## RE: [PrimeNumbers] Re: Finitude of primes

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

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

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• ... 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 Unless my books are out of date!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 2 of 14 , Oct 1, 2003
> 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 Unless my books are out of date!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 3 of 14 , Oct 1, 2003
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

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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
Message 4 of 14 , Oct 1, 2003
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 5 of 14 , Oct 1, 2003
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 6 of 14 , Oct 1, 2003
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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