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 2017-04-21, 01:52 #34 storflyt32   Feb 2013 6538 Posts Anyway, adding a P125 to my list now, together with a P15, I have not checked yet. But also being reminded that unlike the highest point or mountain of my own country, Matterhorn as a mountain is a steep cliff and therefore inaccessible, or not climbable, on both or all sides. Here I was giving that of infinity a thought and also a possible approach when it comes to this subject, at least by means of being a possible number. In the world of Project Management, like a couple of other places, you could be setting possible goals for that of a possible achievement. Meaning that possibly one third of a vertical wall or climb for a mountain could be climbed or ascended in one piece or portion. Such a thing is not available or present when it comes to that of infinity, or even RSA-1024, for that matter. Yes, we call such things "checkpoints" when it comes to that of computing and also such a thing is having a specific or given name when it comes to that of Project Management as well. For perhaps one thing it could be "Mission impossible" when it comes to a given thing, but does that mean Project Management, or possibly goals? "We choose to be going to the Moon..." and so on. Everyone knows that a prime number, or factor like 2^127-1 does not come from either 2, or 10, for that matter. So, which end, if I may ask. The fact is that except for 1, which is either "dubious", or no prime number at all, every or all other numbers could be regarded or viewed as composite for a simple reason. Should it be 2 * 3 * 5 * 7, or perhaps 2 * 3 * 5 * 7 * 11 and so on, only because of the 2? Or is there rather another or different reason for this happening, or being the case? This because you are not supposed to neither factorize, or even be sieving, except for LLR, when it comes to numbers like 100 or 200 for this and this should be quite obvious. The only thing in the end is that you could determine a number to be at least composite, but without knowing the factors, making up such a number. Back tomorrow. Should tell that in the early morning I forgot keying in the whole number using the factorization software and it became a P154 back in return the opposite way. When next using the correct number by adding some nine digits on the second line, it also became a smaller factor, but here it was more difficult. Except for that, the cup of coffee does not help today and I only have for one more over the weekend. Also both a P20 and P30 together with a P108 and I will continue on this now. Last fiddled with by storflyt32 on 2017-04-22 at 15:52
 2017-04-22, 19:52 #35 storflyt32   Feb 2013 7×61 Posts Here is a slightly bad example, but apparently with a happy end. http://factordb.com/index.php?id=1100000000922558273 http://factordb.com/index.php?id=1100000000922558301 Adding a C63 for the P24 and P39 in the first pair, the rest is a P76. Next flipping around the opposite way and at least one of the P21 factors was added. Thinking a little more, it already knew about the smaller P21, but not the P16. The larger of the two P21 factors became part of the final factorization. But for the first part of at least the story, I really do know that I should be doing it one way and not the opposite way around, meaning that of multiplication this time. Here is a bit of difference when it comes to the factors in size and also I was used to the fact that it did not work very well for a couple of other numbers around. Perhaps something to give a thought about for a later time, including that of perhaps keying in the C63 before the rest of it. http://factordb.com/index.php?id=1100000000922501785 http://factordb.com/index.php?id=1100000000922647333 Here apparently a P42 or P43 or so, but it ran in a window and I lost the whole thing. Also it should be only the P113 end factor here, because I think there may be another factorization having a P36 before it. Will be leaving the computer running after the evening cake and will check in tomorrow. There should be no doubt that these large factorizations brings us closer to the target, or final destination, but the question still remains how many such are needed. Multiplying the P99 Fermat factor with another P99 being found today, slightly larger, made for a factorization the other way which was somewhat difficult. For now it becomes lost and close to 2 AM, I am not in for it right now. Checking in with it here at 4 PM, it still says some two hours to go and it has been running since yesterday evening. Anyway, returning back at the computer for the second time, it has been turned off and next losing everything. Only becomes what I was able to save, but for now the work on the C135 is gone and needs a redo. Also I need buying more coffee at the start, or in the beginning of the week. http://factordb.com/index.php?id=1100000000921112604 http://factordb.com/index.php?id=1100000000923441143 An example here. For now perhaps skip the P28 for a moment and look at the remaining composite number. If you compare with the rather large list of factors being stored here, it should be quite clear or evident that there is no P120 or the like in these two. It needs only two minutes of running in order to see or notice such a thing. But also the fact that the prime numbers or factors making up these numbers are or could be the "missing" link when it comes to the remaining part. Factorizing a number like the other C135, if possible, makes for doing such a thing with a number having a larger bit depth and therefore making up a larger part of the whole process. Here it is a P28 preceding it, so perhaps difficult here. The C161 could perhaps return something during the day. The only thing which should be known is that dealing with known prime numbers and their possible relationship could be one thing, but not necessarily for your pocket. When it comes to myself, I am not into that of secret codes or cryptography, but the fact that the possible "King of numbers" is not about neither the square root, or the Golden Ratio, perhaps is the most interesting part of it, or thing to consider. Multiplying the C135 above with the C161 and next the square root and once again it become too high a bit level. But next when flipping it the other way, it becomes a P25 added to the list from a C160. I will add the link later on, but do not forget that I wrote quite a bit of it down yesterday. http://factordb.com/index.php?id=1100000000923445580 Really no point of adding a P11, P13, or a P16 to neither the FDB, or my own list, but here it for now became a P156 added, when flipping around from a C152. Also it became a P175 added to my list right now. I had two above P200 yesterday, meaning factors, which needs reporting. Next both a P179 and a P130, which needs checking for the latter, but I will have the fried eggs for my dinner first. The factor list here got very large right now. The mentioned coffee and I have to go to the shop. http://factordb.com/index.php?id=1100000000923488123 http://factordb.com/index.php?id=1100000000923488465 Here it became a pair of P18 and P128 factors in between, meaning fully factored, which I could add when getting back. Becomes the cup of coffee after getting back from the shop and also a P145 added to my list, together with a P128. Only the result output from the P128 right now, because it was two minutes ago. But supposedly it will not divide and therefore become the same story all over again. Once again that about the corresponding bit length, or perhaps bit depth for such a composite number. Multiplying with the snapshot number, which should be well known and next the square root of the product could return a possible end factor, but only when doing so repeatedly, or at least a couple of times. Therefore, probably the better number, or perhaps factorization from the larger such task, which is not always possible. Giving a try on a C123 being returned, it says or tells that 480144 relations are needed and next this tells me about a possible week of processing. Doing the flip around on this number probably could be somewhat easier, but not having the links right now. I bought two six-packs of beer for the weekend, but one of the bottles was leaking. If it is supposed to be for cryptographic purposes, the .PDF document for that of the factorization of RSA-768 is no exception. Rather I could have wished for a better explanation for this and next the fact that you could be doing one thing using a 8-bit or 16-bit processor and next another with a 64-bit processor. Always the beer at the end of the day, but I could be looking for the one quite big one which made it through. The P128 makes it to a P119 at the other end, so here it becomes an excluding pair. Fun perhaps, but should tell that I have most of the original listings available to me when it comes to the factorizations in the FDB, but not by means of direct copy and paste. In fact, it did not work very well, because of the web-based (.html) format. So for now, apparently 2^12+1 becomes the farewell, or leaving point, but not so because 2^4 = 16. http://factordb.com/index.php?id=1000000000000065536 http://factordb.com/index.php?id=1000000000002000016 Possibly we should know why it happens to be so. Still Fermat numbers rather than Mersenne numbers, you know, but there is really no point of listing the factors for the possible "semiprimes" in full here, because this is not the point. Only that you should know that I happen to know about it. Make it that of perhaps a "numbermaniac" for such a thing, or that of cryptography, I do not think this really matters the most either. Rather my guess is that possible number theory could be about finding the "better number", meaning prime number and for this you have to dig in the sand and not skim the surface. If I multiply the largest Genefer prime with Mersenne 48 (for now being stored locally), what is supposed to be the large, or largest prime number "in between" these two? Is it possible to determine whether or not any of these prime numbers are perhaps the "better" or "best" such numbers, only because they are the largest known? For now unable to get across a possible example number for that of RSA-4096, but for a number being a megaprime, probably no similar thing should be available or present. Anyway, for the first of the two links above, how do I get to the product of the factorized part of this