[QUOTE=axn;379483]I don't see how the last 64 bits help.

Lets say F divides Mp. By Fermat, 3^(Mp/F) = 3 (mod (Mp/F)). Raising both sides to F, we get 3^Mp = 3^F (mod Mp/F). Now if we have the full residue 3^Mp (mod Mp), we can easily calculate 3^Mp (mod Mp/F). But last 64-bits? Are you saying 3^Mp = 3^F (mod Mp/F) ==> 3^Mp = 3^F (mod Mp). I just tried it with M2311 (77567729423209*4514379640917651135021865565129IPRP-652). LHS holds, but RHS doesn't.[/QUOTE]
I now had some spare time to check if the low bits help and indeed they don't* and I didn't find a trick to make them useful (I was thinking that we could bit-rotate the residue, but we can only do that mod M[SUB]p[/SUB], not mod M[SUB]p[/SUB]/F).

The top 512bits, as P.L.M. wrote, work, but one needs a modification to the program, to save those 512-bit residues in a file and later fetch and use them. EWMayer wrote [URL="http://mersenneforum.org/showpost.php?p=342776&postcount=15"]some code like that[/URL]. If I were to implement this, I could write a patch to prime95 (I've written and used small other ad hoc hacks; it is doable).

____
*I [STRIKE]remembered[/STRIKE] was misled into thinking about this possibility by my anecdotal experience with tiny factors, like 5 for some [TEX]2^p \pm 2^{{p+1}\over{2}}+1[/TEX] and 7 for some [TEX]3^p \pm 3^{{p+1}\over{2}}+1[/TEX]. They show up as prpbase^4 and prpbase^6 in the RES64, but this is a pure coincidence: e.g.
[FONT="Fixedsys"]2^1223+2^612+1 is composite: RES64: [0000000000000051] (0.0041s+0.0008s)[/FONT] (where 51[SUB]16[/SUB] = 81 = 3^4)
They are, of course, special for that form.
This small curio does not extend itself to even slightly larger factors, let alone 80-90+ bit factors that are relevant for the OP PRP project.

[QUOTE=R.D. Silverman;379861]Wrong again. Check with David Slowinski.

A long time prior to GIMPS (early 80's), I provided David with a
moderately large list of exponents that did not need to be factored because I
had found small divisors.[/QUOTE]

OK, my fault. I didn't know that. But this is not related to the second category I mentioned before, but more with KWh spent on calculations.

[QUOTE=Batalov;379859]The posts that were less than useful to this thread are now moved to the [URL="http://mersenneforum.org/showthread.php?goto=newpost&t=12945"]eponymous thread[/URL].[/QUOTE]

[URL="http://dictionary.reference.com/browse/eponymous?s=t"][URL="http://dictionary.reference.com/browse/eponymous?s=t"]eponymous[/URL][/URL] - nice word, completely wrongly used.

Nice to see the forum police out and about.

[QUOTE=Batalov;379859]The posts that were less than useful to this thread are now moved to the [URL="http://mersenneforum.org/showthread.php?goto=newpost&t=12945"]eponymous thread[/URL].[/QUOTE]

Which was actually everything from about post 155 onwards, if you want to set yourself as the forum police then at least be consistent :bow:

[QUOTE=alpertron;379831]Using the formulas above I computed the expected numbers of PRP to be found in different ranges. Notice that most Mersenne numbers are not factored up to these bounds because the factorization stopped when the first prime factor was found.

[CODE]
Range Known PRPs 25 digits 30 digits 35 digits
------------------------------------------------------------
1K-2K 45 14 17 20
2K-5K 26 17 20 24
5K-10K 16 12 14 16
10K-20K 10 11 13 15
20K-50K 8 13 16 18
50K-100K 7 9 11 13
100K-200K 5 9 10 12
200K-500K 5 11 13 15
500K-1M 3 8 9 11
1M-2M 3 7 9 10
2M-3M 0 4 5 6
3M-4M 0 3 3 4
4M-5M 0 2 3 3
5M-10M 0 7 8 9
[/CODE][/QUOTE]
I am not convinced by some of those numbers. 10k-20k has had complete 40 digit ecm run but is low. 20k-50k has had 35 digit and some 40 digit but is lower than your estimate for 25 digit. I realize ecm doesn't find 100% of factors upto the ecm limit but those numbers seem a little odd.

[QUOTE=Gordon;379872]Which was actually everything from about post 155 onwards, if you want to set yourself as the forum police then at least be consistent :bow:[/QUOTE]
[I]Genial[/I]!! :big grin:

Thank you for you vital grammatical correction. I've adjusted the above message, perhaps more to your liking. It must be grammatically correct now, because it is grammatically correct. (From the Department of Redundancy Department.)

