20131123, 22:15  #12  
∂^{2}ω=0
Sep 2002
República de California
11660_{10} Posts 
Quote:
Although there is another possible interpretation for the catcalledNeutron comment, other than the "our pointybrassiered science babe here hath flunked out of particle physics" one. Cue Madeleine Kahn in History of the World, Part 1: "We call him that because he has just been snipped!" 

20131124, 08:03  #13  
Romulan Interpreter
"name field"
Jun 2011
Thailand
9,787 Posts 
Quote:
By the way, the number in cause is proven composite, one core of PFGW can show it in less than 3 hours. Code:
(2^1968721+1)/(3*10613583595427) is composite: RES64: [CD2A6ED1468CEDF0] (7234.4788s+27.8081s) Last fiddled with by LaurV on 20131124 at 08:08 Reason: code tags 

20131124, 10:33  #14 
Feb 2010
Sweden
173 Posts 
Indeed I put some irony on purpose in some of my comments, but my primary intention was to reduce the spam with a redirect to FactorDB. To me it seems that the guy is with a positive attitude (this time no pun intended), but I think his age is well bellow the average of this forum. She/he needs a reference for his quests.

20140923, 23:23  #15 
Feb 2013
2×229 Posts 
For orders sake.
Being able to determine, or prove, that a 105 digit number is a prime number is an easy task to carry out. Multiplying two such (different) numbers and then assume that this now composite number is, or possibly represents an almost unbreakable number when it comes to its factorization becomes an almost impossible or incomprehensible task to complete or finish, even when using a powerful personal computer for such a given purpose. Why is this being so? Because the factors becomes almost identical when it comes to size. Both these elements are making some numbers completely impossible to factor, even though some people may be so lucky as to know the individual factors which are representing these numbers. Two classic examples should be mentioned when it comes to this, namely RSA1024 and RSA2048. Both these two composite numbers have yet to be factored. And still, we happen to be so lucky that we "know" the factors which are representing RSA768. Please try factoring this number for me. You will be able to find out that factoring a RSA512 or similar number is an almost impoossible thing to carry out or do, using a regularly available software platform for just such a use. One such example for you right here. Give it a try, will you? 7529315904594771817511864427258894764407713405160355555243610 8811740640162856360514781181695040844760480712732512854358557 6730146689356339498615917 Or, on only just one line, for copying simplicity and use  752931590459477181751186442725889476440771340516035555524361088117406401628563605147811816950408447604807127325128543585576730146689356339498615917 http://factordb.com/index.php?query=...56339498615917 This number is not an "official" RSA512 number, but at least it ends up close to it being such a number. Here is where it is currently standing. 
20140923, 23:45  #16 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,393 Posts 
Why? You can do it yourself and fairly easily.
Bull 
20140924, 03:26  #17 
Romulan Interpreter
"name field"
Jun 2011
Thailand
9,787 Posts 
@storflyt: please use [code] tags when post those long lines, otherwise the posts are very difficult to read, and people may just close the thread without reading it. Non everybody has wide monitors.
The C147 composite you link in the factorDB is a factor of this C161, which is one year old, and seems it comes from an aliquot sequence, according with its structure, but I don't have such sequence in my data base and I could not find another reference to it in the factorDB. It may be an "over a million" starter aliquot sequence. Being one year old (if not fake, and some key for some gaming site, as happened in the past ), it got some ecm done already. You can factor it with yafu in 4 cores in few days (mostly a week), with an average computer. There is nothing "impossible" about it, as Batalov already said. I can factor it for you in 23 days, if you tell me where the number is coming from, and convince me that it is important to factor it. Last fiddled with by LaurV on 20140924 at 03:28 
20141030, 02:29  #18 
Feb 2013
2·229 Posts 
If you did not know this already.
If I try multiplying a prime number (or a composite number for that matter) with something else, I am never supposed to be finding any prime numbers this way. For some reason the process of factorization (meaning factorizing numbers) is not always that straightforward. Certainly you happen to know that all those numbers eventually are there, but in which way am I then able to get to these numbers? As usual, every number has its easy part and its more difficult part. It becomes part of a track, similar to the traversal of a treelike structure (almost hierarchical in nature and shape). Factorizing a number like 10^40321 gives me possible Mersennelike factor numbers (or what?). Also I am getting what appears to be socalled repdigit factors. When it comes to the process of finding large Fermat primes, you assume that a number having a notation like xxxx00000000000.....1 is or the similar is prime. For now, such a number is not assumed to be a repdigit number, whether or not it is prime. So at which point does it converge? Please have a look back to my previous analogy regarding 5*7 = 35 and vice versa. The 5part is supposed to be the easy one. The 7part is the more difficult part of the task. For large numbers like 2^488531 you of course are getting something else back when it comes to the numbers, but the way or method (analogy) of thinking is still the same, no matter else. Last fiddled with by storflyt32 on 20141030 at 02:33 
20141221, 09:51  #19 
Feb 2013
712_{8} Posts 
So, since I have been here for a while now, there is a couple of questions that I would want to ask you.
The subject of prime number finding (or call it factor finding if you wish) is the area or realm or subject field of the mathematicians. In order to properly be able to carry out such a task, you more or less depend on the processing power of the computer, regardless of how sharp minded you may be yourself. It really may become too big numbers at times, even for the sharpest of minds. Not all prime numbers, even the smaller ones, are known today. Some of these may be found by means of factorization. Other factors are being found on their own, not being directly related to other, possibly larger numbers. Some people may think of the order of factors as being directional, only being sorted from smaller to larger in size (or perhaps the opposite way). In other instances or cases, factors or numbers are being related to each other by means of either factorization, or possibly by means of trial division. At times one may be starting thinking about the individual factors possibly being represented by means of a hierarchical tree structure. For every branch of this tree, possibly with a left one as well as a right one, or the similar, one branch of the tree may be regarded as more simple when it comes to factorization. The other branch of the tree then becomes more complex. Some factorizations are simple, because extracting a factor like 3 from even a 10,000 digit number is a quite simple thing. In other cases, factorization becomes more difficult, because the factors of a composite number may eventually show up to be more similar or comparable in size. Examples of such factorizations include the RSAnumbers and the semiprime numbers, including the Mersenne semiprimes. One may get the impression that at times these numbers may only be found by means of trial division and not by means of factorization, because the processing time at doing such a thing becomes very high. This is the reason why such numbers like RSA1024 and RSA2048 have yet to be factorized properly. Assumedly the individual factors of these numbers may be known to a very few people, but that is because these factors were found individually and not as a result of factorization. Even more complex, it may seem to, is the factorization of 2^(2^n)+1, where n>= 4096. Here, apparently no progress is being made despite several attempts. Is it correct to assume that these remaing composite numbers in fact are semiprime numbers and if so being Fermat factors rather than the corresponding Mersenne factors? There may be some reason to speculate whether a couple of numbers currently being discussed may be part of one or more of these factors, but for now the question apparently remains open. It becomes a question about computing or processing power and how much time a specific factorization attempt should be given. At times, no results are being obtained because of the time it may take to be doing so and other events which may take place in the meantime, like system hangs and possible restarts and the like. Last fiddled with by storflyt32 on 20141221 at 09:53 
20141222, 15:00  #20  
"Jane Sullivan"
Jan 2011
Beckenham, UK
425_{8} Posts 
First of all, instead of posting in onesentence paragraphs, which makes it very difficult to read and understand, break your post up into paragraphs of more than one sentence, starting a new paragraph whenever the underlying subject changes.
You asked Quote:


20141225, 11:01  #21 
Feb 2013
111001010_{2} Posts 
Merry Christmas!
Thanks for the reply. Leaving it with one question only today. What is the point of factorizing a given number when the prime factors may already be known individually? Apparently the nextprime command built into Yafu is not that error free and it definitely fails when the number becomes large. Yes, I know that you may be able to find the "previous", or lower factor as well when using this command. Last fiddled with by storflyt32 on 20141225 at 11:02 
20141225, 19:43  #22 
Feb 2013
111001010_{2} Posts 
Just by pure coincidence, or what else might this be?
I used the last part of a big number that became lost when it comes to its actual syntax. The initial number being used I do not have either, right now. I will get back at it. Apparently some small numbers being factors at the start of the factorization of this number. From this last part came a P143 by means of factorization. Probably a C160 or larger just before that. I next divided this P143 from RSA1024 and of course it did not so. The result became a C149 which apparently is a hard one to factorize. Does that imply that I am close to a prime factor (not necessarily that of RSA1024) when such a thing happens, or is there rather another explanation to this instead? If you did not know this already, it is really not that difficult finding the next (or previous) prime factor from a composite number if it is not too large. The question becomes what is most needed since at times factorization may be a hard thing to do and the alternative to a brute force attack on a given, composite number, may be just that  a lot of other factors, of which not everyone is that necessary to be having. Please have a look at 2^1290001 and 2^12900001 in the Factor Database and you certainly will agree with me. Last fiddled with by storflyt32 on 20141225 at 19:49 
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