number, meaning the prime numbers, or factors, except for the four composite numbers at the end? Please have me corrected, but it should be 1252...15 (or 015 for the last three digits) here. From the output, I make it at some 1520 digits in total, because I next get P1 = 3 and C74 = 52441485942607521390693352751866808144157473645328701417880476970246676565, which includes most of it including two P10 factors, but apparently skips 26017793 and 63766529 when it comes to the factorization of the C74. The P1 = 3 makes it one digit less on the last line of the first result output. Did I perhaps make it wrong, but digging a bit further, I do not get these two becoming visible. In the end, the C1133 is a semiprime number when it comes to the factors, but I removed the small mark, or asterisks for the closest match in my list. Better make a copy of the remaining number and use the Yafu factor command instead. http://factordb.com/index.php?id=1100000000923694462 If I let this one run, it will probably end up in the C1133, but are you next supposed to think or believe that 2 could be a prime number when doing the possible loopback, or flip-around? My guess is that I could be able to find these numbers right now. The two small factors became added when trying a little harder. The only thing being noticed is that this may not be necessary, but what next if you do or try it the opposite way, meaning from (2^8192+1 and so on, including perhaps 2^65536+1 for now). Or perhaps 2^127-1 as a prime factor and also Mersenne prime versus the P27 of (2^65536+1) one or the other way? Supposedly this could go on forever and we do not know all the factors yet. Also a little bit of surprise right now. Dividing, or at least "trial-dividing" the remaining C1251 with the C1133 of (2^4096+1), it does not divide, but rather it becomes a separate P85. Down to a C1230 right now and I will give it a little more, because here is apparently something else. Apparently works right now, except for the keyboard and mouse. Adding a P13, P19 and a P256 to my list and now I am off, but check in for the link to the factorization on my mind. Anyway, before I leave off for tonight, the P256 makes it for P1 = 2, P1 = 3, C8 = 40483175 (5 * 5 * P7 = 1619327 * P12 = 307552285267 * P341 the other way, but again I am not a numbermaniac. Skipping the P1 = 5 above for better clarity, but the C597 or so should be having something in between when going in the top-down direction (meaning the C1133). Last fiddled with by storflyt32 on 2017-04-25 at 03:06
 2017-04-25, 03:06 #36 storflyt32   Feb 2013 7·61 Posts And now a PRP1071 being added to my list, which is a titanic prime. http://factordb.com/index.php?id=1100000000923789827 Adding the P14 here, but what is 1071 + 51 ? Becomes P12 = 332244975823 for now. https://en.wikipedia.org/wiki/Titanic_prime https://en.wikipedia.org/wiki/Gigantic_prime But apparently no mentioning of the number of digits in 10^9999 + 33603 FDB says 10000 digits even or straight here, but the isprime command in Yafu is not listing the number of digits. Except for the parentheses around, quite plain or obvious here why no need for punctuation above. Doing it using ecm, it takes almost an hour for the same thing. Not in my list either, so therefore adding the prime number. Could make another post right now, but again was thinking about that of number theory. http://factordb.com/index.php?id=1100000000923887061 Shh, please do not tell. P62 = 55355442522357911987182585300149823795012425450699173116409459 P69 = 266464646194847274613461762045055903679186603153520547486021564492567 http://factordb.com/index.php?id=1100000000923898610 Because for now it becomes only loose factors here and is therefore not a fair way of doing such things. At least it could be fun doing so a couple of times. http://factordb.com/index.php?id=1100000000923897915 Becomes the above for the rest, except for the possible switch-around which could be next done. I still have the beer in my hands and also the rest of it (if any) remaining. My possible problem right now is that of BOINC right now, or for the moment. You probably know that I am perhaps dealing a bit with the part of it which is not necessarily repeatable, or perhaps straight-forward. The PRP12576 I found could perhaps be in my thoughts and next how it perhaps works with, or interacts, with something even bigger or larger. For now the answer may not be known, but my guess is that it could be "jump into the sky and next into the heaven" for such a thing. Although not specifically mentioned, the word "fallibles" versus "infallibles", meaning possible "fallability" versus that of a given "infallability" was not being mentioned here. Rather it could be so, or mentioned at BOINC, but for now just telling, or perhaps explaining, what science is supposed to be all about. If rather "all about" above, I perhaps could be proud, but next perhaps not so. The reason is that the word "Credo" is supposed to mean or meaning "I believe" for such a thing. Next, possibly "Out of the blue" and it could mean that of Credo for this. If such a thing as "I believe" next could be about perhaps doing so, it could be just fine, or great. I got the sense, or perhaps feeling, earlier on when posting, that seeing could perhaps be believing, or in fact it could be even more so. Should tell that from a Moderator's point of view (here Seti@home) and not Mersenneforum.org. the view that science could perhaps be of a priority. Why so? Is it perhaps of possible results, or maybe that of ridiculing instead? Being kind of a scientist myself, I happen to be dealing with, or being concerned, with the Scientific Method currently being used. For one thing, that of possible ridiculing, or even that of blasphemy itself, could mean the possible "dead end" of a scienitst when it comes to his or her doing and also whereabouts. So, for one thing that of science at least, or for sure and next the scientist. "Dig me a grave", perhaps, because it could, or is supposed to be in the history books, So it pehaps could be or mean that of possible "truth", but if not so, are we supposed to be still scientists? What if the method of proof, err. meaning possible science could be about such a "truth" as well and not necessarily about any science. I mentioned the fact before that "science could perhaps be believing" and still we are supposed to believe in the Scientific Method. Except for that possible "witness to the execution" could perhaps be doing it better, but next why possibly so? In fact, am I supposed to believe in possible UFO's, or even aliens, because such a thing could be present, or visible in the sky? Please have me excused right now, but except for that of possible witness, or witnesses, we most likely are back at the original, or perhaps true facts, of this story. Who knows, in fact and the question possibly still is remaining, but except for that, we are supposed to be relying on the sources. Looking for the second, or perhaps third typo above. Last fiddled with by storflyt32 on 2017-04-25 at 15:41
 2017-04-25, 15:37 #37 storflyt32   Feb 2013 7·61 Posts https://www.youtube.com/watch?v=B2qI6UDD2uQ For that of fun of course and not necessarily anything else. Perhaps too much beer the other evening. http://factordb.com/index.php?id=1100000000924249012 Same goes here, because in fact it is still running, by means of ecm. Working on another C88 right now and will have the link in short while. Still a bit left to eat when it comes to the dinner, but the ... (not finished) Oops, again. http://factordb.com/index.php?id=1100000000924280687 http://factordb.com/index.php?id=1100000000924390821 Becomes a SIQS number for the second link above and next you are welcome at giving it a try. Becomes C78 = 183379428322420464701721229273679259235432168721706230357025935095022081476687, for this. Presumably this way of order as well, because I could report the factors, but not necessarily all the factorizations in between, because then it becomes a copy of a Notepad list. Finishing off the coffee and cake first. Before doing the rest above, also thinking about that of a possible overcommitment and the fact that the number above could also relate to the Magic number. Becomes an odd number at first, ending in 7 and possibly not keyed in before. It should have at least one or more small factors, but next I do not yet know the answer. For now it becomes a C231 and also with no factors, but next also the known error message, Assertion failed: (__builtin_constant_p (1UL) && (1UL) == 0 ? ((F[deg])->_mp_siz e < 0 ? -1 : (F[deg])->_mp_size > 0) : __gmpz_cmp_ui (F[deg],1UL)) == 0, file pm 1fs2.c, line 1843 Apparently working in the second attempt, but next could take some time to complete. Becomes both 74/74 curves and also 214/214 curves here for only a P10 or P11 and I will let it continue. Before the cup of coffee, a couple of small factors, but next the same set, or sequence on each side for a couple of previous factors and I did not have the time for it. Also did not make it to my notes, but possibly became keyed in. For this, needs a rewind of the log if possible and it may perhaps not work. http://factordb.com/index.php?id=1100000000924279535 P36 = 150893591465383076176058986471020677 P54 = 163611028396365955823312333320675514474810935635362887 Still running by means of ecm and yet I know the answer. How come? Except for that, becomes a C202 at the other end and I will have the link next. Becomes 3:40 AM in the morning and finishing off with a better one, which actually broke before checking. The rest or remaining part was an easy one, but will have to get back at the links tomorrow, because the computer is telling me so. Becomes the whole text when continuing with the edit, so confused at first. Need doing the weekend shopping again. http://factordb.com/index.php?id=1100000000924403930 http://factordb.com/index.php?id=1100000000924795641 http://factordb.com/index.php?id=1100000000924796125 http://factordb.com/index.php?id=1100000000924404522 Here an example where it becomes way to high, at least when it comes to that of bit depth, or bit size. Needs checking here, but except for that need the correct order of the links. Just in case, but the C117 is not having the P23 or P40 as one of its factors. Becomes the factorization here and also that I did this yesterday. The factors are P30 and P88, respectively. Also breaking up the C179 in the usual way returns a C183, which