20160304, 04:09  #1 
Bemusing Prompter
"Danny"
Dec 2002
California
4407_{8} Posts 
discrepancy in credit calculator for LL tests?
It is my understanding that double an exponent results in an LL test taking approximately four times longer.
From the CPU credit calculator, the 49th known Mersenne prime, M74,207,281, takes around 205 GHzdays. The first Mersenne number of prime index with 100 million digits, M332,192,831, needs around 4,941 GHzdays. This also seems reasonable. M601,248,421, the largest Mersenne number with an LL test to date, requires about 16,584 GHzdays, which closely matches the credit that Never Odd or Even received. However, the numbers become weird after that: the calculator says the first Mersenne number with more than a billion digits, M3,321,928,097, requires just 91,630 GHzdays. The actual value should also be much higher; (3,321,928,097 / 601,248,421)^{2} ≈ 30.5, and multiplying that by 16,584 gives over 500,000 GHzdays. So does the time complexity for LL tests stop exhibiting quadratic growth after a certain point? Or is there an error in the calculator? Last fiddled with by ixfd64 on 20160304 at 04:16 
20160304, 04:25  #2 
"David"
Jul 2015
Ohio
11·47 Posts 
The calculation is based on a timing chart for a hard coded list of FFT sizes matched to exponent ranges. For numbers outside of the maximum measured FFT size the credit value is just an extrapolated point from the largest FFT size.
http://www.mersenne.ca/credit.php?showsource=1 From a quick glance,the largest FFT size is 33.5M or so and credit is computed linearly for larger exponents than 596M Last fiddled with by airsquirrels on 20160304 at 04:29 
20160304, 05:43  #3 
Jun 2003
4,723 Posts 
James should modify the calculator to give an error message for outofrange exponents rather than give out some made up crap. Or try to do a realistic projection.

20190813, 20:11  #4  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
4,643 Posts 
Quote:
Empirical run time scaling for LL, PRP, or P1 are around p^{2.1}. Any fixed overhead appears to lower the power on the scaling and have greater effect in lowering the scaling power at small p. prime95 PRP https://www.mersenneforum.org/showpo...78&postcount=2 prime95 P1 https://www.mersenneforum.org/showpo...92&postcount=3 CUDALucas LL https://www.mersenneforum.org/showpo...23&postcount=2 CUDAPm1 P1 https://www.mersenneforum.org/showpo...27&postcount=2 Last fiddled with by kriesel on 20190813 at 20:12 

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