Number theory & 12024562121
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Nish [BusterBoy] wrote: Perhaps its a prime number. Can someone please tell me why prime numbers are so "fascinating"? Yes I know what a prime number is but, at the chance of being booed out of CP, what is the point of them? Who cares if 12024562121 is a prime number. Does it mean anything beyond the fact that it is one? Are prime numbers used for a specific purpose e.g. computing the best way to make me rich or happy? Or are they simply amazing because they are prime numbers? Which is about as practical as an inflatable dart board, to me at least. regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
Paul Watson wrote: Can someone please tell me why prime numbers are so "fascinating"? The fact that they are not divisible by any number than 1 or itself is and how this can be used to solve other problems (crypto comes to mind) is pretty amazing. One thing that I can't understand is why people are still chasing very large prime numbers. I mean, in algebra 101 I was taught how to prove that there is an infinite number of primes. The proof is very clear and has no logic traps. Then why are some mathematicians so eager to find bigger primes all the time? You can never go past infinity, so what's the point? It's scary when mathematicians break out in a big "YAAAAAHOOOOO!!!" whenever some large cluster crunch out a new "largest known mersienne prime".
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So Colin is giving me his usual run around on Sonork and this time he is off on the number theory or magical number tangent. Now I don't even pretend to know or like numbers. In fact my Math skills are about as long as John's fuse. So anyway Colin said that 12024562121 is a number with "style". To me it is a random collection of meaningless numbers. In fact if that was my credit card number I might be happier as at least it means something. So does anyone have a clue what is special about 12024562121 and in general what do you think of numbers and number theory? regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
Over here in North America, that number could be a ..... PHONE NUMBER. Now I wonder just who would be answering if I dialed that. Anyways, like the song says, "Rickie don't lose that number, it's the only one you got". Chris
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Dear Paul [non-mathematician] Well, my math is not great either, but in crpto the use of primes has something to do with work-divisibility. Lets assume there is an operation X. And we need to calculate 20X3. We can divide it into T1=5X4 and then T2=T1X3 If we had a prime instead of 20 that wouldn't have been possible. Maybe I am wrong. That's just my non-mathematical view of things. Nish [non-mathematician] Sonork ID 100.9786 voidmain www.busterboy.org If you don't find me on CP, I'll be at Bob's HungOut
(This is a very simplified version of why prime numbers are the way to go and it covers only asymmetric cryptography. Symmetric cryptography is a different animal if I'm not mistaken) Basically you want to hide the factors of a cryptographic key. If you can find a factor (keys used to produce the cipher) of a "cryptographic" number you have therefore divided the problem into a "solved" and a "smaller unsolved". Thus you don't want to give a potential cracker that kind of luxury, you wan't to make it as hard as possible for him/her. If you choose a prime number, then you cannot divide the problem so easily, you are forced to do a "brute force" crack, i.e. try all possible combinations. Of course, the real thing is a lot more complicated than what I just wrote, but in a very broad sense, this is the reason why prime numbers are nice. (Sidenote: Most cryptographic implementations does not necessarily use prime numbers. Since the numbers are so large, it would take ages to generate and/or verify a possible prime number. Therefore heuristic approaches are used in an iterative process. Most implementations are 99.999999999% accurate though)
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Paul Watson wrote: Can someone please tell me why prime numbers are so "fascinating"? The fact that they are not divisible by any number than 1 or itself is and how this can be used to solve other problems (crypto comes to mind) is pretty amazing. One thing that I can't understand is why people are still chasing very large prime numbers. I mean, in algebra 101 I was taught how to prove that there is an infinite number of primes. The proof is very clear and has no logic traps. Then why are some mathematicians so eager to find bigger primes all the time? You can never go past infinity, so what's the point? It's scary when mathematicians break out in a big "YAAAAAHOOOOO!!!" whenever some large cluster crunch out a new "largest known mersienne prime".