although larger, is easier to do. The C118 the other way is more difficult and could take a while. Becomes a P27 or more likely P28 here and still running. Next should be adding the link as well. Takes 92.3683 seconds for the redo of the C117, but original running time was 526.9651 seconds. http://factordb.com/index.php?id=1100000000924796125 http://factordb.com/index.php?id=1100000000924796566 http://factordb.com/index.php?id=1100000000924796667 http://factordb.com/index.php?id=1100000000924796677 I think I rather should add the latter pair to my list and continue from there. Posting first before looking at what I have, but for now it becomes in wrong order. Adding the P19 and P147 to my list, but as usual it becomes the "impossible pair" one way versus the easy pair, but without any complete solution. Becomes a P145 as well when back from the shop and still cold and also one of the bottles was leaking in the bag without my fault. I will have the cup of coffee first, because the factor list here became very large. The thing being both noticed and also learnt here is that a factor like the P147 factorizes down into a composite number the other way. Next breaking it up by multiplying with a well-known slingshot number, next taking the square root and continuing the factoring process, this time it becomes a P119 when doing it this way, this time from the P145, which becomes a later reporting. Therefore it is the composite number in the middle which is or becomes the sticking point, or perhaps key here. Depending on both size, as well as that of bit depth, this number could at times be very difficult and at other times easier. Together with a P18, it ended up in my list before continuing here, despite a couple of problems. Right now a P168, which is not that bad and needs checking after the cup of coffee. http://factordb.com/index.php?id=1100000000924900906 http://factordb.com/index.php?id=1100000000924900852 Here a P31, in the second link past midnight, but needed 202123/2097152 curves by means of ecm. I will have it in a short while, but getting a sense that this could soon be coming to an end. Next, becoming P1 = 2, P5 = 11867 and next a P123 and really you should know that I already know. It is like being perhaps a little greedy and having a piece of cake lying on a desk. For some reason I could have the large piece, while I am rather not supposed to be doing so. Each time I do this, it rather becomes a thin piece at the edge, leaving the rest of it still behind. Therefore, I also knew the fact that although perhaps many digits, a factor on its own is still only one single number, or entity. Because of that, not only that of gcd (Greatest Common Divisor) as included or a built-in feature in Yafu when it comes to that of composite numbers, but also that of prime number or factors could be having a possible "weight", not only from their respective digits, but also their difficulty when it comes to possible factorizations. In fact noticing this for at least composite numbers, but right now also becoming evident for that of the individual factors as well. Also the fact that while becoming slightly long, no such thing as RSA-8192, or even RSA-4294967296 and you probably know why. Guess it is supposed to be numbers and I could perhaps make it a bit smaller. Read back at the mentioned cake above and we are supposed to believe that the better prime number could be in the middle and not close to the edge. But next the fact that it most likely becomes a composite number before any factors for such a thing. http://factordb.com/index.php?id=1100000000924897335 Apparently one of the possible failures of the software here, because I went back at the starting file for this. http://factordb.com/index.php?id=1100000000803856575 http://factordb.com/index.php?id=1100000000740541084 But also the fun fact that the software is being left undecided here because of pure multiplication only. Trying with nfs on the C309, which is not the Magic number, by the way and it becomes an endless sequence of failure output still running. Becomes a P27 from a C280 right now, which I think the FDB may not have. Adding it to my notes before continuing from there. Sensing the fact as mentioned, perhaps getting a bit closer just before 2 PM. Here a C369 factorizes into a P21 and a 348 and becomes added to my list. Always the question around how many times this may be needed, because I could grab a piece of cake, not necessarily "mine", while you also could be doing the same thing and next we may never meet or encounter each other in the middle. If Mersenne48 or Mersenne49 could perhaps be the largest prime numbers known, they could still be at close to their end branches and not somewhere in the middle. If I could be able to define that of Mersenne48 versus the largest Genefer prime number at least a composite number, but not necessarily any RSA number, I could next say "nothing in between". But in fact this is probably not true and for this that of the mentioned cake above. In fact, I had a C94 becoming lost in my notes and unable to find it. Here it became almost impossible and next could be the paper in your wallet for the secret code to the safe or vault. Two separate P174 factors in their separate boxes here and I think it became noted down. The product of these two becomes a C348 or the like and theoretically could be a semiprime from a C617 of regular or (perhaps) commercial use. Really, I do not think that P5 = 65537 is a factor of this number, but supposedly this could be the chosen way of doing things, by means of a certain .PDF document. Rather I choose to thread lighter here, as mentioned, because of this, rather than taking this for granted. Needs a possible edit above. Yes, perhaps slips, but next add (or multiply) some 100 P100's (not to confuse). What do you next get? Yes, a composite number which should be hard to factorize. Rather the fact that if I happened to be one of those scientists, I could perhaps choose or go for some 2^152788627 -1 Brr. Needed opening up my small factor list here, but next you probably know the answer. In my opinion, perhaps making it that of 152788627 like above could next make for a possible excuse, because you most likely could tell me the readily answer. What if I rather made it a P10 or above instead and like the movie itself next perhaps ask "Shall we try", or perhaps "Give it at try"? Here I was thinking about that of "War Games", but right now missing both the fictional characters as well as their names. Nice one above, but next getting back at it. Noticing here that one of my C136 in progress apparently blew and needs a very big SIQS for this. Apparently some 844336 relations needed here, which could make for some fun. For now remebering the first four digits and it should become stucked, or perhaps stuffed away in the FDB. Doing it the opposite way from the Magic number should be more easy. Checking and I will add the links here. The P108 here is definitely way of target, like most of it as well, but you probably never know. Last fiddled with by storflyt32 on 2017-04-29 at 14:36
 2017-04-29, 14:26 #38 storflyt32   Feb 2013 7×61 Posts Making a new one and thanks as well. http://factordb.com/index.php?id=1100000000924796667 Running since yesterday afternoon and also could be some four hours left to go. My guess is that this could perhaps not be the whole story. Some P131 * P168 makes for a composite number which except for anything else could be a possible semiprime. Again that discussion as well, perhaps. In the world of 64-bit processors, I am also supposed to be entering the number, or numeric "superhighway". Yes, make it that of numerical. This may not always work and whether or not it is the factorization software, or perhaps something else to blame, could be an open question. The fact is that at times I could be pushed or given the result anyway and it could be kind of below the table, or perhaps "underhand", meaning without notice. Is the possible (still) missing result there because there may another or different way or method of doing this? If it was decided that the case was closed for every number less than 120-150 digits, what next? Should I perhaps believe in the software, or perhaps my ability, for such a thing, or if it happens? http://factordb.com/index.php?id=1100000000924796667 http://factordb.com/index.php?id=1100000000924796677 Not a good one here and you probably know as well. Except for that of possible "number saturation", meaning that of possible overflow of numbers in the FDB, which I also heard about. Really, or in fact, we probably do not know it all, as mentioned above or earlier, because of that cake in question. My personal computer probably makes a guarantee that both 3 * 7 = 21 and also that 5 * 7 = 35. Next the fact that the 7 becomes that of gcd here, meaning that thing. What if I could be able to say the same for that of the larger RSA numbers? Next the answer here that it will probably not work, for a good reason and the same most lilkely goes with that of other numbers of similar size, or possibly larger. Should tell that because of that, there could be a P400+ factor somewhere in my list, but next from where or perhaps what? Doing the same thing over and over again, only returns either a composite number, or perhaps a prime number, meaning factor, which next does not divide. Oh, come on. Should we not be familiar with this story, only because of that little +1 at the end, because it is supposed to be about numbers? Killing off the last sentence, because rather bingo at 3 AM in the morning, both the C104 and the P99 being worked on gave in. The C104 is a P35 and P70 pair and not too difficult. The C99, however, is a big pair of P43 and P57 factors and gave me "failure to equate equation two times", before finally listing the factors. But now I got tired and perhaps I should wait until tomorrow for this, including the links for this as well. Total factoring time = 1161.1184 seconds SIQS elapsed time = 12250.5657 seconds. There is a missing "." in the regular factorization compared with that of the SIQS, which also makes it look better. http://factordb.com/index.php?id=1100000000926692603 Becomes this better one of four factors when starting up today and again the P43 and P57 was a quite difficult one. Continuing after having a break, the C203 is having the P35 as part of a regular factorization. Next dividing with the C99, which is the product of the