Ok.It is clear now.

I finished the GF divisibility test.

46157*2^698207 + 1 is prime! (a = 3) [210186 digits]

46157*2^698207 + 1 is prime! (verification : a = 5)

[210186 digits]

46157*2^698207 + 1 doesn't divide any Fm.

46157*2^698207 + 1 doesn't divide any GF(3, m).

46157*2^698207 + 1 doesn't divide any GF(5, m).

46157*2^698207 + 1 doesn't divide any GF(6, m).

46157*2^698207 + 1 doesn't divide any GF(10, m).

46157*2^698207 + 1 doesn't divide any GF(12, m).

46157*2^698207 - 1 factor : 3

46157*2^698208 + 3 factor : 5

46157*2^698208 + 1 factor : 3

46157*2^698206 + 1 factor : 3

Done.

--- David Broadhurst <

d.broadhurst@...> wrote:

> Pavlos wrote:

>

> > 46157*2^698207+1 is prime! (a=5) [210186 digits]

>

> That was not at issue.

>

> Rather, I wrote:

>

> > We do not yet know whether

> > 46157*2^698207+1 is a Keller prime [not yet

> proven]

>

> and explained what I meant

>

> > i.e. whether 46157*2^n+1 is composite for all

> > natural n<698207, as well as being prime for

> > n=698207.

>

> as in

>

> W. Keller,

> The least prime of the form k.2n + 1 for certain

> values of k,

> ....^^^^

> Abstracts Amer. Math. Soc. 9 (1988), 417-418.

>

> I believe that for k=46157

> only a few exponents n<698207

> remain unanalyzed, at first pass.

>

> David

>

>

>

__________________________________________________

Do you Yahoo!?

Yahoo! Mail Plus - Powerful. Affordable. Sign up now.

http://mailplus.yahoo.com