20061127, 19:36  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
4387_{10} Posts 
We'll be done in no time!!!!
See this link for advances in computing that will allow your computer to be
FAST!!!!! http://www.itworldcanada.com/a/Daily...2077b6848.html It starts with: "Future PCs could run 18 billion, billion times faster By: Chris Mellor Techworld.com (22 Nov 2006) How would you like your computer to run 18 billion, billion times faster? A a University of Utah physicist says he has taken the first step towards creating a quantum computer that can make this feat possible. " Read on 
20061127, 22:24  #2 
"Jason Goatcher"
Mar 2005
5×701 Posts 
I don't think that would help Prime95 do primality tests, but it would certainly help to factor numbers!!!

20061127, 22:48  #3  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·47·61 Posts 
Quote:


20061129, 06:31  #4 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
But a prime is simply a number with no factors other than itself and 1 ... so primality tests are either factoring tests or shortcuts to skip factoring tests! If the first electronic computers had been quantum computers, the LucasLehmer test would now be only a dusty relic of the precomputer era.

20061129, 11:08  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{4}·641 Posts 
Quote:
To prove primality by factorization you must use an algorithm which is guaranteed to find all prime factors. The reason that this more precise statement is needed is that some factoring alogrithms are not guaranteed to find a factorization other than the trivial N = 1 *N. Examples of such algorithms include QS and NFS. This claim may come as a surprise to some. Nonetheless it is true. I'll reveal the reasons why after you've had a chance to think about it. Paul 

20061129, 23:53  #6 
Aug 2002
2^{6}×5 Posts 
Also remember that all QC algorithms, by their nature, are nondeterministic.

20061130, 08:49  #7  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{4}·641 Posts 
Quote:
However, assuming a nontrivial factorization can be found, Shor's algorithm, QS and NFS all expect to find the factors quickly. That is, the probability of failure can be made arbitrarily small with repeated trials (and relatively few of them in practice). What else remains? (Bob: I know you know the answer. Let the others have their chance to find it for themselves. Paul 

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