P43 and P57, leaves only the P70 left alone. Also the C169, where the P35 is subtracted, brrr, by means of division, is having a P134 in the flip-around, with only a couple of small ones in between. Need going for the weekend shopping first and also the cup of coffee and the rest will have to wait, including perhaps a little more upload of numbers. Anyway, thank you for being so friendly with me. Should tell that with a slight problem of my left arm and also an not too clean room, I am doing quite a bit when it comes to the business of numbers. The number of Mersenne primes now stands at 49 and including both 3, 7, 31, 127, 8191, 131071, 524287 and 2147483647 as the starting points, or sequence. But in the end, my guess is that the total number of both prime numbers and factors could be into the millions known. The square root function built into Yafu could be helpful at times, but for the larger RSA numbers still composite, that of the Golden Ratio is not of any help. In the world of numbers, it could at times be that of "summa summarum", or at least a brief summary when it comes to the numbers. My experience with that of factoring is showing me that there could be a possible "proportionality" principle around. Everyone knows that finding a large prime number may be quite difficult, but quite often the smaller factors are more often than wished for. Here it could become a lull as well, because at times not very much might be found, while at other times the opposite. Such a thing as factorizing a couple of numbers for that of RSA could make me dig into the cake at times and not only at the edges. The possible P112 may not divide from a C309, but when next flipping around, using a fixed composite number as a slingshot and next the square root, it could end back at yet another factor at the other end. To me or myself, when looking at this, it becomes kind of "twisted" when being so, or such a thing happens. Despite our computational resources, or at least capabilities, the fact is that there apparently is still no answer to this question. Continuing in the buffer right now. http://factordb.com/index.php?id=1100000000927580933 http://factordb.com/index.php?id=1100000000927580982 Here it became a quite large one, but I have not added it yet. Except for that, a pair of P40 and P135 factors here and took a long time for the whole thing. Total factoring time = 54229.5868 seconds I will have it a little later on, but probably makes for a good continuation of the process. http://factordb.com/index.php?id=1100000000927580982 http://factordb.com/index.php?id=1100000000927583497 Apparently becomes a P120 the other way, or perhaps continuing, when trial-dividing the C160 with the same P40, but the question becomes whether it is worth repeating it. http://factordb.com/index.php?id=1100000000927584041 http://factordb.com/index.php?id=1100000000927584567 Another quite good example above. Struggling a bit with the P23 in a second window, the remaining C183 could be very difficult, or perhaps impossible. When saying so, I check in with the running task and here is a P31 or P32. Probably ends here, but could give it an hour more as stated by the ETA in the task. If possibly ending up with a C152, it once again becomes back at the Magic number for the rest of it. Checking in, it also became the P32 as well, but I had the edited text lying in the buffer. From my factorization windows only and not keyed in as a composite number, although the separate factors should be. C87 = 261208748569169232147807101784997894312094169389780155790648085158086857935801673033619 P40 = 3804903139725301145123939483508603713159 P47 = 68650564541842046369160975803860635081764289941 Try it out yourself if you wish, but for now I will not do this one. In my fridge now for the remaining three beers, one at a time. The sad fact is that numbers alone may not be science to all people. If you happen to join BOINC as a distributed project, it should be well known that computing should both be and mean computing for science. Without necessary critisizing in any way, the possible subject of UFO's, or that of possible aliens or extraterrestrials could be possible science, at least at Seti@home. Some people could perhaps make it "Little Green Men" of the whole thing if not that of such UFO's, but for the sake of possible music and entertainment, we could at times be speaking about the "Children of Earth". Not wanting to stray to far away from the subject here, but that of analog versus digital should be an important subject. Both the scratching sound from the playback of the old turntable before the days of the CD-ROM for such playback, or even computerized in any way, where also that of synthesizers, both hardware and also possible software, using a staple or pin, or perhaps stick, gave sound by means of analog playback and also quite often a similar recording as well. Sound is supposed to be waves and therefore that of frequency for possible radio waves, if not that of decibel when perhaps turning up the volume. The classic reference handbook for that of BASIC as a programming language, is standing in my shelf and here a chapter about sound is included. https://en.wikipedia.org/wiki/Arecibo_message Keying it wrong when halfway in the first bottle, it should still be a difference between the WOW! signal and the Arecibo message. For now the binary output of 23 * 73 lines / columns, making it 1679, lies on my disc and the meaning of it could actually be visible from the output alone. Next I made the perhaps stupid confusion or mixing in believing that a possible "semiprime" also lying around could be possibly related with that above, which it is not. Also the fact that some people think that silly and stupid is not the same and the latter could be a perhaps bad word, but still apparently being used. For now this semiprime number is having no listed factors, but the factors are probably known here. http://factordb.com/index.php?id=1100000000496571310 Only the fact that for now, apparently all the Mersenne prime numbers including M23 ended up in full on my disc and also Mersenne 48, but for now, not the most recent find. The C94 once stumbled across did not make it anywhere when trying and later became lost. Should that of factoring, or factorization of numbers be perhaps "processor independent", or should it still be about the numbers themselves? Apparently an unanswered question here. Also another disappointment visible right now. Just for fun I picked up some larger factorial numbers using Yafu. Keying in XXXX# where the "#" stands for factorial, either "+1", or more preferably, "-1" should next be added. For many of these numbers, P1 = 3, could be a factor, but using DOS in a window, the factor becomes listed at the top and next the whole remaining number, without anything else. Not only does it cover the whole screen at times, but also the visible buffer when scrolling upward, without reaching the initial start or beginning of the number, including the possible factor. The only possible solution is noticing any difference in the output, at least when it comes to the ending part, but with a couple of bad eyes, including that of being nearsighted and also a couple of beers, it becomes a bit difficult. Here a fix could perhaps be needed in order for the possible factors being visible at the end, or bottom part of the output, as well. Anyway, 09:45 AM in the morning right now and it could still be one more beer left in the fridge. http://factordb.com/index.php?id=1100000000927645041 Getting a bit tired now, but using the usual or standard method, or perhaps chosen way of doing this, the C174 is at least one level too high up. Doing the square root and next flipping it around, it becomes a P137. Still thinking about a bit of factor upload here, at least when it comes to possible numbers, but next the fact that I am not here for only that of posting Mersenne 49 in full. http://factordb.com/index.php?id=1100000000926692603 Back here right now and perhaps feeling a bit ashamed. First of all, by first look, the C203 as a whole does not relate to any possible higher, at least the one possibly in my thoughts. Therefore, this rather becomes more or less "loose factors" in one way or another. Next, the fact that Yafu was able to come up with at least the P35 and also the C99 making up the P43 and P57 made for a quite good on its own. What is missing here? Is it perhaps still trial-dividing or division for the rest, or remaining part, or could it perhaps be something else? Getting back at this later, when the beer has been consumed. I canceled the edit and rather saved it, because it could have left the tracks. The C82 mentioned above did not make it with ecm using 2^21 curves, but still apparently is a valid pair. Also should make it a bit further as well, but needs checking. Here the whole problem becomes quite evident, because supposedly there should always be a prime number in between a composite number and next guess what that might be. The flip-around of the large factorization became the same P40, together with the P120 and initially a PRP120 for the latter. http://factordb.com/index.php?id=1100000000927583497 Total factoring time = 83001.4024 seconds My guess is that there still remains much to be discovered or found, but also that a P100 may take a second or two, while still a PRP10000 could take several minutes or more only for its factorization. Except when perhaps running blind and think that you could do it by means of LLR instead. The coffee is not helping right now, so I better have a short break, but with a C170 in a window and in the process of 4480 curves, the question is whether that of direct factor reporting should perhaps be better. A P105 versus a P140 is not supposed to factorize, at least when being a composite number, but rather could become a more likely fact. But next perhaps you should still be with your software for such a thing and not your way of thinking. Still the middle of the day here, so anyway... http://factordb.com/index.php?id=1100000000928497840 Here is a nice one that I have the factors for. Therefore no need to try it out, but rather the flip-around here is having a P14 for now and I will let it continue. This number I could well key in before the rest of it. Last fiddled with by storflyt32 on 2017-06-16 at 06:14
