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Senior Member
Bounds
OK, I've been looking at the results.txt file and seeing what we can work out based on previous factors. It's a 3 or 4 week old results.txt file but it should show the general trend.
I've factored every p-1 in the results.txt factor file and computed B1 and B2 for these numbers. A quick summary is here:-
size=44 count=14199 avgB1=39831 avgB2=482409760958
size=45 count=55314 avgB1=53624 avgB2=692779684881
size=46 count=44620 avgB1=68881 avgB2=1391798543402
size=47 count=37615 avgB1=99281 avgB2=2525446194684
size=48 count=98548 avgB1=131137 avgB2=4993330745133
size=49 count=71495 avgB1=154455 avgB2=7787886979296
size=50+ count=833 avgB1=1731790 avgB2=1.05555454971016e+15
although it ignores any factors over 2^64
size is in bits
count is the number of factors of that size
avgB1 is the average B1 value
avgB2 is the average B2 value
The data for size=50+ will be skewed as many of those factors were found with p-1 factoring programs themselves!
The B2 value as presented in the output above is a bit useless so does anyone have any suggestions of graphs or other ways to show the data?
I was thinking along the lines of a table for each factor bit size (44, 45, 46, 47, 48, 49). Each row would represent a B1 value (1000, 2000, 5000, 10000, 20000, 40000, 50000, etc). Each column would represent a B2 value and the cell would show the percentage of factors would have been found with this combination. (Working on this at the moment).
I might also limit it on ranges of n too (i.e. 9M < n < 10M).
It's also available for download at (6.5MB):- http://www.greenbank.org/sob/factb1b2.txt.bz2
The format of the file is:-
<p-1>: <factors> : B1=x B2=y
I wouldn't mind getting my hands on the lowresults.txt file too, to have the data for < 44 bits. Infact, I'd like to get my hands on every factor found (i.e. factrange and factexcl included however I know these are not complete). Why?
Consider a k,n pair that we have found a low factor for (say 43 bits) however its p-1 is nowhere near smooth (B1=80000, B2=4000000000). Later on we find a much larger factor whose p-1 is smooth (say B1=1000 B2=20000), this will only be recorded in the factexcl files and not in results.txt.
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