## 46157*2^698207+1

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• [Please note new title, for change of focus.] We do not yet know whether 46157*2^698207+1 is a Keller prime [not yet proven] i.e. whether 46157*2^n+1 is
Message 1 of 8 , Dec 2, 2002
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[Please note new title, for change of focus.]

We do not yet know whether

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

i.e. whether 46157*2^n+1 is composite for all
natural n<698207, as well as being prime for n=698207.
[The odds are very good!]

The eventual announcement of that proof (or otherwise)
will, one trusts, acknowledge the role played by
Wilfrid Keller and Ian Lowman, among others.

I reserve my congratulations, to all concerned,
until such a proof is completed, since the original
intent of the Sierpinski project, as I understand it,
has not yet been fulfilled for k=46157.

David (trying to be even handed)
• 46157*2^698207+1 is prime! (a=3) [210186 digits] 46157*2^698207+1 is prime! (a=5) [210186 digits] I havent completed the Generalized Fermat divisibility test
Message 2 of 8 , Dec 3, 2002
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46157*2^698207+1 is prime! (a=3) [210186 digits]
46157*2^698207+1 is prime! (a=5) [210186 digits]
I havent completed the Generalized Fermat divisibility
test yet.Still 5 hours remaining
Regards
Pavlos
> [Please note new title, for change of focus.]
>
> We do not yet know whether
>
> 46157*2^698207+1 is a Keller prime [not yet proven]
>
> i.e. whether 46157*2^n+1 is composite for all
> natural n<698207, as well as being prime for
> n=698207.
> [The odds are very good!]
>
> The eventual announcement of that proof (or
> otherwise)
> will, one trusts, acknowledge the role played by
> Wilfrid Keller and Ian Lowman, among others.
>
> I reserve my congratulations, to all concerned,
> until such a proof is completed, since the original
> intent of the Sierpinski project, as I understand
> it,
> has not yet been fulfilled for k=46157.
>
> David (trying to be even handed)
>
>
>

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• ... That was not at issue. ... and explained what I meant ... as in W. Keller, The least prime of the form k.2n + 1 for certain values of k, ....^^^^ Abstracts
Message 3 of 8 , Dec 3, 2002
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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
• 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 =
Message 4 of 8 , Dec 3, 2002
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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.

> 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
>
>
>

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• ... I have just finished my search for a GF(m,b) dividing 46157*2^698207+1. And here is the result: It divides none of the GF(m,b) with 19-smooth bases less
Message 5 of 8 , Dec 3, 2002
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> 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.

I have just finished my search for a GF(m,b) dividing 46157*2^698207+1. And here is the result:

It divides none of the GF(m,b) with 19-smooth bases less than 200000.

Note that Yves's Proth.exe which is used by Pavlos checks only the 5-smooth bases less than 13.

Payam

PS. keep visiting http://www.seventeenorbust.com in the next few hours to see the big news as soon as possible.

[Non-text portions of this message have been removed]
• Payam: Did I just detect a FoB warning :-? David
Message 6 of 8 , Dec 3, 2002
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Payam: Did I just detect a FoB warning :-? David
• ... Payam [Non-text portions of this message have been removed]
Message 7 of 8 , Dec 3, 2002
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Oh, a small mistake in my previous post:

> my search for a GF(m,b) dividing 46157*2^698207+1.

corrected as:

> my search for a GF(m,b) divisible by 46157*2^698207+1.

Payam

[Non-text portions of this message have been removed]
• Can he call it or what? :-)
Message 8 of 8 , Dec 3, 2002
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Can he call it or what? :-)