 2017-05-07, 17:02 #39 storflyt32   Feb 2013 7×61 Posts Making a new one here because here perhaps something of importance. But here it apparently "divided" straight on by means of that of the "non-divisable" built into Yafu and for the Magic number it became the other immediately or straight on. Actually did not test it further because of the daylight, but my guess is that it also will do so the other way around and not the flip-around here, but rather the factor itself. Almost going to say that I did not do so, because it became a little up my list, but rather doing so anyway, one factor ends with "7" and the other with "3". Therefore not the correct one this time either, but if next continuing, it becomes that of a rewind to something much farther back and I do not think this is the correct answer or thing to say. The smaller factor is a P133, while the larger one is a P176. Multiplying the factors next should get it pretty close, I think. I will have the cup of coffee first. http://factordb.com/index.php?id=1100000000926692603 Starting up a new day, I still feel a little bad about this one. In fact, the whole number is a "multiply". The P35 may be factorized from the C203 and I probably did so and choose to go for a repeat today. Also the C99 making up the P43 and P57 pair became factorized and here it was a bit of work for this. What is perhaps remaining for the ... http://factordb.com/index.php?id=1100000000930103302 Here it should be the C203 except for the P70, but again, this could take the whole day. Going for the weekend shopping right now, I do have a couple of these in running, but it could take some time. I will have the rest of it when back from the shop. http://factordb.com/index.php?id=1100000000930601955 Sorry about the dashes. The C84 at the end needed 349008/2097152 curves by means of ecm and took much of the day. This is a better one and should be put in your pocket in order to unlock the safe. Back later. http://factordb.com/index.php?id=1100000000930616638 At 06:15 AM in the morning. Ring a bell, or what? Needs possible trial dividing here, because this one may never show up. http://factordb.com/index.php?id=1100000000926692603 Here it should be the P43 for this, but apparently still in the blue, or at least running. Always the left-over, or perhaps flip-around and during the week I had P2 = 19 in between, among a couple of others. Also the fact that the current way of doing things could be something else than perhpas pretending that a * b = c, rather than perhaps the opposite way. At least most of the time. One of the things which separates, or makes a possible difference between such numbers as these and that of a megaprime, is that of computation time. Most likely the same principle or method could be used for very large numbers, but here it becomes both cumbersome and time consuming. Prime numbers, or at least composite numbers are not . . . (thinking) A good example is 17 * 19, which is 323. Always a composite number for this if it should be a larger number for possible reference. Just for fun, 617 alone is a factor. 617 / 323 is roughly or ~ 1.910 for that of an approximation of the answer (or when it comes to such a thing). Multiplying by 10 using Windows Calculator returns 955108359133126934984520123839, which makes for factors 13, 181 and P27 = 405910904858957473431585263 when the decimal point vanishes out of sight. My guess is that the P27 needs to be added and next being so. Next makes for a never ending story when it comes to the whole thing. Back later. Adding a PRP3605 to my list while still in the chair. Oops, sorry about that but actually hurting a bit while sitting in the chair most of the day. Found several good factors today, among them a P149 and at least two or three, or perhaps more P150 + factors. Testing out, none of these divides however, but in fact quite close at least at one occasion, or perhaps rather time. If not wrong, we could be speaking about possible bit length at times, despite the size of the complete or overall number. If it rather could be that of bit depth instead, it could perhaps add a bit more to the subject. If some of, or at least a couple of these numbers remain to be factorized, it is not necessarily because they are "tail numbers" or factors and in this case composite, but rather the fact that we think of both the "Magic number" as well as its larger cousin as being composite numbers made up from, or representing individual prime numbers, which then or next are factors. Therefore that of possible bit length above, because for at least one such number, we think it could be a 1024-bit number. Next make it 2^1024 for such a thing and following that, add or subtract 1 to the number. Easy as cake perhaps, but next perhaps not. Compare with that of PrimeGrid, where not unexpectedly it is now the preferred method, or chosen way of increasing the value of b, or p, rather than that of n. Probably we should know the reason for this happening as well. If I for some reason could find a prime number rather than only just a factor, I could end up perhaps relating such a number with something else even larger. Next which possible number, except for either 2^1024, or even 45786^4194384+1 . Becomes only a random example here, because at least 45786^32+1 makes it an odd number and next composite. Increasing the value of n by possbly doubling or squaring, most likely do make any such number still composite even in the long run. So what next about possible factors in between, both when it comes to their sizes, as well as individual number of separate factors? If I happen to run the Factor Database, or perhaps being in charge of it, which I am not, I could be making possible Statistics on it, or the whole thing. If rather choosing to be doing so, it could become sieving at best and possibly nothing more. Make p * 2^n +1 a composite number, next legally divide by means of sieving and (p * 2^n +1) / (2^n-1 +/- 1) becomes a possible prime number. And not necessarily any composite number either, despite such a thing happening most of the time and next the rest of it should not be in the cards either. If so, except for that of sieving, of course, where should such a thing be the perhaps more important? Should it perhaps be the Riesel problem, because it is about a "conjecture", or should it rather be the 321 Prime Search, because here that of n could be both +1 and -1 ? Now I am off and enjoying the rest of the beer. Oh, even the PRP22084 at the bottom of my list probably does not make it any news. So why the point here, except for perhaps that of Cryptography or secret codes? You should know that possible science, except for that of numbers, also could be making the difference between the idiot and the single or regular user. Perhaps the reason for this could be that of thinking about a possible "result" versus an "achivevment", or perhaps "goal". I happended to be mentioning that of the Apollo program somewhere else during the week and also the fact that such a program, or perhaps mission, could be stated, or otherwise given using a couple of other words. Before checking, it probably became that of a "venture" for such a thing and next a "joint venture", at least when it comes to that of space. As "per se", or at least by definition, there is no secret in the fact that possible numbers could be there for a given purpose, whether or not it is supposed to be your wallet or maybe kind of a science which may not be comprehended by anyone. A factor P31 is supposed to be so or such when it comes to a composite number n, or maybe even n+1. Presumably at least that of n alone makes it odd, rather than even, but next when adding (or subtracting the 1), should the answer still be the same? I guess that the answer eventually makes possible fools of ourselves and not necessarily about the numbers themselves. Numbers alone in my opinion are not about any moderation issue at all. Look at such a project like Seti@home and next you could believe that it may be about possible numbers alone, but the fact is that this in fact may not be true. If you assume a possible Method, or at least a way of progress, you next probably, or most likely would blame the end user if such a thing does not happen, or is otherwise unsuccessful. If such a thing as the Apollo program could perhaps "I wish to go to the Moon, not because it is easy, but because it is hard", the answer may be far from the actual Truth. Are you supposed to be in the "high seat", because at times you could be a scientist? Or rather the fact that astronauts visiting the surface of the Moon was of the opinion that they were not alone when doing so. At PrimeGrid, we choose to make it "Astrophotography for rats" for the lack of any better. At BOINC you could also end up being a possible stupid idiot. For this to ever happen, guess we had that of the possible user versus the possible scientist and next that of a given "Idiosyncracy" as well. Becomes a "Copy and Paste" for that above, because I think it is slightly better when it comes to contents. Last fiddled with by storflyt32 on 2017-06-18 at 01:05
 2017-05-14, 09:36 #40 storflyt32   Feb 2013 1101010112 Posts Should I perhaps make it a new one here? http://factordb.com/index.php?id=1100000000930103302 In fact there should be even one more here, because it is part of a C203. http://factordb.com/index.php?id=1100000000926692603 This one is perhaps a bit tricky, or at least difficult as you probably know. Rather it becomes the flip-flop side which becomes the question here. http://factordb.com/index.php?id=1100000000930107231 The C157 here is not going to make it, as far as I can tell, like my own keyboard and also near-sighted eyes. Ran it most of yesterday and when returning back after sleeping off the last three beers, it was still running. Here, in fact, you do have some three or four quite nice factors and therefore one could assume that both the number as a whole and also its part or parts should be "weighted" of sorts. The C157 is a semiprime number of sorts,meaning two factors. Is it possible to trick or perhaps fool a bit around and next make me think that I could have the factors in some way? I went a little down my PList for the factors and came across two such below the lines for the factors of RSA-155 (the "slingshot" number), Therefore it became two P78 factors for this. Next "dividing" (supposedly means trial-dividing, but may not always work either), first gave me a couple of small ones, next a P13 and a P62, which for both I kept. The larger of the two next did the same, but except for the small ones, once again, here it became a P14 and next a C60 which needed a little more. With 2^21 curves using ecm it became a pair of P23 and P37 factors. Next, that none of this has been reported yet, only lies around here. The point is that multiplying the P37 with the P62, for example, it becomes not that easy. C99 = 107697754157460129081548455186886430139227760179467616771326956041448673303218637276768466821961457 P62 = 64673383884991095148967654883745938257171644262615403280008869 P37 = 1665256210328802682226191058712930653 I could perhaps switch the order of the factors for readability, but except for that I have not tried out the C99. Last fiddled with by storflyt32 on 2017-05-14 at 09:37
