20120911, 16:58  #1 
"James Heinrich"
May 2004
exNorthern Ontario
6147_{8} Posts 
Known factors distribution graphs
I've now got some graphs depicting the distribution of both quantity and size of known factors, as well as TF level for exponents with no known factors:
up to 192M: http://mersenne.ca/graphs/factor_bits_100M/ up to 4294M: http://mersenne.ca/graphs/factor_bits/ The smaller graph is focused on the most active range, and each column represents 100k range of exponents. The larger graph covers the entire range up to M2^{32} in my database, and each column represents 1M exponent range. Gray background is total exponents in that range (the part you can see represents exponents with no known factor). Coloured parts of the graph represent known factors: overall height of the coloured portion (relative to the gray portion) is the number of exponents with known factors. Colours vary according to the distribution of size of known factors (per the legend), scaled such that the overall height of the coloured portion matches the total number of factored exponents. This can get a little weird if more than one factor is known per exponent, especially across larger ranges, for example between 122M and 133M someone has spent considerable time making sure everything is TF'd to the full level, not stopping after finding the first factor as is normally done (at least with Prime95). Light red line represents default TF level that Prime95 would take the exponent to; light blue line is this plus 3 bit levels, approximating what level GPU72 would TF the exponent to. The black line represents average TF level for exponents in the range with no known factor. 
20120911, 17:08  #2 
If I May
"Chris Halsall"
Sep 2002
Barbados
10010001100101_{2} Posts 

20120911, 18:27  #3 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·2,399 Posts 

20120911, 20:12  #4  
"James Heinrich"
May 2004
exNorthern Ontario
110001100111_{2} Posts 
Quote:
Well, as close as I can approximate it, anyways. Going on a few assumptions:


20120911, 20:36  #5 
If I May
"Chris Halsall"
Sep 2002
Barbados
7×11^{3} Posts 

20120911, 22:49  #6 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·599 Posts 
All of them. as well as a bunch of banana peels in my local landfill^{*}. :)
   ^{*} Landfill is tapped to gather methane gas which is then used to generate electricity. Last fiddled with by cheesehead on 20120911 at 22:50 
20120911, 23:25  #7 
"James Heinrich"
May 2004
exNorthern Ontario
110001100111_{2} Posts 
Around here: none. All our power comes from hydroelectric, wind and solar.

20120911, 23:36  #8  
If I May
"Chris Halsall"
Sep 2002
Barbados
7×11^{3} Posts 
Quote:
Here in Barbados we're not so smart... we burn diesel for all of our electricity. Which is pretty stupid considering we get approximately 12 hours of sunshine year round. Plus, a heavy draw is air conditioning, which is mostly used during the day.... 

20120911, 23:54  #9 
"James Heinrich"
May 2004
exNorthern Ontario
5^{2}×127 Posts 
It's only in the remote snowy places that we use solar. So that you have to go out and shovel the panel at 10am sunrise to get power to your block heater
In densely populated places, naturally, we use better things. Like nuclear. 
20121206, 13:29  #10 
"Victor de Hollander"
Aug 2011
the Netherlands
2·587 Posts 
What is causing the "weird" lines between 20M40M and 120M135M ? Were these parts poorly TFed to 2^50 or something?

20121206, 13:59  #11  
"James Heinrich"
May 2004
exNorthern Ontario
5^{2}·127 Posts 
Quote:
If I had to offer a theory, I'd say that most of the PrimeNet range has had factoring done and stopped upon finding the first factor, but in those ranges I'd speculate that someone has done TF to (2^66?) but not stopped after finding the first smaller factor. So you end up with proportionately more factors in the 2^552^66 range that wouldn't have been found if TF was stopped as soon as the first factor was found. That's my theory anyways, competing theories are welcome. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Progress graphs  fivemack  NFS@Home  3  20160506 22:09 
Distribution of Mersenne Factors  tapion64  Miscellaneous Math  21  20140418 21:02 
strange factors distribution??  pegaso56  Information & Answers  19  20090629 15:04 
Distribution of Mersenne prime factors mod 6  alpertron  Math  0  20060623 20:07 
Silverman & Wagstaff on Joint Distribution of Ultimate and Penultimate Prime Factors  wblipp  Math  12  20060402 18:40 