Current Factor Depth - Page 2

cheesehead · 2005-07-19, 19:35

Furthermore, the formula in my preceding post is for percentage complete in terms of number of factor candidates to be tried, not percentage of time required.

Here's an excerpt from a recent benchmark:

Code:

Best time for 58 bit trial factors: 9.173 ms.
Best time for 59 bit trial factors: 9.169 ms.
Best time for 60 bit trial factors: 9.168 ms.
Best time for 61 bit trial factors: 9.191 ms.
Best time for 62 bit trial factors: 12.579 ms.
Best time for 63 bit trial factors: 12.570 ms.
Best time for 64 bit trial factors: 14.762 ms.
Best time for 65 bit trial factors: 14.714 ms.
Best time for 66 bit trial factors: 14.654 ms.
Best time for 67 bit trial factors: 14.651 ms.

Note that higher factor candidates take longer to test when they pass certain levels. So, to get an estimate of percentage of time completed, you'd need to weight each bit level's relative number of candidate factors by the corresponding relative time per factor tested.

Also, different CPU models will have different relative trial factor times. The example quoted above was for a Pentium D 3.0GHz. For my old Athlon T-Bird 1.2 GHz it was:

Code:

Best time for 58 bit trial factors: 10.165 ms.
Best time for 59 bit trial factors: 10.155 ms.
Best time for 60 bit trial factors: 10.134 ms.
Best time for 61 bit trial factors: 10.156 ms.
Best time for 62 bit trial factors: 18.032 ms.
Best time for 63 bit trial factors: 18.074 ms.
Best time for 64 bit trial factors: 43.608 ms.
Best time for 65 bit trial factors: 44.544 ms.
Best time for 66 bit trial factors: 45.312 ms.
Best time for 67 bit trial factors: 45.577 ms.

So whereas the Pentium D took only about 60% longer to test a 64-bit factor than to test a 61-bit factor, my T-Bird took over 300% longer for the same comparison. (Both benchmarks here were with v24.13 Prime95.)

JHagerson · 2005-07-20, 02:02

Based on Cheesehead's formula for progress based on number of factor candidates to be tried, here is my analysis. The bottom line for those who choose not to download the file is that we have accomplished 0.55% of our goal.

JHagerson · 2005-07-20, 02:47

Well, well. Maybe I goofed again...

I tried to keep the calculations simple. I computed the quantity factor_depth - desired_factor_depth for each exponent, summed them up, divided by the count of factors, raised 2 to the power of that result and multiplied by 100 to provide a percentage. However, maybe I should have first computed 2 to the power of (factor_depth - desired_factor_depth) for each exponent, summed those up, divided by the count of factors and multiplied by 100 for a percentage.

Performing the calculation just on the 33 line using the first method gives a value of 60.90% while the second method gives 149.68%.

Stay tuned for another table.

JHagerson · 2005-07-20, 03:11

This one is a bit more encouraging. The bottom line on this one shows that we are 6.38% of the way toward our goal.

I have a math question regarding my two tables tonight. Could I have salvaged the first table if instead of dividing the sum of the deficits by the number of exponents, I would have taken the (number of exponents)th root of that sum? (Of course, the sum was negative so I would have to compute [the opposite of the root] of [the opposite of the sum] to get a meaningful number.)

Oh well. Thank you for allowing me to do this.

JHagerson · 2005-08-03, 03:43

Here is a report of my analysis of the current factoring information. I hope that you find this to be helpful. As before, 100% "complete" indicates that the exponent is factored to the depth specified for Prime95. If you have any questions, please post or PM me.

lycorn · 2005-08-03, 22:57

Good job, JHagerson

. It is very interesting to have a summary of the current bit depth for the different ranges. Just one suggestion: you could start at 25M instead of 30, so it would match the range reported in the "LMH Status" thread (25-79.3M).

JHagerson · 2005-08-04, 12:07

That's a good suggestion, Lycorn. I have all of that data. I'll plan to run the numbers this evening and post another version.

JHagerson · 2005-08-05, 01:35

Here is the updated table. We are making progress!

JHagerson · 2005-08-17, 02:47

Go Team!

lycorn · 2005-08-17, 08:55

The average bit level has just passed 62 bits!

JHagerson · 2005-09-05, 02:41

Here is the Factor Depth Summary through the 3-SEP-2005 data file.

2005-07-19, 19:35	#12
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	Furthermore, the formula in my preceding post is for percentage complete in terms of number of factor candidates to be tried, not percentage of time required. Here's an excerpt from a recent benchmark: Code: Best time for 58 bit trial factors: 9.173 ms. Best time for 59 bit trial factors: 9.169 ms. Best time for 60 bit trial factors: 9.168 ms. Best time for 61 bit trial factors: 9.191 ms. Best time for 62 bit trial factors: 12.579 ms. Best time for 63 bit trial factors: 12.570 ms. Best time for 64 bit trial factors: 14.762 ms. Best time for 65 bit trial factors: 14.714 ms. Best time for 66 bit trial factors: 14.654 ms. Best time for 67 bit trial factors: 14.651 ms. Note that higher factor candidates take longer to test when they pass certain levels. So, to get an estimate of percentage of *time* completed, you'd need to weight each bit level's relative number of candidate factors by the corresponding relative time per factor tested. Also, different CPU models will have different relative trial factor times. The example quoted above was for a Pentium D 3.0GHz. For my old Athlon T-Bird 1.2 GHz it was: Code: Best time for 58 bit trial factors: 10.165 ms. Best time for 59 bit trial factors: 10.155 ms. Best time for 60 bit trial factors: 10.134 ms. Best time for 61 bit trial factors: 10.156 ms. Best time for 62 bit trial factors: 18.032 ms. Best time for 63 bit trial factors: 18.074 ms. Best time for 64 bit trial factors: 43.608 ms. Best time for 65 bit trial factors: 44.544 ms. Best time for 66 bit trial factors: 45.312 ms. Best time for 67 bit trial factors: 45.577 ms. So whereas the Pentium D took only about 60% longer to test a 64-bit factor than to test a 61-bit factor, my T-Bird took over 300% longer for the same comparison. (Both benchmarks here were with v24.13 Prime95.) Last fiddled with by cheesehead on 2005-07-19 at 19:42

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2005-07-20, 02:47	#14
JHagerson May 2005 Naperville, IL, USA 2·107 Posts	Well, well. Maybe I goofed again... I tried to keep the calculations simple. I computed the quantity factor_depth - desired_factor_depth for each exponent, summed them up, divided by the count of factors, raised 2 to the power of that result and multiplied by 100 to provide a percentage. However, maybe I should have first computed 2 to the power of (factor_depth - desired_factor_depth) for each exponent, summed those up, divided by the count of factors and multiplied by 100 for a percentage. Performing the calculation just on the 33 line using the first method gives a value of 60.90% while the second method gives 149.68%. Stay tuned for another table.

2005-08-03, 22:57	#17
lycorn "GIMFS" Sep 2002 Oeiras, Portugal 1582₁₀ Posts	Good job, JHagerson . It is very interesting to have a summary of the current bit depth for the different ranges. Just one suggestion: you could start at 25M instead of 30, so it would match the range reported in the "LMH Status" thread (25-79.3M).

2005-08-04, 12:07	#18
JHagerson May 2005 Naperville, IL, USA 2×107 Posts	That's a good suggestion, Lycorn. I have all of that data. I'll plan to run the numbers this evening and post another version.

2005-08-17, 08:55	#21
lycorn "GIMFS" Sep 2002 Oeiras, Portugal 2·7·113 Posts	The average bit level has just passed 62 bits!