 2017-05-16, 03:51 #41 storflyt32   Feb 2013 6538 Posts 02:37 AM local time right now. http://factordb.com/index.php?id=1100000000930519825 Dang, this one did not make it with 2^22 curves using ecm (and not 2^21 curves). Apparently stuck on this one for now. Two others apparently came loose and one of them needed quite a bit. At least only composite in the FDB when I last checked, perhaps earlier today. Possibly adding the factors before going to bed, but the funeral today took a toll and needs continuation, or perhaps restart tomorrow. This processor probably is a bit better on the somewhat larger factors and except for the stuck fingers and hands, I got most of it back in return. The only thing possible for now is perhaps relate a couple of hundreds of these against each other by just multiplying. If so, it perhaps could become a "stacked" nature where almost everything could be possible. If I am not wrong, the Mandelbrot set is not necessarily a wild guess, or even speculative theory either, although or even not being about perhaps prime numbers or factors either. Meeting up with a couple of relatives today for the funeral, including an aunt I had not seen in a while, makes a reminder of both ageing and also the battle of the sexes. The aunt who chose to give me some help with both the flies, as well as that of too much food being stored, making it a surplus, is having her own habits, as well as personality. Next the fact that you next could ask yourself where it all came from, because it is supposed to be a shared thing, including responsibility. The likelihood that a carpenter becomes the father of a genius, only because the mother was in the kitchen, is when it comes to me not too much likely. Oh, me getting drunk, perhaps. Where are the factors? Do not take me literally, by the way. Became a new post, but meant to continue. Last fiddled with by storflyt32 on 2017-05-16 at 22:39
 2017-05-16, 22:35 #42 storflyt32   Feb 2013 6538 Posts Perhaps a line a bit too long above, but I ended up with a couple a beers last evening and also quite tired after the funeral. Noticing that someone did the mentioned C98. Quite a feat, or perhaps accomplishment there and I could have a look at the flip-around for this in order to see where it gets. http://factordb.com/index.php?id=1100000000930523910 Here is another one for you, if you happen to be interested. Also this one did not make it with 2^22 curves using ecm. Giving it yet another try with SIQS, it says 107696 relations is being needed. http://factordb.com/index.php?id=1100000000932062488 Also noticing this C80, which by means of ecm using 2^22 curves is some halfway right now. I think a glass of milk, or perhaps mineral water is needed, because I ended up putting the soup in the bottle for cooking and next it does not become any coffee at all. http://factordb.com/index.php?id=1100000000932062488 Becomes yet another day and next continuing the session. Apparently someone did me a favor, because I did not do this one. But what about the individual factors here? In fact I think this is a quite nice one when it comes to such. Giving a try on a C103 right now and this could probably take a day or two. The number of relations needed for the SIQS is here some 141440, so therefore not a quick one. Becomes at least the dinner first, before anything else, but supposedly there should be more P70 factors or the like than similar P130 or P140 factors. Still, the fact that we are supposed to do our factorizations on the smaller numbers rather than the larger ones. http://factordb.com/index.php?id=1100000000933975091 http://factordb.com/index.php?id=1100000000933975393 The P38 in the second link is more or less like climbing Matterhorn rather than Mount Everest. This one took a little while at getting at and is quite similar to that of possible RSA-128 number in size, at least when it comes to a single, or individual factor. Now I will finish off the second beer before next going to bed. http://factordb.com/index.php?id=1100000000933971070 Also here is a P38 which could next be added to the rest of it. The remaining, composite number here becomes a C639. 07:20 AM in the morning and I need the cup of coffee first. This one is slightly larger than the previous one of same size, but except for that, not related. Becomes the 1016... number at the other end and the second P38 definitely does not "divide" in that direction. http://factordb.com/index.php?id=1100000000822445183 First idea of thought is multiplying the C456 with the C639, next take the square root and after that, or subsequently, next use ecm on the answer. Yes, it apparently works and becomes a PRP522, but directly from the plate or oven and needs storing locally first. Next it becomes at least a P16 and P17 from the C1133 of (2^4096+1), but next "trial-dividing" illegally once again, or perhaps in error, it becomes the small ones as usual, next a P19 and P394 pair of factors. Also the top part of it, meaning the output, vanishes from the buffer and needs a redo in order to make it complete, or perhaps get it all. I better start working on the rest of it. Last fiddled with by storflyt32 on 2017-05-28 at 22:34
 2017-05-28, 22:37 #43 storflyt32   Feb 2013 7×61 Posts Anyway, starting up another session here by keying it in the wrong way when it comes to direction. My apologies, but here it became a better set and also the C72, which I was able to do, became part of the factorization. Meaning that when trying to do the factorization of the "multiplication" and here the C150, this time it was able to do that above. Needed a little help with the C78, because still running by means of ecm here. Also a pair of P32 and P123 factors at the other end here as well, but needs finishing up locally first, before adding the links. Perhaps not too bad idea after all, because the P123 gives me just 2^2 * 5 * 11 * 13 * P183 the flip-around way. Quite good factors here and I have the links later on. Sorry, almost forgot this, but at least I was working on it. I will have the weekend beer in less than 90 minutes, but before that, here was a somewhat better one for the Magic number during the day. Factors 2, 5, 7, 17, 2351 and 2383. The two larger factors are a P115 and a P184, respectively. Sorry, but right now it became the Friday beer. Bite my own tongue perhaps, but at least I should know where it is supposed to go. That of factorizing of numbers, including a factorization process (oh me) for such a thing also got better. What if such a thing as numbers could be that of any science, but next perhaps not so. P71 = 11595361855419450045829934323497035471131423617894659246753149374071801 Perhaps worth a closer look, because I think this is a better one. Now it becomes the quite big system hang. Got a pretty large one for you right now which took quite a long time. A bit up my list, so please have me excused. Should add that it became perhaps too many beers yesterday evening and now I should go for the cup of hot chocolate, because the links below became wrong. I will get it sorted out, but next was thinking that a possible look-ahead around the corner could perhaps give me something else in return, meaning either a new factor, or perhaps make up the factor still not reported. http://factordb.com/index.php?id=1100000000935382325 Needs checking, but can you deduce the P48 from the link above? Needs a fix below. http://factordb.com/index.php?id=1100000000934949129 http://factordb.com/index.php?id=1100000000935382086 Switching order of the links above, but still working on this and not finished yet. Here it became a pair of P48 and P142 factors, but only after running at least one whole day and also the following night. But only for the first link above. Total factoring time = 143493.0370 seconds Doing the same in the second link by means of trial-dividing the C148 with the P48 above, it becomes a known P100, but next a little larger for the rest. I will have it later on, but for now it becomes at least a logoff, or perhaps restart in order to continue. Possibly only the P100 here, but next should be the flip-around for the C148, which I think at least trial-divides with the same P48 into the P100. http://factordb.com/index.php?id=1100000000935382325 Also that here in fact is the secret answer and also the question perhaps mentioned if the P48 could be deduced from here? This one perhaps I will not do for now. Also I was thinking of multiplying a P67 with the mentioned P71 in order to see what I get. Also becomes the next thing to do, because here it should be something like a C171 or so at the other end. Multiplying the C172 with the well-known slingshot number and next the square root, it became a P138 added to my list, which could become part of a later upload session. Also the post is getting a bit long right now as well. Became a restart of the computer because of a blue screen, but this is supposed to be Windows updates. Having a cup of hot chocolate, it should be fixed quite soon, but there should be the links for two composite numbers here and not only one. Needs checking, but at least I will add the P48 within an hour or two. Next trying out, it becomes the larger factor here, so here you have the answer to this question. It follows that the smaller factor, the P48 should come from the answer above as well, making it even more fun. Or rather it should be the C189 for this. Assuming the number to be still composite only, also a pair of P15 and P124 factors when again multiplying with the slingshot number, but then only from the flip-around side. First ends up with a C162, which could perhaps be a difficult one, but next doing it the other way around, it becomes that above. The C162 is having a P35 or P36 