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 2017-07-01, 04:45 #45 storflyt32   Feb 2013 6618 Posts Making a new one here. http://factordb.com/index.php?id=1100000000938270361 http://factordb.com/index.php?id=1100000000938278465 The C77, because it is still two factors, but next fully factored, I think was done on the server. The C195 at the other end next is having a quite good factor as well, namely a P49, which could be added. Still a C146 to go here though, so not yet finished here. A couple of other factors as well in my list, which could be added first. This when keying in n!-1 and n!+1 in the FDB, which is relating to that of Factorial numbers. Here a little bit in the dark on the subject, but both Factorial numbers and Primorial numbers are part of the Project Staging Area at PrimeGrid. The pocket calculator could be able to come up with 69! before unable to do any more, but next it becomes even at the end, before either subtracting or adding. As usual not all the odd numbers being returned are prime either, but for each of these types we apparently are having record primes. Perhaps a little more could be done with those numbers which are only composite or factors here, because finding anything larger could be a difficult thing. Another thing, I happened to be something funny before signing off yesterday. For that of Astronomy as a subject, we could be having the Arecibo message in our lists, or perhaps memory. And here about a message being broadcast from Earth towards a globular cluster and not something that was picked up. Making it a binary output or representation, it becomes some 23 lines and 79 columns of the whole message. I chose to remove or omit the starting 0's and next used copy and paste in order to copy part of the output to Notepad. Ending on a single line, with a couple of 1's in consecutive order at the end, the number, when being thought of as decimal such, is having factor P1 = 3 and the remaining number a rep-digit factor or prime, some 300 - 400 digits or so. Only to have it mentioned, because I am finishing off the rest of the beer right now, but could have it tomorrow. So, while still having fun, of course keying it wrong and it becomes a P59 at the end. http://factordb.com/index.php?id=1100000000938435249 http://factordb.com/index.php?id=1100000000938435263 P49 = 6384627520682549821072782803042294957487643979279 P59 = 24805184834556493674296971841383950146529962250161488466941 Both factors are known, but except for keying it wrong, also luck perhaps were striking back here as well. http://factordb.com/index.php?id=1100000000938509033 Also mentioning a possible overcommitment at other places, but here not difficult at all, when next excluding the P14. Total factoring time = 2938.1431 seconds Having the coffee and cake shortly before 11:30 AM in the morning, because I sat the night over, I keyed in both n!-1 and n!+1 in the FDB for their respective outputs. But if next doing the same related to the possible factorizations of RSA numbers, particularly those already known, my guess is that there is no similar syntax here. http://factordb.com/index.php?id=1100000000937794539 Continuing here right now, because it could be an adjacent run, or factorization corresponding to this number. Next needs checking, but as previously mentioned, got slightly overcommitted right now and experiencing a bit of difficulty. http://factordb.com/index.php?id=1100000000938599206 http://factordb.com/index.php?id=1100000000938599225 Making it a new session here as well, here became a triple pair or set of factors which were not that difficult. Total factoring time = 647.1420 seconds The first one becomes a loose pair of P40 and P54 factors from my list and if you wish, you may give it a try. Except for that, I could put these factors up here a bit later on. Also that when looking at the results, the P38 and P50 pair of factors is definitely a quite nice pair from its appearance. Also checking in with that funny looking C174, it now is at 600/7553 curves after finishing off both 2350 and 4480 curves first. Either it becomes a restart first, but for now ETA is listed as 375.71 hours here and perhaps or probably will not succeed. Now at 703/7553 curves and still running, ETA is now being given as 369.01 hours. Also giving a try on the C145 in the middle, but here it could take some 6 more hours. Last fiddled with by storflyt32 on 2018-07-26 at 22:58
