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Old 2005-11-15, 19:25   #1
bearnol
 
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Sep 2005

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Default Fermat's Fuzzy Theorem - any good for new prime test?

Hi all,
This is a genuine question - I'm hoping someone will be able to enlighten me, especially if it's ground that's been covered before - I don't know the answer...
IF this test works at all/can be made to work at all, then it _would_ be valuable as it would potentially allow reuse of exponents.
Anyway, I've noticed [from experiment inspired by one of my previous discoveries :-)] the following:
"Fermat's Fuzzy Theorem"
a^p often == a [mod 2^n]
The primality test would therefore be like a PRP test, only mod 2^n, rather than mod p.
Looking forward to your comments...
Thanks,
J
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Old 2005-11-15, 20:53   #2
xilman
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Quote:
Originally Posted by bearnol
Hi all,
This is a genuine question - I'm hoping someone will be able to enlighten me, especially if it's ground that's been covered before - I don't know the answer...
IF this test works at all/can be made to work at all, then it _would_ be valuable as it would potentially allow reuse of exponents.
Anyway, I've noticed [from experiment inspired by one of my previous discoveries :-)] the following:
"Fermat's Fuzzy Theorem"
a^p often == a [mod 2^n]
The primality test would therefore be like a PRP test, only mod 2^n, rather than mod p.
Looking forward to your comments...
Thanks,
J
Hi James.

it would be good to hear your views on mathematical truth in the context of non-Euclidean geometry.

To remind you: your thesis is that there is but one Mathematical Truth. The three fundamentally different versions of geometry are each internal consistent and each lead to provable theorems. Unfortunately, each lead to theorems which are inconsistent with theorems from either of the others. Which is True and why, and why are the other two not True?

When we've heard your contribution to a discussion you left hanging in mid-air, perhaps people will be more inclined to indulge you with discussion of your latest.

Paul
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Old 2005-11-15, 21:26   #3
R.D. Silverman
 
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Nov 2003
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Quote:
Originally Posted by bearnol
Hi all,
This is a genuine question - I'm hoping someone will be able to enlighten me, especially if it's ground that's been covered before - I don't know the answer...
IF this test works at all/can be made to work at all, then it _would_ be valuable as it would potentially allow reuse of exponents.
Anyway, I've noticed [from experiment inspired by one of my previous discoveries :-)] the following:
"Fermat's Fuzzy Theorem"
a^p often == a [mod 2^n]
The primality test would therefore be like a PRP test, only mod 2^n, rather than mod p.
Looking forward to your comments...
Thanks,
J

Since you do not define the word "often", your question is not mathematics.
It is handwaving. Nor do you define or quantify 'n'. Nor do you say or
indicate how often it is true for COMPOSITE p.

Just trying numbers at random, I note that 7^27 = 7 mod 8 = 7 mod 16.

I also suggest that you look up "Hensel's Lemma". Numbers that are
a mod 2^n can often be a mod 2^(n+1).

In fact, here is some homework for you: Lookup Hensel's lemma and then
tell us the conditions under which if x = a mod 2^n then x = a mod 2^(n+1) as well.

Try doing some real mathematics.
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Old 2005-11-16, 09:54   #4
bearnol
 
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Quote:
Originally Posted by xilman
Hi James.

it would be good to hear your views on mathematical truth in the context of non-Euclidean geometry.

To remind you: your thesis is that there is but one Mathematical Truth. The three fundamentally different versions of geometry are each internal consistent and each lead to provable theorems. Unfortunately, each lead to theorems which are inconsistent with theorems from either of the others. Which is True and why, and why are the other two not True?

When we've heard your contribution to a discussion you left hanging in mid-air, perhaps people will be more inclined to indulge you with discussion of your latest.

Paul
Hi Paul,
Thanks for your message.
Each of the three versions you describe are simply subsets of geometry. They cannot all _simultaneously_ be true, since this _would_ lead to a contradiction in the overarching single Truth that is Geometry. [however there is no problem with having as many subsets as you like, each dependent on differing, incompatible, extra axioms]
(Absolute) Truth _never_ contradicts itself (absolutely).
HTH,
J
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Old 2005-11-16, 09:58   #5
bearnol
 
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Quote:
Originally Posted by R.D. Silverman
Since you do not define the word "often", your question is not mathematics.
It is handwaving. Nor do you define or quantify 'n'. Nor do you say or
indicate how often it is true for COMPOSITE p.

Just trying numbers at random, I note that 7^27 = 7 mod 8 = 7 mod 16.

I also suggest that you look up "Hensel's Lemma". Numbers that are
a mod 2^n can often be a mod 2^(n+1).

In fact, here is some homework for you: Lookup Hensel's lemma and then
tell us the conditions under which if x = a mod 2^n then x = a mod 2^(n+1) as well.

Try doing some real mathematics.
Hi Bob,
Thanks for your message, and yes, I have now done some real math and written a little Java program to test out this suggestion.
The upshot is:
It doesn't work (reliably/correctly) at all!!!
I hereby officially renounce any future attempt to find a _reusable_ prime test - and y'can all hold me to that! :-)
James
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Old 2005-11-16, 10:04   #6
xilman
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Quote:
Originally Posted by bearnol
Hi Paul,
Thanks for your message.
Each of the three versions you describe are simply subsets of geometry. They cannot all _simultaneously_ be true, since this _would_ lead to a contradiction in the overarching single Truth that is Geometry. [however there is no problem with having as many subsets as you like, each dependent on differing, incompatible, extra axioms]
(Absolute) Truth _never_ contradicts itself (absolutely).
HTH,
J
So which is true?
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Old 2005-11-16, 11:42   #7
Greenbank
 
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There is some irony here:-

Quote:
Originally Posted by R.D. Silverman
Since you do not define the word "often", your question is not mathematics.
It is handwaving. Nor do you define or quantify 'n'. Nor do you say or
indicate how often it is true for COMPOSITE p.

Just trying numbers at random, I note that 7^27 = 7 mod 8 = 7 mod 16.

I also suggest that you look up "Hensel's Lemma". Numbers that are
a mod 2^n can often be a mod 2^(n+1).

In fact, here is some homework for you: Lookup Hensel's lemma and then
tell us the conditions under which if x = a mod 2^n then x = a mod 2^(n+1) as well.

Try doing some real mathematics.
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Old 2005-11-16, 12:52   #8
R.D. Silverman
 
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"Bob Silverman"
Nov 2003
North of Boston

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Quote:
Originally Posted by Greenbank
There is some irony here:-
It is too bad you can't read. In the sentence that follows *my* use
of the word often, I state EXACTLY what quantifies the use of the word.
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Old 2005-11-16, 13:03   #9
Greenbank
 
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Come on, why let facts get in the way of a little humo[u]r?
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Old 2005-11-16, 13:19   #10
R.D. Silverman
 
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"Bob Silverman"
Nov 2003
North of Boston

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Quote:
Originally Posted by Greenbank
Come on, why let facts get in the way of a little humo[u]r?
I apologize. Since this medium does not convey any kind of body language,
or tone of voice, I tend to simply take what is written quite literally.....

I thought I was being chided for, shall we say, "stowing thrones in grass
houses".
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