Jörgen Sigvardsson wrote: One thing that I can't understand is why people are still chasing very large prime numbers. Because they can Jörgen, because they can. When the dude who conquered everest was asked why, he said "because it is there". Same thing. Though I think the math guys are way lamer running after large primes than the guy who conquered mt everest. I wonder if they could put their number crunching to better use. Like helping out the cancer cure search or for SETI. regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
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12024562121 = 0x1011001100101110000100000111001001 - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
It's also 12024562121 = 2CCB841C9h 12024562121 = 131456040711o :-D
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Over here in North America, that number could be a ..... PHONE NUMBER. Now I wonder just who would be answering if I dialed that. Anyways, like the song says, "Rickie don't lose that number, it's the only one you got". Chris
Chris Meech wrote: Now I wonder just who would be answering if I dialed that Hello, Microsoft Global Domination slave support line, Tina speaking, how may we help you? :-D regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
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Nish [BusterBoy] wrote: this link might help de-mystify prime numbers; on the other hand it might just be further proof that mathematicians are a weird lot thanks for the link. So what I could gather prime numbers are useful in crypto apps. If so then that is pretty useful, but why are primes useful in crypto and other numbers not so useful? i.e. why use a prime for crypto rather than a normal number? And don't worry, I already think mathematicians are a weird lot. regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
Paul Watson wrote: So what I could gather prime numbers are useful in crypto apps. And in hash tables too... Crivo Automated Credit Assessment
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It's also 12024562121 = 2CCB841C9h 12024562121 = 131456040711o :-D
The most amazing is that: 12024562121 = 1 (base 12024562121) ;P - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
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The most amazing is that: 12024562121 = 1 (base 12024562121) ;P - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
Kastellanos Nikos wrote: The most amazing is that: 12024562121 = 1 (base 12024562121) Hmm. no. Sorry ;) 1 = 1 (base 12024562121) However: 12024562121 = 10 (base 12024562121) Remember hex, bin, and oct? 1 dec = 1 hex 1 dec = 1 oct 1 dec = 1 bin Sorry, but I won't buy your statement.. ;P
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Paul Watson wrote: Can someone please tell me why prime numbers are so "fascinating"? The fact that they are not divisible by any number than 1 or itself is and how this can be used to solve other problems (crypto comes to mind) is pretty amazing. One thing that I can't understand is why people are still chasing very large prime numbers. I mean, in algebra 101 I was taught how to prove that there is an infinite number of primes. The proof is very clear and has no logic traps. Then why are some mathematicians so eager to find bigger primes all the time? You can never go past infinity, so what's the point? It's scary when mathematicians break out in a big "YAAAAAHOOOOO!!!" whenever some large cluster crunch out a new "largest known mersienne prime".
Jörgen Sigvardsson wrote: One thing that I can't understand is why people are still chasing very large prime numbers. One reason you already know - crypto stuff. If you know the numbers greater than your enemy then your data are safe. If not - you may as well send all data in the open text. I think they also look for large numbers to test speed/accuracy/whatever. Just like with the PI - who needs all those billions decimal point digits?
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Kastellanos Nikos wrote: The most amazing is that: 12024562121 = 1 (base 12024562121) Hmm. no. Sorry ;) 1 = 1 (base 12024562121) However: 12024562121 = 10 (base 12024562121) Remember hex, bin, and oct? 1 dec = 1 hex 1 dec = 1 oct 1 dec = 1 bin Sorry, but I won't buy your statement.. ;P
My statement is true for a 12024562121-dimensinal space projected to the 11-dimension. I guess it was obvious. Nobody else complain except you! :cool: - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
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Jörgen Sigvardsson wrote: One thing that I can't understand is why people are still chasing very large prime numbers. One reason you already know - crypto stuff. If you know the numbers greater than your enemy then your data are safe. If not - you may as well send all data in the open text. I think they also look for large numbers to test speed/accuracy/whatever. Just like with the PI - who needs all those billions decimal point digits?
George wrote: One reason you already know - crypto stuff. If you know the numbers greater than your enemy then your data are safe. If not - you may as well send all data in the open text. I don't follow your logic here. Whenever they find a really large prime number, it is published freely. There are numerous sites which carries HUGE textfiles of recently found primes. And when that information is published, then your enemy have the same information as you do. Perhaps you are thinking about ciphers using key lengths which to this date are not feasible to crack? And I also fail to see where this helps crypto. Asymmetric ciphers doesn't test if the generated numbers are 100% prime numbers. They use heuristic approaches which gives you about 99.9999999% accuracy (give or take a couple of decimals :)). Sidenote: Verifying a prime number requires lots of computation. How pleased would you be while waiting for PGP to generate your keys? Verifying one key would probably take a couple of minutes (greatly depending on key length). And lets not forget that it will draw a random number. How many random numbers must you draw until you find a prime number? A perfect solution is not tractable. Therefore cryptography in practice doesn't benefit from finding larger prime numbers. And I don't think cryptography in theory benefits either, how could it? Generation of primes is a numerical/analysis thing while cryptography (and cryptology for that matter) is a purely symbolic algebraic thing. George wrote: I think they also look for large numbers to test speed/accuracy/whatever. Just like with the PI - who needs all those billions decimal point digits? This I can agree on to some degre. If you for sure knows which numbers are the first 100 million decimals of PI, then calculating PI is a really good accuracy measure. But.. how can we be sure that those 100 million decimals are the correct ones? Has anyone verified them by hand? And even if so, how can we be sure that no one made a mistake? (Let's not forget the last election in the US.. ;)). I understand that numerical programming techniques will improve over time. And this is probably the only useful thing I see in generating large primes, PI, e, .