 2017-07-07, 00:37 #46 storflyt32   Feb 2013 433 Posts http://factordb.com/index.php?id=1100000000939236158 I could end up repeating myself because of having an Edit box open and next adding contents where it already may have been posted. I will try to avoid it, but if so, I could edit it away later on if it happens. But here an example of something neither easy or directly hard, but rather something in between, at least when it comes to my own computer. I needed a break a short while ago and for now have not continued with the session, except for adding three more P100+ factors, without continuing from there. And also it mostly blew right now, because it became a restart of the computer which I tried to abort, but next it turned or shut off without warning. Back again after shuffling my equipment in the living room, because here it becomes a purchase of a second computer and also a quite powerful one. So rather I gave the following a thought. RSA-768 as you may know, is a 232 digit composite number having two P116 factors. If I was unable to use the hard switch or button on this number, we probably could be having the discussion about cracking of numbers, or the similar, where For now lacking the proper word or syntax which should be used here, but a similar discussion could be that of RSA numbers versus possible encryption, meaning cryptography. Again, I am not into that subject, but still give a thought of the way a given number is supposed to be "cracked". I prefer to make it that of numbers only, but still was able to come up with a name for such a number. Are we still assumed to believe that being able to factorize a RSA number means a possible method of elimination, in that between for example 0 or 1 as a starting point and the number itself, there could be numbers still left to factorize? http://factordb.com/index.php?id=1100000000942499068 http://factordb.com/index.php?id=1100000000942711949 Above is one such example currently being worked on. This pair becomes one of probably many such left before the factors are known for each and all. Therefore the assumption is that those still remaining makes for the number in question still not factored at all. Again that of the elimination method as mentioned above and next that of perhaps making a given or better guess, or perhaps assumption, before trying out anything else. Yafu, as you may know, includes the sqrt() function in order to make the square root of an integer number. Do it the opposite way and the result becomes undesired or not being wished for, in that two or more factors are being returned, rather than a single one. So, perhaps no point in that of addition or subtraction either, except for a couple of times. I mentioned at BOINC a while ago that the factorization of the number in question perhaps may not be possible and still this question could be an open one. Again, a couple of reasons for this being are being mentioned above. The fact is that with the computer at my disposal, I did not find any relationship between the mentioned RSA-768 and other numbers which could be present. Next I am not assuming or thinking that this in fact became loose numbers for which a documented method was being produced and distributed. http://factordb.com/index.php?id=1100000000943449750 http://factordb.com/index.php?id=1100000000943536563 Apparently closing in a bit here now and could take the product here for the contining process. Last fiddled with by storflyt32 on 2017-07-23 at 03:47
 2017-08-09, 05:49 #48 storflyt32   Feb 2013 1B116 Posts http://factordb.com/index.php?id=1100000000949341665 Here a nice one and this time by the server, because it is a difficult one. Adding a bit more later on. Like the following, which could be about the time it takes for a given factorization. http://factordb.com/index.php?id=1100000000954075995 Total factoring time = 17887.5671 seconds http://factordb.com/index.php?id=1100000000954236739 Total factoring time = 3656.9122 seconds The first one should be the longest here and should be added first above, but the similar factors makes for a bit of confusion. Working on it and when doing so and using cut and paste in order to get it fixed, the copied text being inserted makes the lines above (and not below this time) vanish, or disappear. Next entering a carriage return and it again vanishes at the top, which makes me think that the line width of the buffer (top to bottom) could perhaps benefit from having one more line being added. The second, or latter came in after the first one above and I did not think of any trial division before after a while, because it was in the middle of the day. Except for that, I let it run to finish and also took a while for the second one as well. Next it becomes a P131 twice, or in both results, adding to the confusion. One thing to notice is that the first one came from the P131 (1161777693...<131>) which was already known, but then only with small factors being added. So therefore the loopback at the P131 (1161...<131>) from the P131 of the first factorization (4772124691..<131>). Always the comment at the end. Last fiddled with by storflyt32 on 2017-08-11 at 02:55
