Here's some LLR data that would help you guys to scroll [URL="http://www.doublemersennes.org/sieving/validi.php"]some of these columns[/URL] a screenful down (first four columns for p<3,030,000)

P.S. Because I actually ran (some months ago) a lot of ad hoc tests on smaller MMp (and I also have the divisibility test binary built from a modified Prime95), I know that the most optimal representation for a candidate factor appears to be
k*2[SUP]p+1[/SUP]-(2k-1), or in (k,b,n,c) form: k,2,p+1,-(2k-1) (for P95's worktodo.txt or for an LLR input file). I.e. extra two goes into the exponent, to keep "k" low.

P.P.S. I wanted to mention this before but didn't. Here it goes now:
It is easy to demonstrate that if a 2kM[SUB]p[/SUB]+1 is a factor of MM[SUB]p[/SUB] (with conventional, i.e. rather small, values of k), then it doesn't need a proof of primality - it has no room to have smaller factors of 2k[SUB]1[/SUB]M[SUB]p[/SUB]+1 form => it is prime. The converse, of course, is not true; rather we'd expect to need to collect a lot of primes of form 2kM[SUB]p[/SUB]+1 to finally hit a divider of MM[SUB]p[/SUB].

[QUOTE=aketilander;351720]Excellent Batalov, I had not seen that! Thank you!

Luigi, if we get the permission, it may be nice including this information at the Double Mersenne page also?[/QUOTE]

I will ask Will about it, but I can't promise to update immediately after: I'm losing my "real-life"[sup]TM[/sup] job and am quite nervous about it.

Luigi

[QUOTE=Batalov;351768]P.S. Because I actually ran (some months ago) a lot of ad hoc tests on smaller MMp (and I also have the divisibility test binary built from a modified Prime95), I know that the most optimal representation for a candidate factor appears to be
k*2[SUP]p+1[/SUP]-(2k-1), or in (k,b,n,c) form: k,2,p+1,-(2k-1) (for P95's worktodo.txt or for an LLR input file). I.e. extra two goes into the exponent, to keep "k" low.

P.P.S. I wanted to mention this before but didn't. Here it goes now:
It is easy to demonstrate that if a 2kM[SUB]p[/SUB]+1 is a factor of MM[SUB]p[/SUB] (with conventional, i.e. rather small, values of k), then it doesn't need a proof of primality - it has no room to have smaller factors of 2k[SUB]1[/SUB]M[SUB]p[/SUB]+1 form => it is prime. The converse, of course, is not true; rather we'd expect to need to collect a lot of primes of form 2kM[SUB]p[/SUB]+1 to finally hit a divider of MM[SUB]p[/SUB].[/QUOTE]

Thank you Serge, I will update the table later today. :bow:

Luigi

[QUOTE=ET_;351836]I'm losing my "real-life"[sup]TM[/sup] job and am quite nervous about it.[/QUOTE]

I am sorry to hear that! I hope everything will be OK.

[QUOTE=ET_;351836] I'm losing my "real-life"[sup]TM[/sup] job and am quite nervous about it.
[/QUOTE]
Don't be. We use to say: Every kick in the butt means a step ahead. You will find better, I am sure.

[QUOTE=ET_;351719]Please send me your results with a couple of lines that explain what to update,[/QUOTE]
Ok, I checked all the log files I have, and updated this (very old!) table, here and there. Only the third sheet is updated, and from it, only the columns G, H are important. That is for your history page. The values in the blue rows were all tested from scratch (i.e. double-checking the already-known results) and few of them were extended to higher limits. The pink lines were already too high to be tested from scratch and therefore I only re-tested a bit of the "tail" (for example, only the last 156M were tested for MM#13, as explained in the yellow cells).

There are some question marks for MM#29-MM#31 (in columns H-I), that is because the values were written in the table, but I did not find any log file with the "extensions". I will re-check them anyhow.

Also, for MM#34, at the time when I did the tests, k=91 was last tested, and I checked 92 and 93, they did not divide, so the next k would be 112 (see a former post in this thread) but when I checked your tables today, MM#34 (same as #35-#38) seems to be bloody-much advanced.

[QUOTE=aketilander;351865]I am sorry to hear that! I hope everything will be OK.[/QUOTE]
Ditto

If I want to TF one specific MMp with one specific possible factor 2*k*Mp+1 which program is best to use? (I am now thinking of medium to large sized MMp:s).

[QUOTE=aketilander;351987]If I want to TF one specific MMp with one specific possible factor 2*k*Mp+1 which program is best to use? (I am now thinking of medium to large sized MMp:s).[/QUOTE]

See post #122 - #131 in this thread.

[QUOTE=LaurV;351915]Ok, I checked all the log files I have, and updated this (very old!) table, here and there. Only the third sheet is updated, and from it, only the columns G, H are important. That is for your history page. The values in the blue rows were all tested from scratch (i.e. double-checking the already-known results) and few of them were extended to higher limits. The pink lines were already too high to be tested from scratch and therefore I only re-tested a bit of the "tail" (for example, only the last 156M were tested for MM#13, as explained in the yellow cells).

There are some question marks for MM#29-MM#31 (in columns H-I), that is because the values were written in the table, but I did not find any log file with the "extensions". I will re-check them anyhow.

Also, for MM#34, at the time when I did the tests, k=91 was last tested, and I checked 92 and 93, they did not divide, so the next k would be 112 (see a former post in this thread) but when I checked your tables today, MM#34 (same as #35-#38) seems to be bloody-much advanced.[/QUOTE]

Thank you for the updates, LaurV! :bow:

I am going to ask Tony Forbes if there are news in the ranges he is working on, update the table on Doublemersennes, and finaally apply your updates.

I am also asking Will Edgington about his databases, waiting for a reply.

Before any modificaton is shown, I'd like that no one steps over pre-owned ranges.

Thanks to everyone for the infos! :bow:

Luigi