and still running. I will give it a little more before breaking off. Another C156 is not going any similar way or place for now and could take a while. If it says almost 500 hours of ETA (estimated time), meaning for that of completion, it really makes no sense in my opinion, but at least being noticed for that of a C161. Of course you never know, but at least it becomes the initial result and also a similar way of thinking. So what about the P48 versus the mentioned the P71 and next it becomes a C118. The flip-around is having a P22, which will be added in a short while. The flip-around should be more easy, like that of the C156 above, but if not so, rather make it a product of these two and next take the square root. This was found to be working quite well yesterday and it became a P138, if not wrong. Still not there of course when it comes to the main number in question, but at least working on it. http://factordb.com/index.php?id=1100000000935428706 http://factordb.com/index.php?id=1100000000935439919 Becomes a P124 at the other end here perhaps mentioned earlier and could also add the link which it became. But perhaps even better is that the C156 together with the slingshot number has a P149 when multiplied and next taking the square root. Also a small P6 before that. Possibly two more beers in the fridge and next I am off to bed, but adding the P149 to my list for a later upload session of factors. http://factordb.com/index.php?id=1100000000935428350 Continuing here after both the coffee and cake did not help too much yesterday. Therefore this one ended up in my window as well and is a quite nice one. Makes me think of the P71 above and after keying in, becomes a C106. Next, both a P22 and a P21, following a P10 and also hanging, or thinking a little. Links coming up in a short while, but I need the cofffee first. That makes it a C200 + at the other end and I will have the cup of coffee first. The remaining C129 makes for a C124 when used together with the slingshot number, but needs checking for its possible location. It could be somewhere up or down the list. The next or remaining part has yet to be carried out, so now I am off to it. Also once again it should be remembered the main point here that even a P90 + P90 pair of factors may not perhaps help. so therefore the old question about that of (weighted) distribution among such numbers, or factors. http://factordb.com/index.php?id=1100000000935775515 Perhaps worth its own post, but here a PRP916 from the C1133 of (2^4096+1) with only small factors 2, 13, 2269, 17627 and 78583 in between. Definitely one of the better ones here. http://factordb.com/index.php?id=1100000000936077577 Became this P239 yesterday, or perhaps earlier on, but testing, or checking today, here is P1 = 2 both ways from a number of interest. Could also add that one of my recent factorizations became not too pretty when it comes to appearance. Sorry about that. The factor list becomes quite large here now and while struggling with both bad fingers and also the sausage and peas for the dinner, most of it end up in the logs. Choosing to make an edit above, it is not supposed to be premature in any way either. Not everyone around are supposed to be doing this either, so whether or not any conjecture for this, it may perhaps not be readily visible. But rather the fun of it when making perhaps a C200 a pair of P100 factors and next be able to see the individual factors and also relate the whole number to someting else. For the sake of a good example, there should be no point at doing this with a PRP22084 or so, which is the largest prime in my factor list. Rather a P67 and P71 should be a better example here and testing, it only becomes a composite number at the other end here in the first run. http://factordb.com/index.php?id=1100000000936645757 Perhaps this one instead, but using Yafu I key in rsa(512) on the command line, both because it is half the size of a rsa(1024) number and theoretically square root (twice) in that of complexity. Here it becomes the flip-around size of such a number and next could be added that only the P3 = 911 initially showed up. >> help rsa searching for help on 'rsa' usage: rsa(expression) description: form a difficult to factor number of a specified bit size. NOT FOR CRYPTOGRAPHIC USE. With the above in mind and also that I am not into this business at all, but only numbers, should I perhaps continue on this? Then or if so, how much is perhaps needed? Multiplying the P26 with the P94 and next the flip-around once again does not return back at the C512, but rather becomes a quite easy factorization with a P158 at the end. Anyway, something else right now. http://factordb.com/index.php?id=1100000000936655202 http://factordb.com/index.php?id=1100000000936655271 Anyone willing to give a hand on the C90 here and it will be appreciated. http://factordb.com/index.php?id=1100000000936561836 http://factordb.com/index.php?id=1100000000936563514 Here is a slightly better one which is not easy at all and took a while. It became a pair of P38 and P97 factors here. Total factoring time = 38908.7405 seconds I will add the factors in a short while before I end the current session. http://factordb.com/index.php?id=1100000000936672721 Here as well, only because I am having a bit of fun. Anyway, I finally logged off the session, because I left the computer running for a couple of days. It became at least two more P39 factors or so, where it supposedly are a bit difficult and I will have the links later on. Anyway, with a bit of fiddle during the week, it became a better one only a couple of minutes ago and needs checking. http://factordb.com/index.php?id=1100000000937162999 Above an example of such a thing and here I do not think it is possible, or at least easy. P56 = 24563543054842900957346493006143166848706836255373386869 P66 = 940247923605107153636108709031616399006367848476115246900184862877 http://factordb.com/index.php?id=1100000000937159099 Both factors are already known individually. Becomes the flip-around side here, which is not necessarily that easy either, but at least a number which could be factorized, rather than being only loose factors. Still perhaps a couple more to be added, but apparently not successful on quite much during the week as well. The factorization just in my door is apparently a better one and I will have the link for this next, but perhaps not the factors at first. More to come. http://factordb.com/index.php?id=1100000000937062695 In the small hours of the morning. Not an easy one here and took quite a while. Becomes a P37 and PRP107 here, which makes for a P107. Total factoring time = 28789.4697 seconds Check in for the factors, because I have not added it yet. So, in the middle of the night, except for perhaps the safety net, because I do not want to stray too much off. Really, except for perhaps RSA being an abbreviation, or perhaps acronym for some three persons bearing the signature of this or such a name, I perhaps should not bother or be too much concerned about this here. But rather the fact that perhaps doing such a thing, or rather working with that of a 1024 bit number makes it perhaps "coming all through" in a way. Make it simple and 2^1024 is a number that is both composite and also even. Therefore not any fun or exciting at all. The perhaps more interesting thing is that as soon as you either add or subtract 1 to the number, the whole thing, or issue becomes a different one. Therefore the whole issue of perhaps 2^n+1 and its respective factors. If you do not mind, such a thing is perhaps not about a factorization at all, but perhaps rather that of trial division, in hope of catching possible factors. Brrr, I guess sometimes it may work, perhaps other times not, but presumably a P90 versus P90 (meaning P90 * P90) next could perhaps lead nowhere, because the flip around side could return 3 as the first factor. So here, or perhaps right now, I get or catch the words "I feel good" and next the musical melody for this. https://www.youtube.com/watch?v=QXCGnTy-v2M If I am not wrong, RSA-768 became factorized, either because of decent work being work, or perhaps something else. Next you probably know that this number, or numbers, do not necessarily fit my computer at all. The problem is that I always or sometimes need to choose the largest number at hand in order for possible factors to be obtained. Such a thing is not always possible, or successful and therefore we should know about these composite numbers as well. The perhaps "fake" story could be, or perhaps being told, about a C180 being factorized into a pair of P90 factors, but next the story may be far from true as well. In fact I added a P17 here during the day and next losing where it came from. Also a P26 ended up in my list as well and here I probably have the rest of the numbers. The fact is that a P564 making up the largest known Fermat factor (and not prime number) should be a large or substantial contribution to a possible structure of numbers. But next the fact that even the P564 does not divide from such a number like the C1133 of (2^4096+1). Oh, by the way, where is perhaps the discussion for this? It should be known and also quite obvious, that the factorization of this number still remains in the blue. Next, perhaps,how much? A given factorization of a number is supposed to give, yield, or perhaps return a couple of factors back in return. My guess is that the Factor Database should not be that much concerned with perhaps 2 * 2 * C400 or the like, because it could lead nowhere. So what next about perhaps C1133 / C400? Always the same old question, I guess, or surmise, because in between there should be at least a couple or more factors. Buh! What if I perhaps made a "best guess" here and next the fact that I lost it, or the complete meaning, because of removing an asterisk (*) for that of importance, or significance? If so, perhaps needs a redo, but next such a factorization (if any) is not supposed to be a valid one either. At least I do have the factors here. http://factordb.com/index.php?id=1100000000937158125 Adding a P34 which should be shortly visible, it became 1685/2350 curves using Yafu, meaning that the remaining part should be quite obvious (or perhaps not). At least it took most of the day, or perhaps even more here. Better make a new one here, I think, Really, because there could perhaps be some people around, or maybe someone here, thinking