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So Colin is giving me his usual run around on Sonork and this time he is off on the number theory or magical number tangent. Now I don't even pretend to know or like numbers. In fact my Math skills are about as long as John's fuse. So anyway Colin said that 12024562121 is a number with "style". To me it is a random collection of meaningless numbers. In fact if that was my credit card number I might be happier as at least it means something. So does anyone have a clue what is special about 12024562121 and in general what do you think of numbers and number theory? regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
The phone number Tim Smith Descartes Systems Sciences, Inc.
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My statement is true for a 12024562121-dimensinal space projected to the 11-dimension. I guess it was obvious. Nobody else complain except you! :cool: - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
Hahaha! :-D Ok. You got me there. But then again, the course in "Linear Algebra" was not a requirement for me. :cool: so I may be excused for my ignorance. But I do have a question. How does dimensions relate to numbers? If I remember correctly, numbers are just names or symbols for "pure values". How can a value in the most abstract sense be related to dimensions? Wouldn't a value in an n-dimensional space (or whatever the terminology is) be an n-tuple of values? (Is there a short answer to this...? If not, don't go out or your way to explain it to me.) Sidenote: If you wan't to make best friends with a functional programmer (Haskell junkie or the like), tell them that numbers are nothing more than named constant functions. You'll have a friend for life.. :-D
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The phone number Tim Smith Descartes Systems Sciences, Inc.
Tim Smith wrote: The phone number :omg: :omg: :laugh: :omg: :laugh: :eek: :rolleyes: Good old Colin and well done to you Tim for figuring it out. I hope the secret service does not break down my door tonight for posting the number all over a website :-O :eek: :laugh: regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
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Hahaha! :-D Ok. You got me there. But then again, the course in "Linear Algebra" was not a requirement for me. :cool: so I may be excused for my ignorance. But I do have a question. How does dimensions relate to numbers? If I remember correctly, numbers are just names or symbols for "pure values". How can a value in the most abstract sense be related to dimensions? Wouldn't a value in an n-dimensional space (or whatever the terminology is) be an n-tuple of values? (Is there a short answer to this...? If not, don't go out or your way to explain it to me.) Sidenote: If you wan't to make best friends with a functional programmer (Haskell junkie or the like), tell them that numbers are nothing more than named constant functions. You'll have a friend for life.. :-D
All I can say is "WOW". Do you guys actually think and understand things like that? I mean when you write down "n-tuple of values" are you just doing a bullshit salesman talk or is this matrix of n-dimensional* values spiralling in your head and you understand it like I understand the LOTR? Either way it all sounds impressive. * this is salesman talk as you can see, I have no clue what it means regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
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George wrote: One reason you already know - crypto stuff. If you know the numbers greater than your enemy then your data are safe. If not - you may as well send all data in the open text. I don't follow your logic here. Whenever they find a really large prime number, it is published freely. There are numerous sites which carries HUGE textfiles of recently found primes. And when that information is published, then your enemy have the same information as you do. Perhaps you are thinking about ciphers using key lengths which to this date are not feasible to crack? And I also fail to see where this helps crypto. Asymmetric ciphers doesn't test if the generated numbers are 100% prime numbers. They use heuristic approaches which gives you about 99.9999999% accuracy (give or take a couple of decimals :)). Sidenote: Verifying a prime number requires lots of computation. How pleased would you be while waiting for PGP to generate your keys? Verifying one key would probably take a couple of minutes (greatly depending on key length). And lets not forget that it will draw a random number. How many random numbers must you draw until you find a prime number? A perfect solution is not tractable. Therefore cryptography in practice doesn't benefit from finding larger prime numbers. And I don't think cryptography in theory benefits either, how could it? Generation of primes is a numerical/analysis thing while cryptography (and cryptology for that matter) is a purely symbolic algebraic thing. George wrote: I think they also look for large numbers to test speed/accuracy/whatever. Just like with the PI - who needs all those billions decimal point digits? This I can agree on to some degre. If you for sure knows which numbers are the first 100 million decimals of PI, then calculating PI is a really good accuracy measure. But.. how can we be sure that those 100 million decimals are the correct ones? Has anyone verified them by hand? And even if so, how can we be sure that no one made a mistake? (Let's not forget the last election in the US.. ;)). I understand that numerical programming techniques will improve over time. And this is probably the only useful thing I see in generating large primes, PI, e, .
