- On 2/21/07, Phil Carmody <thefatphil@...> wrote:
> --- plesala <plesala@...> wrote:

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

> > 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.

Christ van Willegen > > > How does one test primality of a series like

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

> > >

> > > 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?

[Non-text portions of this message have been removed]- --- Christ van Willegen <cvwillegen@...> wrote:
> On 2/21/07, Phil Carmody <thefatphil@...> wrote:

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

> > --- 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?

Phil

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http://tools.search.yahoo.com/toolbar/features/mail/ - 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 don't know what the original poster

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

>

intended, we can't really answer his question.

Tom Hadley - 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

To: primenumbers@yahoogroups.com

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]