## Re: [PrimeNumbers] Primaliy test for a series

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• ... ...except for 3, 7, and loads of other Mersenne numbers? Christ van Willegen
Message 1 of 7 , Feb 21, 2007
On 2/21/07, Phil Carmody <thefatphil@...> wrote:
> --- plesala <plesala@...> wrote:
> > Hi to all,
> >
> > How does one test primality of a series like
> >
> > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
> >
> > for example, using primeform?
>
> It's the sum of a geometric progression, so has a closed form representation.
> Just test that closed form instead. However, I think you won't find any
> primes in that series.

...except for 3, 7, and loads of other Mersenne numbers?

Christ van Willegen
• ... No, only except for 3. All of them are divisible by 3. :) [Non-text portions of this message have been removed]
Message 2 of 7 , Feb 21, 2007
> > > How does one test primality of a series like
> > >
> > > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
> > >
> > > for example, using primeform?
> >
> > It's the sum of a geometric progression, so has a closed form representation.
> > Just test that closed form instead. However, I think you won't find any
> > primes in that series.
>
> ...except for 3, 7, and loads of other Mersenne numbers?

No, only except for 3. All of them are divisible by 3. :)

[Non-text portions of this message have been removed]
• ... I can t get that expression to sum to 7, 31, 127, ... Phil () ASCII ribbon campaign () Hopeless ribbon campaign / against HTML mail /
Message 3 of 7 , Feb 21, 2007
--- Christ van Willegen <cvwillegen@...> wrote:
> On 2/21/07, Phil Carmody <thefatphil@...> wrote:
> > --- plesala <plesala@...> wrote:
> > > Hi to all,
> > >
> > > How does one test primality of a series like
> > >
> > > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
> > >
> > > for example, using primeform?
> >
> > It's the sum of a geometric progression, so has a closed form
> representation.
> > Just test that closed form instead. However, I think you won't find any
> > primes in that series.
>
> ...except for 3, 7, and loads of other Mersenne numbers?

I can't get that expression to sum to 7, 31, 127, ...

Phil

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• The original series is not specified correctly. The last term implies that all exponents must be odd, yet the first and third exponents are even. ... Since we
Message 4 of 7 , Feb 21, 2007
The original series is not specified correctly.
The last term implies that all exponents must be
odd, yet the first and third exponents are even.
>
> 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
>
Since we don't know what the original poster
intended, we can't really answer his question.

• Pardon for the clumsy statement I made. Of course the summation I give is easy to simplify. Actually my interest is summations that are slightly more
Message 5 of 7 , Feb 22, 2007
Pardon for the clumsy statement I made. Of course the summation I give is easy to simplify. Actually my interest is summations that are slightly more complicated.

Whenever I try to search for primes of the form
6*n*(2^p - 1- n) + 2^p - 1, where n = 1, 2, 3, ... and 2^p - 1 is a Mersenne prime, I find that the factors are of the form

2^(3*k) - 1 = (2^3 - 1)( (2^3)^(k - 1) + (2^3)^k - 2) + ...
(2^3)^2 + (2^3) + 1),

or alternatively

2^(3*k) + 1 = (2^3 + 1)( (2^3)^(k - 1) - (2^3)^(k - 2) + ...
+ (2^3)^2 - (2^3) + 1), where k is odd.

I wonder whether some of these factor summations cannot yield fairly large primes.

Peter.
----- Original Message -----
From: plesala
Sent: Wednesday, February 21, 2007 1:54 PM
Subject: [PrimeNumbers] Primaliy test for a series

Hi to all,

How does one test primality of a series like

1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),

for example, using primeform?

Thank you.
Peter.

[Non-text portions of this message have been removed]
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