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Mathematics Forum
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| Author | Message / Information |
| illoyd Quote | Reply | | Further to factorising a number posted on: 1/29/2007 1:36:14 PM If the claim is correct that it is quicker to find the difference of two prime factors in a composite, then the solution for the primes is deterministic. e.g. If ab = X, where a and b say prime and a-b=2Y say ; we are only interested in odd fatcors. Then it is a simple piece of algebra to show: a=Y(1+sqrt(1+X/A^2)) So I will be interested in ways of finding the difference of any two prime factors. |
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zoenkol
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Further to factorising a number
replied on: 1/31/2007 10:31:37 AM Thanks for replying to my message. Yes, thats correct, you need only simple algebra to factor a number if you have the difference between its factors. I have found a way to get that difference directly without any algorithm. For example the number 391, 17 x 23, semiprime. To factor this number you start dividing until you get to one of its factors or you can use any other algorithm like NFS. Other than that there is no direct way to factor this number that I know of. Maybe the CIA can, I don't know. But I lied, I know a way. The whole number system is structered in such way so that it is very easy to get the number 6 for 391, without any algoritm, and that happens to be 23 - 17. Then just use your simple algebra. But, the method is easy for only a subset of all numbers, otherwise I would have factored all the RSA challenges. But luckely I can say exactly why some numbers are more difficult, no matter what their type, eg. semiprime, but that is still classified information. That means the method works for all numbers and it is completely natural, its part of the comstruction of oll numbers. The trick is to look at the whole number system as one structure. I'm not going to say how, just that it is possible. Sometimes something random becomes ordered when you look at it from a different angle. Before I tell everyone exactly how I do it, I first wan't to convince everyone that I am for real. Just to make you jealous, I have factored a 20000 digit semiprime, with just the difference of the factors a lot larger than the largest RSA number, thats pretty big. -In a few minutes! So let me know what you think and if you want to test me Il show you what kind of numbers to give me. |
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illoyd
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Further to factorising a number
replied on: 1/31/2007 12:47:57 PM Hi so what are the factors of : 103070911131721232729313337394347495981 love to see your answer |
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illoyd
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Further to factorising a number
replied on: 1/31/2007 1:21:10 PM Sorry finger trouble: that was a list of primes. I meant to paste in this number: 1378950543258271 |
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illoyd
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Further to factorising a number
replied on: 2/3/2007 2:45:03 PM if that one is proving difficult, try this one: int[44] 02664644045087669067553126845935607031022431 ivor |
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zoenkol
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Further to factorising a number
replied on: 2/6/2007 2:39:32 AM I dont know if you are trying to make fun of me. But anyway, I don't care. 103070911131721232729313337394347495981 This is actually a number. A few of its factors are 151, 193, 22801, 29143, 215051, 4400593, 32472701, 41504843... 1378950543258271 This is a very small number, easy to factor. 36852523 x 37418077. Last one. 2664644045087669067553126845935607031022431 Easy. 1632373745527558118201 x 1632373745527558118231 |
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zoenkol
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Further to factorising a number
replied on: 2/6/2007 2:50:39 AM But this doesn't prove anything or it wouldn't have proved anything to me if I were you. |
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illoyd
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Further to factorising a number
replied on: 2/6/2007 3:58:54 AM The first number I gave you was a genuine mistake. Some will recognise it as a concatenation of the numbers mod(x*y,100), where x any y each go from 1 to 9. I use this to speed up the analysis. The second I used as a test to see if you were genuine and could cope with numbes out of normal range. When I did nort hear from you for several days I gave you an easy one, albeit with longer digits. Above all of course I do not know what computing power you have available; I am using my PC at home. So try this one: 21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471 |
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Euler
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Further to factorising a number
replied on: 2/19/2007 12:21:09 AM What are you taking about- viewing the whole number system as one structure being classified? That's what mathematicians have been doing for many, many years. |
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illoyd
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Further to factorising a number
replied on: 2/23/2007 4:03:20 AM Yes it will be intersting to know what zoenkol has in mind. He has not responded yet. |
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