Hello, I hope this question is germane to this group, and reasonable. Modular arithmetic is also known as clock arithmetic therefore my question is: Given a...
16355
Décio Luiz Gazzoni...
deciogazzoni
Apr 1, 2005 4:00 pm
... Yes, use the Chinese Remainder Theorem: http://mathworld.wolfram.com/ChineseRemainderTheorem.html In fact, you can use a weaker version, if you assume that...
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John W. Nicholson
reddwarf2956
Apr 1, 2005 11:15 pm
do the following (note the plus/minus and what it equals also notice the 137 and 173 between the two groups): factor ((23#)^3 +/- 1) = 2^12 * 3 * 5^12 * 137 *...
16357
Mark Underwood
marku606
Apr 3, 2005 6:12 pm
Hi all, Some observations follow. These will be old news to number theorists (I assume), but I've found it quite interesting. I make no guarantee that the...
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Michael Gian
pastmyprime2
Apr 3, 2005 7:16 pm
Mark, Please humor a newbie; I'm not sure I understand what "has a solution" means in context of this message. ... theorists ... guarantee ... correct :) ... ...
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Mark Underwood
marku606
Apr 4, 2005 2:49 am
Hi Michael Yes I wasn't very clear. Here's an example. The prime 17 is in the mod8==1 group. (Actually the smallest member.) According to the model there...
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Décio Luiz Gazzoni...
deciogazzoni
Apr 4, 2005 3:28 am
... Fermat has proven that all primes p == 1 mod 4 are uniquely represented as a sum of two squares, while primes p == 3 mod 4 have no such representation. p ...
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Dario Alpern
alpertron
Apr 4, 2005 1:51 pm
... Solutions of x^2 - 2*y^2 = 100999: x0=357, y0=115 Xn+1 = 3 Xn + 4 Yn Yn+1 = 2 Xn + 3 Yn so we can deduce: x1=1531, y1=1059 x2=8829, y2=6239 x3=51443,...
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Mark Underwood
marku606
Apr 4, 2005 3:05 pm
Thank you Decio and Dario Decio I looked up Fermat's "4n+1" Theorem and it is as you say, and proved by Euler. (That is, every prime of the form 4n+1 can be ...
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Robin Garcia
sopadeajo2001
Apr 4, 2005 6:24 pm
Mark wrote: <<Compare this to the composite number 100521. x^2 + y^2 = 100521 has 2 solutions.>> 100521=3^4*17*73 For a prime to be sum of 2 squares ,one must...
16364
Mark Underwood
marku606
Apr 4, 2005 6:45 pm
As they relate to primes, of course :) Fun with successive numbers: 18,164,161 is a prime times 1 18,164,162 is a prime times 2 18,164,163 is a prime times 3 ...
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reney_nl
Apr 4, 2005 8:30 pm
A prime puzzle, I have 6 numbers: 1,2,3 22,25 and 1111 find a primeformula using these numbers (hint: divide 1111 into 2x11).. success! RJ...
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Jens Kruse Andersen
jkand71
Apr 4, 2005 11:13 pm
... 2,918,756,139,031,688,155,200 + k is a prime times k, for k = 1..14 See http://www.primepuzzles.net/puzzles/puzz_181.htm 5,516,280 + k is the smallest...
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Mark Underwood
marku606
Apr 5, 2005 1:30 am
Hi Jens The (N+k)/k prime puzzle. If I've read it before I don't remember it! Perhaps it was posted on this site a year ago or so when I was visiting, and it...
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Gary Chaffey
garychaffey2
Apr 5, 2005 1:39 pm
I have been looking at Henri Lifchitx's site on numbers of the form (2^n-b)*2^n-1. I decided to look at a similar form (2^(3*n)-b)*2^(2*n)-1 and...
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Robin Garcia
sopadeajo2001
Apr 6, 2005 1:23 am
Was just listening now to the last spanish tv -news and they were talking about a story of the danish writer Andersen called (at least in spanish) : The ugly...
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John W. Nicholson
reddwarf2956
Apr 6, 2005 2:52 am
Mark, What if you did this: 788 = 61 + 727 {61,727} twin p,p+2 {59,61} cousin p,p+4 {none} sexy p,p+6 {61,67},{727,733} See now you can state it as one twin...
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xeipon2
Apr 6, 2005 4:42 am
I claim that the following primes are unnecessary for GC. 11, 17, 29, 41, 59, 67, 71, 73, 89, 97, 103, 127, 137, 149, ... Here are the even numbers up to 400...
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chrisdarroch
Apr 6, 2005 11:15 am
Hi all, Can anyone tell me, the best method to post a proof proposal? Do I simply type it into this posting window? It it quite short! Chris. Edinburgh, UK. ...
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Jose Ramón Brox
ambroxius
Apr 6, 2005 12:00 pm
And how do you know that there aren't even numbers bigger than 400 that would need 11, 17... as necessary primes for achieve GC? Do you have a proof? If not,...
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Jose Ramón Brox
ambroxius
Apr 6, 2005 12:01 pm
You can either post it in plain text in an email here, or upload it in pdf or postscript format in a webpage, sending us (and anyone more you trust) the link...
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Sudarshan Iyengar
sudarshansr
Apr 6, 2005 12:13 pm
but you never know what is unnecessary and what is not... just that 11 doesn't alone play a role until 400 doesn't mean that it doesn't play a role at all.. ...
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ed pegg
xeipon2
Apr 6, 2005 12:22 pm
... I have numerical evidence up to 30000. ... Of course I don't have a proof. :) I'm appealing to just numerical evidence. I would be curious to see the...
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Sudarshan Iyengar
sudarshansr
Apr 6, 2005 12:26 pm
Hi, I would be very interested to know the best possible primality testing technique the world ever knew. Best in terms of Checking speed and the magnitude of...
16378
Chris Caldwell
primemogul
Apr 6, 2005 12:56 pm
... Specify the size of the integers! IMO: For the first primes the best algorithm is a lookup table. If they are a little larger, trial division (when...
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Jacques Tramu
echolalie
Apr 6, 2005 3:38 pm
First me need some definitions : A Minimal GC-set , M-GC(N), is a set of prime numbers of minimal cardinality, which may be used to build the even numbers up...
16380
Mark Underwood
marku606
Apr 6, 2005 4:55 pm
Based on your great idea John, we'll tighten Goldbach's conjecture and say that any even number > 4 is the sum of two primes, one a prime twin and the other a...
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antonioveloz2
Apr 6, 2005 6:45 pm
I remember reading about a similar problem a while ago and I came across this paper by Patson MR1812793 (2001m:11010) Patson, Noel(5-CQLI) Interesting property...
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Robin Garcia
sopadeajo2001
Apr 6, 2005 6:55 pm
Chris Cadwell wrote: <<Of course the above assume (semi)sequential computing. Quantum computing will change the world, just not for awhile yet.>> Do you mean...
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Mark Underwood
marku606
Apr 6, 2005 7:50 pm
Thank you Antonia. Those clusters of three, that rings a bell. When I first posted here about this type of thing, (a year ago?) I too noted the cluster of...
