases its chance of finding a factor!

Last fiddled with by cheesehead on 2006-10-13 at 23:16
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