Jörgen Sigvardsson wrote: I don't follow your logic here. Whenever they find a really large prime number, it is published freely. Nah, that is a mere catching up. The really large numbers are to be found amoung CIA, FBI, military and the like. Jörgen Sigvardsson wrote: And I also fail to see where this helps crypto. The whole crypto sits on large primes actually. Do the research on your own ;) Jörgen Sigvardsson wrote: Sidenote: Verifying a prime number requires lots of computation. http://www.utm.edu/research/primes/prove/
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So Colin is giving me his usual run around on Sonork and this time he is off on the number theory or magical number tangent. Now I don't even pretend to know or like numbers. In fact my Math skills are about as long as John's fuse. So anyway Colin said that 12024562121 is a number with "style". To me it is a random collection of meaningless numbers. In fact if that was my credit card number I might be happier as at least it means something. So does anyone have a clue what is special about 12024562121 and in general what do you think of numbers and number theory? regards, Paul Watson Bluegrass Cape Town, South Africa Do you Sonork? I do! 100.9903 Stormfront "The greatest thing you will ever learn is to love, and be loved in return" - Moulin Rouge
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Hahaha! :-D Ok. You got me there. But then again, the course in "Linear Algebra" was not a requirement for me. :cool: so I may be excused for my ignorance. But I do have a question. How does dimensions relate to numbers? If I remember correctly, numbers are just names or symbols for "pure values". How can a value in the most abstract sense be related to dimensions? Wouldn't a value in an n-dimensional space (or whatever the terminology is) be an n-tuple of values? (Is there a short answer to this...? If not, don't go out or your way to explain it to me.) Sidenote: If you wan't to make best friends with a functional programmer (Haskell junkie or the like), tell them that numbers are nothing more than named constant functions. You'll have a friend for life.. :-D
You made me suspicious. My first guess was that the dot-product of a vector of value 12024562121 with the 11-dimension, is a point. ;P Let me redo my calculations and i will let you know the result. ;) Jorgen Sigvardsson wrote: Sidenote: If you wan't to make best friends with a functional programmer (Haskell junkie or the like), tell them that numbers are nothing more than named constant functions. You'll have a friend for life.. If someone believe that, then the universe is a computer, in which the numbers are evaluated each time we refer to them. Even if numbers were written as static functions, God is smart enough to pass the universe application through an opimizing compiler that turn them all into inline. :laugh: - - - - - - - - - - - - - - - - - - Memory leaks is the price we pay \0 01234567890123456789012345678901234
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How about raw hex? 420665C20E480000 Or even base 5? 12045A2121 * * is that even remotely right? ________________ David Wulff http://www.davidwulff.co.uk "I loathe people who keep dogs. They are cowards who haven't got the guts to bite people themselves" - August Strindberg
nope. :) here it is in a variety of different bases: base: num 2: 1011001100101110000100000111001001 3: 1011001000100001020122 4: 23030232010013021 5: 144111241441441 6: 5305104033025 7: 603660043265 8: 131456040711 9: 34030301218 10: 12024562121 11: 5110608550 12: 23b7002775 13: 1198284620 14: 820db30a5 15: 4a59c334b 16: 2ccb841c9 17: 1c52e8f6a 18: 11b9bee0h 19: d8b4f36b 20: 97hda561 21: 6e44kcg5 22: 4i14ikdb 23: 3c55625h 24: 2em307lh 25: 1o67lo9l 26: 1co18hkd 27: 1410916h 28: oqj23j5 29: k6735g4 30: gep44hb 31: dh0aljl 32: b6bgge9 33: 9a8e5gb 34: 7qm5cbr 35: 6ix192q and here's the code to do it:
char buf[40];
for (int i=2;i<36;i++)
{
_i64toa((__int64)12024562121, buf, i);TRACE("%d: %s\\n", i, buf);}
-c, geek