 2017-08-19, 12:10 #50 storflyt32   Feb 2013 433 Posts http://factordb.com/index.php?id=1100000000956564228 http://factordb.com/index.php?id=1100000000956565023 Here a bit interesting, because I noted down the loose factors for the C116. The C189 on the other hand, has a P21, P34 and P135 as its three factors and next continuing on the C116, in order to get it right. Factors coming up shortly but also it should be a flip-around for the P135 as well, which should be different than the one previously mentioned. http://factordb.com/index.php?id=1100000000956576336 http://factordb.com/index.php?id=1100000000956014448 And next perhaps bit of a strange or goofy thing, because I went for the first of the last beers remaining in the fridge and will soon be off. Adding the P30 in the second link for possible completeness. Am I not wrong, but is not there such a thing as factor dependency, or perhaps interdependency when it comes to these numbers? Depending on both size of factors and also their relative difference within a factorization and also that there are many of them as well, how far are we still off when it comes to this? Is it possible to give an answer here? Suggestions welcome. The C189 is having a P42 and as thought, a bit more easy than the C107 which still has one hour or two left. This should be because of both the preceding factors, as well as the initial starting point, or reference on each side, which should differ for each such number. My guess is that it could be getting more difficult, because you are progressing in towards the center, but next a valid factorizaton of a C180 into two P90 factors could be yet another issue. Last fiddled with by storflyt32 on 2017-08-22 at 14:31
 2017-08-31, 09:13 #51 storflyt32   Feb 2013 433 Posts http://factordb.com/index.php?id=1100000000964713629 Adding here when on 32 bits, but perhaps not in correct order, because I had a break right now. Also a P147 in my list as well. http://factordb.com/index.php?id=1100000000964955877 Total factoring time = 4452.6960 seconds Initially a PRP99 before the final output, so no big secret here, because currently running on a 32 bits partition because of a software installation failure. A new computer being turned on today for the first time and doing quite well on the motherboard and graphics card, but for now unable to connect with a monitor because of a connector mismatch. Also two more disks lying on the shelf for possible use, so it bit of excitement around right now. I will be checking the two factors later on, but my guess is that we are closing in a little here. http://factordb.com/index.php?id=1100000000965087791 http://factordb.com/index.php?id=1100000000965089453 Here a quite good factor in the first link, considering the size of the whole number. Continuing, it becomes the same P17 in both, but need to do the shopping first and also that I am on a 32 bits partition for now. At least I know the name for this, namely semiprime and also its intended function or purpose. Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away. Right now experiencing a problem with that of editing, because having two or more different e-mail accounts, each lies in separate tabs and when next using Notepad as well, I am losing track of it despite a possible draft for some of these things, at least when it comes to that of e-mail. If this is because of a recent Windows update, it is not working very well with me and perhaps needs a closer look. The problem is that it is not worth wasting 300 KB of space here only for a given example, so here it becomes only a similar comparison for that of shorter, or "feasible" numbers. Two recent factorizations gave me a composite number when multiplying the two larger factors in each and next flipping around, it becomes a P149 factor. Not reported yet at all, but will be doing so coming up. Only goes or comes to show that perhaps cheating in such a way as mentioned above could also return possible results. The computer being turned on for the first time earlier today could perhaps be able to factorize one number which I think could be a RSA-512 number. Starting with the four digits 9712... from my recall, it could be more difficult than RSA-155, so here a quite good example. But first I will need a Windows installation or setup and for this I will probably go for Windows 10. Now I suddenly found the other tab for this and next it becomes something else. Doing a cut and paste below and will edit it later. Last fiddled with by storflyt32 on 2017-09-01 at 18:11
 2017-09-01, 18:11 #52 storflyt32   Feb 2013 433 Posts Next at least I know the name for this, namely semiprime and also its intended function or purpose. Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away and again you need to know the intended purpose or meaning, because "*" or "x" (small or large caps) is the multiplication symbol and "/" is the division symbol. Next perhaps needs the correct translation, because in my native language, it translates into divisor and dividend, respectively. https://en.wikipedia.org/wiki/Dividend https://en.wikipedia.org/wiki/Division_(mathematics) https://en.wikipedia.org/wiki/Divisor Notice the ambiguation here for the first term, but if I make it 1/7, here 1 should be the possible dividend by means of Mathematics and not any Finance, in the same way as 7 should be the divisor. Suggestions welcome, but will make a fix here. Becomes like that of div and mod for that of integer numbers ("%" when using Yafu) and now my edit disappeared, or vanished. And no need for any draft here