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Old 2006-11-27, 19:36   #1
petrw1
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"Wayne"
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Talking 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
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Old 2006-11-27, 22:24   #2
jasong
 
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Quote:
Originally Posted by petrw1 View Post
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
I don't think that would help Prime95 do primality tests, but it would certainly help to factor numbers!!!
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Old 2006-11-27, 22:48   #3
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Quote:
Originally Posted by jasong
I don't think that would help Prime95 do primality tests, but it would certainly help to factor numbers!!!
And search databases.
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Old 2006-11-29, 06:31   #4
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Quote:
Originally Posted by jasong View Post
I don't think that would help Prime95 do primality tests, but it would certainly help to factor numbers!!!
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 Lucas-Lehmer test would now be only a dusty relic of the pre-computer era.
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Old 2006-11-29, 11:08   #5
xilman
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Quote:
Originally Posted by cheesehead View Post
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 Lucas-Lehmer test would now be only a dusty relic of the pre-computer era.
Be very very careful when making statements like this.

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
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Old 2006-11-29, 23:53   #6
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Also remember that all QC algorithms, by their nature, are non-deterministic.
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Old 2006-11-30, 08:49   #7
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Also remember that all QC algorithms, by their nature, are non-deterministic.
That's part of the answer, and a property shared by QS and NFS.

However, assuming a non-trivial 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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