that perhaps a semiprime could be a prime number against another, If I happened to be stupid or naive, it rather could become that of 31 * 127 for such a thing and next, or perhaps not anymore, You probably know that the business of factoring such, or possible numbers mean not so, or such a thing at all. At the bottom of my PList, I am having a PRP22084. Perhaps not the largest one, but next perhaps who should such a number be credited? Really, or honestly, the smartest thing for me to do is perhaps looking up a 2^n (where n is a power of 2) and next deduce the possible "difference" between such a number and next the number being being obtained. Next, being said so, should perhaps such a number be a "difference" by means of that of subtraction, or should it perhaps be a division in the ordinary way? Fiddle, fiddle, first of all, a PRP22084 needs it first number above when it comes to that of 2^n. Then, which next? Perhaps you should be looking for a prime number starting with 363481163587852082267000322216366657889100350280669235752528839341758 and so on. Next the remaining part, of course and it should not be a RSA number either. Such a process is only for that of file management or handling and here on the spot I do not have this one. If perhaps the PRP22084 should be questioned alone, perhaps the answer might be given. Next returning back at the computer at 6:15 PM after having the Thursday evening beverage. http://factordb.com/index.php?id=1100000000937059633 http://factordb.com/index.php?id=1100000000937189569 Here it becomes a P41 as a factor, which is a pretty good one. The second link is from the resulting, or remaining C134 and here it becomes the same P41 by means of trial division, next a P122 already known. The C134 could be a different thing, however and here it perhaps may not be readily done. I could give a try for the second link as well, using Yafu, but it could be more difficult here. It may have been the weekend beer above, because perhaps shouting, but could tell that apparently it broke, or perhaps rather fell apart a little with at least three such which probably are a bit better than usual. The slightly hurting arms makes it difficult right now, because of using the mouse, but at least quite pleased with the results. http://factordb.com/index.php?id=1100000000937233236 I could perhaps start above, because here it became a pair of P46 and P48 factors, being a very nice pair. Also the C94 does it the other way around as well, with a pretty large one and also there became another such as well, with the second, or end factor being somewhat smaller, but still taking more time. Yes, not for starters here, but rather a P40 and a P155, respectively for the shorter one and a P41 and P122 for the longer one. These are pretty good factors, in my opinion and I will have the factors and also links later on. Clicking on the link above for the C162, I think the factors for this number came in here as well, among those two and here it should be the latter. Getting tired right now and I will better continue tomorrow. Last fiddled with by storflyt32 on 2017-06-17 at 23:42
 2017-06-22, 04:56 #44 storflyt32   Feb 2013 7×61 Posts P17 = 94294949437693673 Here a small, but sharp factor I came across. Next it "divides" from the C1133 of (2^4096+1) with only small factors 2^4 and 7 in between, returning a PRP1114 back as result. This because I chose to look at the number 7000000140000002800000056000001 by next adding it up with itself, making it a copy or double of its listing, meaning replication. Also notice what you get if taking the inverse of the number above, meaning 1/x . Factors 173, 107999 and P24 = 374655585282394383120763 for that above. Doing it so in pairs, meaning multiples of each other, I get at least a P250 when "dividing" against the "Magic number" at the proper place. Some of these numbers could perhaps be extended to large numbers and eventually could be returning quite large prime numbers in this way, but for now I have not yet tried. Here I perhaps could ask for some help. http://factordb.com/index.php?id=1100000000937714008 http://factordb.com/index.php?id=1100000000937714079 http://factordb.com/index.php?id=1100000000937714024 Again my bad for keying it in wrong order, but should note that here it became only a multiply of numbers for now. The C133 is having a P45 as one of its factors. If someone could give a try on the C89, I could do most of the rest of it, but would need a restart, or logoff in order for this to be done. Next the C133 gives directly the C89 when giving it a try and the P45 becomes the factor in between. Need checking for the links above and next adding the P45, the middle link is perhaps not needed anymore. Also it apparently becomes success at the other end as well and also not too difficult here. http://factordb.com/index.php?id=1100000000937733102 Also could add the two remaining factors here, but need the dinner first, but here it also became the "failure to equate relation" listed some 39 times in a row. Factors are a P36 and P41 here and someone else apparently did the job. http://factordb.com/index.php?id=1100000000937795327 http://factordb.com/index.php?id=1100000000937795361 https://en.wikipedia.org/wiki/Euler%...eroni_constant Try Eulers constant here and next make it a P40 factor. P40 = 5772156649015328606065120900824024310421 The second factor should be easy to get at, but perhaps not so when it comes to a given factorization. http://factordb.com/index.php?id=1100000000937803043 http://factordb.com/index.php?id=1100000000937803124 http://factordb.com/index.php?id=1100000000937793673 Adding for the first link above in the middle of the night, before having the dinner, because here it did not became that difficult. The flip-around becomes the second link and next I am having a bit of a problem getting back at the third link, which is having a P36 factor. Also the third link should be a separate one and next the fact that I am looking around for the flip-around here. Except for that, no secret code for the locker or safe here, in my opinion, but except for that quite good factors here. Total factoring time = 7408.3902 seconds http://factordb.com/index.php?id=1100000000644791218 Adding a P30 here while finishing off the rest of the beer. Notice the flip-around here if you have the time. http://factordb.com/index.php?id=1100000000938060841 http://factordb.com/index.php?id=1100000000938061079 Apprently one more less to go before getting to the finish. The first one becomes only loose factors and could be almost impossible to do. The second ended up in a P42 and a PRP100, respectively, which next became a P100. Total factoring time = 37719.4810 seconds But perhaps a couple of hours of rest before adding the factors, because here it became a bit of a strain. http://factordb.com/index.php?id=1100000000938149609 http://factordb.com/index.php?id=1100000000938149644 Also here it could be added as well, including the P16 and P17 for this in the second link. Same as before with again loose factors in the first link, but here the second one became a quite big one when it comes to pairs. Here a P46 and PRP97, next P97 and also a whopping factoring time. Total factoring time = 234773.8876 seconds Next of course I keyed in two numbers in the wrong order, because I did not get to the coffee first. The loose factors here should be the end factors for their other respective factorizations, but here I have not looked at it yet. For now the only hope is that it gets stored and not vanishes away. Next making a check on this and the loose factors for both of the pairs above for now made it to the records. Becomes a P55 and P90 pair for the first such one and next a P61 and P63 pair for the second one above. Next I will need to look for the factorizations themselves. P61 = 1446403891874653874622255715541971931090691429384249195337019 P63 = 542491783147206011677983642245579602238171266154650110648391211 Becomes loose factors here, but already in the FDB. http://factordb.com/index.php?id=1100000000938151070 http://factordb.com/index.php?id=1100000000938151171 Here above for the first and also it became added here as well. http://factordb.com/index.php?id=1100000000937852900 http://factordb.com/index.php?id=1100000000937853044 Here for the second, which I think was already there. Back again at just past 1 AM local time, noticing that I do not have the C123 in the list and working on it right now. Perhaps some 5 hours 15 minutes to go, so in the meantime I will do the weekend shopping and perhaps have the rest before sigining off for the day. http://factordb.com/index.php?id=1100000000938293723 http://factordb.com/index.php?id=1100000000938294489 Here perhaps something a bit nice. The two large ones here, or the pair, is having factors 2^8, a P26 and a P218 on the flip-around side of that number in question. Not added yet, but this was possible, although barely so, using ecm with 30 curves and giving it two consecutive tries. If I am not wrong, there could be quite much else or different which does not make it in such a way. I could perhaps run it once more using the factor command while I get the clothes on for my shopping, which I almost forgot. For some reason it takes much longer when using the factor command. Guess what, but this number, 3424931, or 337 * 10163, is having a P1113 at the other end from the C1133 of (2^4096+1) . Factors in between are 3, 13, 29 and P11 = 33009737377 . Adding the prime to my list. Edit: Suffice to say when checking that the C123 is the product of the P61 and P63. So, where did I get those two factors from? Checking, they should both be known and there ... (I will have more here, but the mouse on battery said goodbye right now). Anyway, I perhaps mentioned that of privacy on the net or web in the past and in fact should tell that it bothers me. Taking it into consideration here. http://factordb.com/index.php?id=1100000000938341430 http://factordb.com/index.php?id=1100000000938341446 The C266 I could perhaps give the factors for, but next you already should perhaps know. Canceling the edit above because despite perhaps shouting, actually makes for better language. Next the PRP339 becomes the next working factor, because this should once again be having composite or intermediary numbers in between. Perhaps should start a new one here. Last fiddled with by storflyt32 on 2017-07-01 at 04:50

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