20080821, 11:09  #1 
1101011010010_{2} Posts 
list of untouched exponents
how to get the list of all untouched exponents?

20080821, 13:15  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2483_{16} Posts 
If you mean all that have had no testing on them, that list is infinite. The exponents are all prime numbers, of which there are infinitely many.
What area are you concerned with, 'low', those that have not yet been LL tested? Or higher, those that have had no trial factoring effort? 
20080822, 02:54  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Here's one way, though it's tedious:
Go to the Version 5 server (still in beta test) at http://v5www.mersenne.org/. Click on "Exponent Status" under the "Results Queries" heading in the leftside column (that takes you to http://v5www.mersenne.org/report_exponent/). There, you can get the current status (prime, factored, no factor below 2^xx, no factor to P1 limits, verified LLtested, unverified LLtested) of up to 100 candidates at a time, within a range you specify. (Currently, it won't report on exponents greater than 1,000,000,000.) Last fiddled with by cheesehead on 20080822 at 03:03 
20080822, 06:59  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×4,663 Posts 
Ostensibly (except for some legacy untouchable ranges where weird things happen sometimes), at this time, every exponent under 1,000,000,000 was touched.
(There were some untouched exponents even two monts ago. Then typical TF jobs were TF to 60 bits above 720,000,000; then 800,000,000+ then some lower ranges... But now the typical factoring jobs are TF from 60 to 64 bits in the 171,000,000+ range  http://v5www.mersenne.org/report_recent_cleared/ Apparenly, all was touched, otherwise server would have reassigned it to someone.) If you will find some, it will be interesting in some sense. 
20080822, 08:50  #5 
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}·3·5^{2} Posts 
If you look at Will Edgington's tables of factors, you'll see that the factors sequence grows for exponents well over 3 billions. I'm pretty sure Will did some factoring work (though at very low bit depth) on all of them.
Luigi 
20080822, 16:26  #6 
Nov 2003
1D24_{16} Posts 

20080822, 21:08  #7 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 

20080822, 22:00  #8  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
 For those new to the idea of trialfactoring Mersennes with larger exponents than the fewmillion we've been used to discussing: Note that TF up to 2^60 on an exponent around 999,000,000 is roughly a thousand times as fast than a TF to 2^60 on an exponent around 999,000. Why? Because the potential divisors are about a thousand times as far apart for the former than for the latter, as one can deduce from the 2kn+1 requirement, so there are only one onethousandth as many to test in the range of factor sizes up to 2^60. It's true that there's a logarithmic factor in individual trialdivision times, but that's much less significant than the linearwithexponent decrease in number of potential candidates to be tested. Last fiddled with by cheesehead on 20080822 at 22:04 

20080823, 05:24  #9 
Dec 2007
Cleves, Germany
2·5·53 Posts 

20080823, 07:01  #10 
Sep 2006
Brussels, Belgium
2·3·5^{2}·11 Posts 

20080823, 11:03  #11  
Einyen
Dec 2003
Denmark
7×433 Posts 
Quote:
Last fiddled with by ATH on 20080823 at 11:03 

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