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Old 2021-10-24, 23:43   #34
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Mar 2017
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Default Optimal prp proof power versus exponent

Re prime95 / mprime at least, assuming enough disk space is available, overall-compute-optimal (proof & server & cert total effort) proof powers are thought to be, based on information provided by George Woltman, for some version v30.x of mprime/prime95, perhaps v30.3:
Originally Posted by Prime95 View Post
1.7M - 6.7M = 7
6.7M - 26.6M = 8
26.6M - 106.5M = 9
106.5M - 414.2M = 10
414.2M+ = 11
Originally Posted by Prime95 View Post looks like the next transition will be near 1600M.
So power 10 is the best choice for first test wavefront through 100Mdigit and somewhat higher.

Originally Posted by kriesel View Post
Looks like about every 2 bits on fft length is +1 on proof power. So (extrapolating in Mlucas fft lengths) that would imply power 12 would be sufficient to ~6.2G, ~1.87 Gdigit, not something of concern for decades or centuries.
(See table at end of Mlucas source code file get_fft_radices.c)
Extrapolating higher, power 13 would cover optimal up to 414.2/106.5 * 6.2 G ~ 24. G, well past the maximum fft length 512 Mi of Mlucas v20.x which will support up to ~8.9 G exponent.

And extrapolating as needed to go lower, than prime95's commonb.c source code provides (power 5):
420K - 1.7M power 6
105K - 420K power 5
~26K - 105K power 4
~6.5K - 26K power 3
~1.6K - 6.5K power 2
~400 - 1.6K power 1

The crossover exponent values are somewhat dependent on program efficiency, so somewhat subject to change among mprime/prime95 versions, and across applications (gpuowl; eventually Mlucas).
Recent attempts to re-derive the proof power transition points for mprime/prime95 from program runs, source code examination, and cost function analysis have not duplicated the above, giving different results instead.

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Last fiddled with by kriesel on 2022-05-06 at 16:10 Reason: added dependency on program efficiency & rederivation
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