20140718, 07:55  #1 
"Adolf"
Nov 2013
South Africa
3E_{16} Posts 
Just curious
Just curious.
What is the highest an exponent has been TF'ed to? I saw some to 2^79. 
20140718, 08:06  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010110001000_{2} Posts 
M1267650600228229401496703205653 is tested to 100bits.
...And that's just by writing it out. No actual tests have been run, but it cannot have factors that are less than 100 bits in size. And M1606938044258990275541962092341162602522202993782792835301611 is tested to 200 bits. ;) 
20140718, 10:49  #3 
Romulan Interpreter
"name field"
Jun 2011
Thailand
23120_{8} Posts 
Actually that is wrong. The prime has 101 bits and it is 1 (mod 4), so the smallest factor can be 6 times higher. Therefore 103 bits. But 6p+1 and 8p+1 are composite (easy), so your number is tested to 104 bits...
[edit: the first candidate is q=2*52*p+1, which has 107 bits, didn't check if it is a factor] (gotcha!) Last fiddled with by LaurV on 20140718 at 10:56 
20140718, 10:56  #4  
"Tapio Rajala"
Feb 2010
Finland
3^{2}·5·7 Posts 
Quote:
Answering to the original question: M(2^{57885161} − 1) should give you a good record candidate then... 

20140718, 11:17  #5 
"Adolf"
Nov 2013
South Africa
2·31 Posts 
Maybe my curious question was not asked properly.
If one look up an exponent status in full detail, it will say, for example the prime exponent in the previous post, "no factor from 2^72 to 2^73". So my question was, what is the highest "from x to y" an exponent has been TF'ed. Because with a decent GPU I imagine it still took some time to do. 
20140718, 11:57  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,301 Posts 
I would imagine MM127 would be a contender for the distinction of having the most TF trial division operations.

20140718, 12:06  #7  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AD_{16} Posts 
Quote:
Last fiddled with by MiniGeek on 20140718 at 12:07 

20140718, 12:06  #8 
"Brian"
Jul 2007
The Netherlands
2×3×5×109 Posts 
They're trying to tell you that your question makes no sense. By choosing a sufficiently large Mersenne number, you can arbitrarily raise the number of bits its smallest factor can possibly have.
Then, if anyone wishes to do so, they can easily do a bit of TFing on that number from that arbitrarily high bitlevel and pronounce that it has been "TF'ed" to 100 bits, 1000 bits, you name it. 
20140718, 12:32  #9 
"Adolf"
Nov 2013
South Africa
3E_{16} Posts 
Ouch! Getting slammed here.
But I will try again. Eventually someone will either understand what I'm asking, or I might eventually ask the right question. I'm not including MM exponents. I think MiniGeek put my question the best: What Mersenne number within some range p_min <= p <= p_max has been searched to the highest bit level? If you look at 700,001,011, it says no factor below 2^80. Has there been other exponents that has been TF'ed higher than 80?That is all I want to know. 
20140718, 12:39  #10  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·7·13·37 Posts 
Quote:
Quote:
Last fiddled with by Uncwilly on 20140718 at 12:48 

20140718, 12:48  #11 
"Adolf"
Nov 2013
South Africa
2·31 Posts 
Thank you Uncwilly!
That is all I wanted to find out. Even with a good GPU that still would have taken many days to complete. 
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