since I am lucky to edit my own stuff. The reason for this is the mentioned semiprime or semiprimes and the possible need, or even lack of it becomes to that of possible cheating. If any such, I have never seen a discussion of this and next it should not be about the Scientific Method, or the Method of Proof here either for this. I will do the weekend shopping first, but it could next be split in two parts or halves here as well. I will keep the line above for now, but next did the shopping and are looking for the rest of it. More technically speaking, a RSA number is probably not having any syntax at all. Therefore one set for that of Mersenne prime numbers and also possible factors (2^61-1) and (2^89-1). Is it possible to value a prime number or factor against another when it comes to type, except for being perhaps Mersenne, Fermat, or possibly rep-digit? If I multiply all the Mersenne factors up to a reasonable size (Mersenne23 or less), I could get a decent composite number, but next I do not think that C46 = 1427247692705959880439315947500961989719490561 is such a RSA number either. http://factordb.com/index.php?id=1100000000193090724 This because if so, it has to be specifically designated as such and one reason is the possible bit length of the composite number. Press the More information button here and for the 4246 digit number in the middle, we have a quite good 4182 digit prime. The only reason you sometimes know for that or such for even larger numbers is because you choose to multiply those numbers. http://factordb.com/index.php?id=1100000000964936507 http://factordb.com/index.php?id=1100000000964928845 http://factordb.com/index.php?id=1100000000964928928 Here now three good examples for this, because I added one in the middle and next that these are not easy ones, at least not with 32 bits, running overnight using ecm and still not finished. You are welcome at giving a try, because here no problem with me. Next that this could become a double semiprime of sorts by means of multiplying, or product and could relate to an even bigger number with their respective factors the usual way. Because this is supposed to be about factoring, you also should know in which way it is supposed to be working. A good example is 2 versus 3, or 3 versus 5, because here it becomes either 0.66666...., or 1.66667 if I am not missing something. Next make it an integer number for at least the latter and add a million "6" digits before the final "7". Unable to do it right now, I sometimes am having fun when on a 64 bit partition and next I may possibly get access to another second one in spare. I will be counting my disks later on and will give you a rough number, but for now it became mostly Windows XP here, making for a big problem. Again no point of listing a million digits here, so rather about a given Methodology and this time for that of numbers and not necessarily any science. https://en.wikipedia.org/wiki/Methodology You perhaps know that I perhaps gave mentioning of that of numbers being "poor man's science". In order not to insult anyone, I will perhaps refrain from that, but rather there could still be a possible difference. Getting back at it when I have read the article. Because of the possible limits of factorization, I checked with the msieve application, which for now is a .zip file, but also 64 bits only. I will return back to this when the other computer is up and working. Only that a given C313 or C314 (needs checking) could be having a P156 and a P157 as its possible factors and here we are back to that above. But for now only being aware of the possible limits of factoring and not necessarily "as is" in one given way or another. Checking with the edit for this later on. Last fiddled with by storflyt32 on 2017-09-01 at 23:07
 2017-09-01, 18:55 #53 storflyt32   Feb 2013 1B116 Posts One thing of possible concern, or at least thinking about, is the possible "superhighway" of prime numbers which possibly could be there. Many numbers still remain to be factorized, like that of RSA-1024 and RSA-2048. Either they are at least semiprimes, or possibly RSA numbers, but if together with family of friends, it could end up being 2, 3, 5, 7 and so on and next not much more. The reason why at least RSA-256 is no problem today and RSA-512 could be factored at times, is no excuse for the fact that the number of possible factors in total could be very large. RSA-1024 is not possible to factor directly, so here another example. First of all, this has not been keyed in yet, so please if you could skip this for now, I would be very glad or happy, because this became a sequence and having it keyed in in a proper order, could make for both me and others feeling better. P40 = 1206141817390868369904697458937941898139 P89 = 15316861479442889529311995789441719383377177013171568971730011284995339928476982696581569 Becomes a C128 as the product here and probably possible to factor using msieve. Next try the C128 from RSA-1024 (the Magic Number) and you get the P149 with a little in