## Re: Finitude of primes

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• How abot one-digit-primes? ;-) Well there surely are more interesting ones ... richyfourtythree
Message 1 of 14 , Oct 1, 2003
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How abot one-digit-primes? ;-)

Well there surely are more interesting ones ...

richyfourtythree

> Are there any types/forms of primes of which there are definitely
> only a finite number? I'm sure there must be, but can't think of
> any off the top of my head. I'd be interested to see the proofs of
> finitude...
• ... Even primes? Chris __________________________________________________________________ McAfee VirusScan Online from the Netscape Network. Comprehensive
Message 2 of 14 , Oct 1, 2003
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>
>Are there any types/forms of primes of which there are definitely
>only a finite number? I'm sure there must be, but can't think of
>any off the top of my head. I'd be interested to see the proofs of
>finitude...
>
Even primes?

Chris

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• ... Even primes... Primes divisible by three... Primes of the form x^2-1 (or x^n-1)...
Message 3 of 14 , Oct 1, 2003
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At 01:33 PM 10/1/2003 +0000, mad37wriggle wrote:

>Are there any types/forms of primes of which there are definitely
>only a finite number? I'm sure there must be, but can't think of
>any off the top of my head. I'd be interested to see the proofs of
>finitude...

Even primes...
Primes divisible by three...
Primes of the form x^2-1 (or x^n-1)...
• OK let me attempt to rephrase that so as to avoid trivial solutions... Are there any types/forms of primes of which there are definitely only a finite ( 1
Message 4 of 14 , Oct 1, 2003
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OK let me attempt to rephrase that so as to avoid "trivial"
solutions...

Are there any types/forms of primes of which there are definitely
only a finite (>1 and taken over all possible primes so that
"primes less then N" or "primes with k digits" etc. are not
permissible) number?

Richard

>
> >
> >Are there any types/forms of primes of which there are
definitely
> >only a finite number? I'm sure there must be, but can't think of
> >any off the top of my head. I'd be interested to see the proofs
of
> >finitude...
> >
> Even primes?
>
>
> Chris
>
>
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• Fermat Primes are only finite in number. I think I would be right in saying there are infinitely many types of primes which yield only a finite number of
Message 5 of 14 , Oct 1, 2003
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Fermat Primes are only finite in number.
I think I would be right in saying there are
infinitely many 'types' of primes which yield only a
finite number of primes
Gary

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• ... The heuristics certainly say that, but has it been definitely proven? __________________________________________________ Virus checked by MessageLabs Virus
Message 6 of 14 , Oct 1, 2003
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> Fermat Primes are only finite in number.

The heuristics certainly say that, but has it been definitely proven?

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• ... Still, that restriction allows trivial solutions. I came up with this one in just a few minutes, and there are an infinite number of examples like this:
Message 7 of 14 , Oct 1, 2003
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>
> OK let me attempt to rephrase that so as to avoid "trivial"
> solutions...
>
> Are there any types/forms of primes of which there are definitely
> only a finite (>1 and taken over all possible primes so that
> "primes less then N" or "primes with k digits" etc. are not
> permissible) number?

Still, that restriction allows "trivial" solutions. I came up
with this one in just a few minutes, and there are an infinite
number of examples like this:

There are exactly two primes which are of the form:

4*x^2 - 31*x + 60, with x an integer
• ... Not true. The number of Fermat primes is suspected to be finite, but it has not been proved. As far as I know, anyway. Unless my books are out of date!
Message 8 of 14 , Oct 1, 2003
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> Fermat Primes are only finite in number.

Not true.
The number of Fermat primes is suspected to be finite, but it has not
been proved. As far as I know, anyway. Unless my books are out of date!

Andy
• In a message dated 01/10/03 15:25:15 GMT Daylight Time, caldwell@utm.edu ... Not the second of these: restrict to x = 2 and you have made a probably-false
Message 9 of 14 , Oct 1, 2003
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In a message dated 01/10/03 15:25:15 GMT Daylight Time, caldwell@...
writes:

> Primes of the form x^2-1 (or x^n-1)...
>
Not the second of these: restrict to x = 2 and you have made a probably-false
statement:-)

Mike

[Non-text portions of this message have been removed]
• In an earlier mail I stated:- Fermat Primes are only finite in number. I think I should of worded this more carefully . I know that this is only a conjecture
Message 10 of 14 , Oct 1, 2003
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In an earlier mail I stated:-
Fermat Primes are only finite in number.
I think I should of worded this 'more carefully'. I
know that this is only a conjecture but it is another
one of those conjectures which although hasn't been
proven most evidence points this way.

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• Fermat Primes are only finite in number. P.S. I do have a proof for this but it will not fit in the margin!!!
Message 11 of 14 , Oct 1, 2003
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Fermat Primes are only finite in number.
P.S.
I do have a proof for this but it will not fit in the
margin!!!

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• On this subject, is there any set of primes that has been shown to have a finite - but unknown - number of elements? I can t think of any, though there are
Message 12 of 14 , Oct 1, 2003
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On this subject, is there any set of primes that has been shown to have a
finite - but unknown - number of elements? I can't think of any, though there
are many which are heuristically thought to be finite (such as the Fermat
primes).

- Paul.

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