Now, here's why messages from about post 155 onwards are not moved. Some (not all of them) were useless. Humor, wordplay, flirtations are fine - especially, in a thread that started to devolve into a philosophical/philological debate veering into Clintonesque defenses based on a convenient redefinition of the meaning of the word "is" (or "sex", or "probable", or whatever).

But that thread is for messages that are [B]less[/B] than useful: mud fight, name-calling, non-sequiturs, bragging, and such. Into the "less than useful" thread such messages go, regardless of the size of the brain of whoever throws :poop: in the fan.

Also, in my humble opinion, [SPOILER]Rules of MENSA:
1st RULE: You do not talk about MENSA. 2nd RULE: You DO NOT talk about MENSA. 3rd RULE: If someone says “stop” or goes limp, taps out of a fight, pay attention, they are most likely in MENSA and way more intelligent than you! (c)[/SPOILER]

:goodposting::batalov:

[QUOTE=henryzz;379883]I am not convinced by some of those numbers. 10k-20k has had complete 40 digit ecm run but is low. 20k-50k has had 35 digit and some 40 digit but is lower than your estimate for 25 digit. I realize ecm doesn't find 100% of factors upto the ecm limit but those numbers seem a little odd.[/QUOTE]
The problem in your reasoning is that the 40-digit level is only complete in the cases that no factors were found. According to [URL="http://www.mersenne.org/report_ecm/default.php?txt=0&ecm_lo=10000&ecm_hi=20000&ecmnof_lo=10000&ecmnof_hi=20000"]the official report[/URL], the 35-digit level is complete up to 11.5K, and the 30-digit level is (almost) complete up to 16K. The other numbers are in the range 25 to 30 digits. So I think the estimate for 10K to 20K is OK for me. Notice that completing the n-digit level means that about 30% of the prime factors with that number of digits were not found because of the statistical nature of ECM.

In the range 20K to 50K only the 25-digit level was completed according to [URL="http://www.mersenne.org/report_ecm/default.php?txt=0&ecm_lo=20000&ecm_hi=50000&ecmnof_lo=20000&ecmnof_hi=50000"]this report[/URL].

[QUOTE=alpertron;379921]The problem in your reasoning is that the 40-digit level is only complete in the cases that no factors were found. According to [URL="http://www.mersenne.org/report_ecm/default.php?txt=0&ecm_lo=10000&ecm_hi=20000&ecmnof_lo=10000&ecmnof_hi=20000"]the official report[/URL], the 35-digit level is complete up to 11.5K, and the 30-digit level is (almost) complete up to 16K. The other numbers are in the range 25 to 30 digits. So I think the estimate for 10K to 20K is OK for me. Notice that completing the n-digit level means that about 30% of the prime factors with that number of digits were not found because of the statistical nature of ECM.

In the range 20K to 50K only the 25-digit level was completed according to [URL="http://www.mersenne.org/report_ecm/default.php?txt=0&ecm_lo=20000&ecm_hi=50000&ecmnof_lo=20000&ecmnof_hi=50000"]this report[/URL].[/QUOTE]
Good point. Sorry for the mistake.

[QUOTE=Batalov;379888][I]Genial[/I]!! :big grin:[/QUOTE]

I must bow to your far superior knowledge of the nuances of the English language

[QUOTE=Batalov;379888]Now, here's why messages from about post 155 onwards are not moved. Some (not all of them) were useless. Humor, wordplay, flirtations are fine - especially, in a thread that started to devolve into a philosophical/philological debate veering into Clintonesque defenses based on a convenient redefinition of the meaning of the word "is" (or "sex", or "probable", or whatever). [/QUOTE]

But by your reasoning anything that adds nothing to the discussion must be considered less than useful, so you fail again.

You see when you decide to set yourself up as the arbiter of what does and doesn't add value, don't be surprised that when you act inconsistently based on your prejudices that the thread holding up the Sword of Damocles is cut.

Or you could simply in future decide not to act like the thinkpol.

You are kidding yourself if you think that moderation is a police work. It is mostly waste disposal. If you always wanted to apply but were too shy to ask about it, don't be, write to Mike. Waste has to be disposed of. Spam and lunacy, too. Nonsense can stay.

The sewer thread for the waste was not always called what it is called now. It used to bear names of those prolific individuals who made most contributions. Its current name is a bit too kind (you can thank Mike). It is for posts with negative usefulness, if you insist on a better definition. "Less than useful" - not quite the same, I agree.

Some posts are deleted altogether, if this is news to you (e.g. commercial spam). Require the proverbial "CODE OF CONDUCT" if you absolutely demand to know what particular flavor of 1984 is implemented on this forum.