between. http://factordb.com/index.php?query=%282%5E48853-1%29 My favorite above, except for perhaps the syntax, but should read (2^48853-1). Here the P1764 became my first better find or discovery and working hard here, it mostly sorted out. The remaining C12593 is a "beast" of a number and perhaps not doable at all, even with a new computer soon ready. My current record is not the P1764, however, but rather a PRP12576, which is a gigantic prime and also that there is a 17 digit difference from the C12593 above. I happen to know that the P1764 and PRP12576 are related with each other in one way or another, but which one, or how, I really do not know. Next that I also know that it does not divide the other way either, even when making the C48853 twice, or four times as large in size. You always make it 210 for that of 2 * 3 * 5 * 7, but next "what next" in such a sequence when a possible relationship between numbers is not directly available or present? I definitely know that regular sieving is one possible option or alternative for finding prime numbers, but perhaps not the perfect solution either, because a 321 number or Cullen/Woodall number always needs to be processed by means of LLR. My guess is that the P1764 and next the PRP12576 could theoretically be making the next number in the sequence a possible megaprime, but here I would like to ask for a possible way of getting at such a number. Because the PRP12576 is not readily available or in front of me (I could be checking in with BOINC for this), I do not have it right now. But only that I mentioned the fact earlier on my possible guess or suspicion that it could go straight up for some of the factors in a sequence and next I did not know the way in which to proceed. Last fiddled with by storflyt32 on 2017-10-15 at 14:19
 2017-10-15, 05:53 #54 storflyt32   Feb 2013 433 Posts Continuing on a Windows, 32 bit partition right now, because of a bit of problems being experienced. Also need ticking the stay logged in box here in order to keep the current session, so now this was done as well. http://factordb.com/index.php?id=1100000001053969348 http://factordb.com/index.php?id=1100000001053969978 P64 = 6521004766994961131998652758478623734567850934300959187999440927 P72 = 132630796754188196686159842513385353980595967923227514053572714567610003 Here both are end factors from two different factorizations, multiplied with each other. Not that unusual perhaps, but here both slightly easier and also slightly better as well. http://factordb.com/index.php?id=1100000001054063735 http://factordb.com/index.php?id=1100000001054062880 The second link above has a pair of P40 and P96 factors and next took some four hours on Windows, 32 bits. Initially a PRP96 here, except for perhaps the dinner in the meantime. The second was started only a couple of minutes before, so here no factors yet. Returning back to the desktop, apparently more easier here, because the word or phrase "either / or", could sometimes be part of Logic, but next also which one should come first, or be better. Also when editing that above, for some reason I had become logged out and therefore made it impossible to post. A little bit of unusual perhaps, but at least now I know when it happens. Here a pair of P26 and P129 factors, respectively and perhaps could be added first when having the early dinner put away. Also that here it took 3 minutes and 30 seconds only. But except for that, the first pair is a pretty good one here and I will have it in a short time. But rather becoming a bit confused that only a C99 makes for a bit of a show, or at least juggling, by walking through the complex process of echoing lines like "Bpoly 3484 of 4096: buffered 538 rels, checked 105253 (8.95 rels/sec)" to the screen in successive or repeating order. Taking a long time as well, here perhaps yet another example of factors which could be sometimes individually known, but when next multiplied, it makes for such complexity. Perhaps not directly stated, but we may eventually find ourselves in a situation where we need to know each small part or step of the whole road, leaving nothing in between, or left. If I ever asked myself what is on the "other side" of that of the Magic number (RSA-1024) and the larger cousin RSA-2048 and next the fact that it does not divide here, but only becomes smaller factors. So here not a good example at all, but also that a P153 was being found earlier today from doing it the opposite way, namely by means of multiplication and next the regular thing. http://mathforum.org/kb/message.jspa?messageID=7890114 Here a quite good example of such factorization which is next some 5 years old, but is perhaps known. Except for that, possibly will need to break off a little in order to not disappoint those in charge of running the projects under BOINC and their respective deadlines. Perhaps needs a bit more editing above, because it became a little bit of butter on bread here. Last fiddled with by storflyt32 on 2017-11-06 at 03:40

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