20091022, 15:21  #1 
Dec 2008
Boycotting the Soapbox
2^{4}×3^{2}×5 Posts 
Trial factoring benchmark interpretation
http://www.mersenne.org/report_bench...Get+Benchmarks
How do I interpret the value in the last column? Doesn't it matter how many bits 2^N1 has? Does it describe the time taken to check whether 2^N1 is divisible by all possible factors with less than 65 bits? If it describes the average time taken to check whether 2^N1 is divisible by a 65 bit number, wouldn't this be very slow, since we're only checking about 10 million factors per day? Because, if one multiplies ~500.000 factors with divideandconquer, then computes the remainders with divideandconquer (using Newton's method and fast multiplication for the division), then one could check 10 million factors for a 33 million bit Mersenne number in a couple of minutes. 
20091022, 20:32  #2 
P90 years forever!
Aug 2002
Yeehaw, FL
2·3,701 Posts 
I'd have to check the code to answer your question exactly.
It is something like the time it takes to trial factor M35000001 with all possible factors in a 12KB sieve. A 12KB sieve = 96K bits. The small factors sieve would eliminate a large percentage (maybe 7590% ?). So the benchmark times ~1015 thousand trial factoring attempts? Maybe someone can look at the code and give you a more accurate answer. 
20091022, 21:09  #3 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
http://mersennearies.sili.net/throughput.php contains some reverseengineered estimates for the number of iterations used for various TF bit levels. (i.e. (the timing listed for bit level 65) * (iterations for bit level 65) = (total time for bit level 65))

20091022, 21:50  #4  
Dec 2008
Boycotting the Soapbox
2D0_{16} Posts 
Quote:
If we assume that we can do a multiply in 1.5x3x the time for an LLiteration, the division/mod is 2x3x multiplies, then for ~600.000 possible factors with 64bits, the runtime for the method that wouldn't assume any special form would be something around 15x30x an LLiteration for M35000001, which is slower (but in the same ballpark). Quote:


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