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 2014-07-18, 07:55 #1 houding     "Adolf" Nov 2013 South Africa 3E16 Posts Just curious Just curious. What is the highest an exponent has been TF'ed to? I saw some to 2^79.
 2014-07-18, 08:06 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100101100010002 Posts M1267650600228229401496703205653 is tested to 100-bits. ...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. ;-)
2014-07-18, 10:49   #3
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

231208 Posts

Quote:
 Originally Posted by Batalov M1267650600228229401496703205653 is tested to 100-bits.
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 2014-07-18 at 10:56

2014-07-18, 10:56   #4
rajula

"Tapio Rajala"
Feb 2010
Finland

32·5·7 Posts

Quote:
 Originally Posted by LaurV 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 is not prime, so your number is tested to 103 bits... (waited so long to catch you! :P)
Actually, it was right. Being tested to n bits it surely was tested to n-1 bits.

Answering to the original question: M(257885161 − 1) should give you a good record candidate then...

 2014-07-18, 11:17 #5 houding     "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.
 2014-07-18, 11:57 #6 retina 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.
2014-07-18, 12:06   #7
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

Quote:
 Originally Posted by houding 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.
Your question (as written) is nonsensical, since "x to y" (with p, or its range, unspecified) is not a way to measure work. For any y, you can trivially find a number that is known to be factored from 0 to y just by its very nature...that is, without doing any TF work at all. This comes from the fact that all factors of Mersenne numbers are of the form 2kp+1 for some natural number k. This gives a minimum factor size of 2p+1, or log_2(p)+1 bits. Here are some similar questions that are valid (though I don't know the answers to them):
• What Mersenne number within some range p_min <= p <= p_max has been searched to the highest bit level?
• What Mersenne number has had the most TF work (in time on a reference CPU or GPU) done on it?
• What Mersenne number has had the most non-trivial bit levels TFd?
• What Mersenne number has had the most k's searched?
MM127 and the other status-unknown double Mersennes would surely be near or at the top of some of these lists.

Last fiddled with by Mini-Geek on 2014-07-18 at 12:07

2014-07-18, 12:06   #8
Brian-E

"Brian"
Jul 2007
The Netherlands

2×3×5×109 Posts

Quote:
 Originally Posted by houding Maybe my curious question was not asked properly.
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 TF-ing on that number from that arbitrarily high bit-level and pronounce that it has been "TF'ed" to 100 bits, 1000 bits, you name it.

 2014-07-18, 12:32 #9 houding     "Adolf" Nov 2013 South Africa 3E16 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 Mini-Geek 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.
2014-07-18, 12:39   #10
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

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Quote:
 Originally Posted by houding Has there been other exponents that has been TF'ed higher than 80?That is all I want to know.
332250257 has been tested to 85 bits. That is 11,792 GHz-days for the effort from 84->85.
Quote:
 Originally Posted by Mini-Geek MM127 and the other status-unknown double Mersennes would surely be near or at the top of some of these lists.
MM127 is at 178 bits

Last fiddled with by Uncwilly on 2014-07-18 at 12:48

 2014-07-18, 12:48 #11 houding     "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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