## 2^7911907+3

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• Hello! I I have a candidate p. Can everyone find a small factor of 2^7911907+3 or make PRP test ? Norman
Message 1 of 6 , May 1, 2002
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Hello! I

I have a candidate p. Can everyone find a small
factor of 2^7911907+3 or make PRP test ?

Norman

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• ... I can find no factor
Message 2 of 6 , May 2, 2002
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> From: Norman Luhn [mailto:nluhn@...]

> I have a candidate p. Can everyone find a small
> factor of 2^7911907+3 or make PRP test ?

I can find no factor <500 million (test continuing, p increasing by 1/2
million per second). I am very interested in how you found this candidate -
can you give us the details?

Regards,

Paul.

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• ... schrieb: From: Norman Luhn [mailto:nluhn@yahoo.de] ... Yes Paul, i can. It is just a conjecture! Well, i had say P=7,67 are primes of form 60k+7.
Message 3 of 6 , May 2, 2002
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--- Paul Jobling <Paul.Jobling@...>
schrieb: > > From: Norman Luhn [mailto:nluhn@...]
>
> > I have a candidate p. Can everyone find a small
> > factor of 2^7911907+3 or make PRP test ?
>
> I can find no factor <500 million (test continuing,
> p increasing by 1/2
> million per second). I am very interested in how you
> found this candidate -
> can you give us the details?
>
> Regards,
>
> Paul.

Yes Paul, i can.

It is just a conjecture!

Well, i had say P=7,67 are primes of form 60k+7.

2^7=30 mod 7^2
2^(2^7)=16 mod 30, you see, a power of 2

2^67=1342 mod 67^2
2^(2^67)=256 mod 1342 you see ,256 is a power of 2

And a look for a prime p=60k+7 and i found the next
is 7911907.

2^7911907=6508160636248 mod 7911907^2
2^2^7911907=2^26 mod 6508160636248

that is all.

Norman

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• Hi Norman, ... It has no prime factors
Message 4 of 6 , May 2, 2002
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Hi Norman,

> It is just a conjecture!

It has no prime factors<2 billion (unless I have done the coding wrong) - do
you intend to spend the time PRPing it? I am not sure that there is any hope
of proving primality, unfortunately, though.

Regards,

Paul.

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• Hi, Running the prp -m command in the latest development version of OpenPFGW on around a PIII 933Mhz shows 5 days for 4194304 and 24 days for 8388608. Your
Message 5 of 6 , May 2, 2002
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Hi,

Running the "prp -m" command in the latest development version of
OpenPFGW on around a PIII 933Mhz shows 5 days for 4194304 and 24 days
for 8388608. Your number is in between there. Plus, if you have an
Athlon or Pentium IV, it would be faster. I would say go ahead and
run a PRP test through OpenPFGW, and let us know if it is indeed a
probable prime. It would lend more credibility to your conjecture.
I would try to get a special version of OpenPFGW that will save your
progress every so often so you don't lose your work. Best wishes.

william

--- In primenumbers@y..., "Paul Jobling" <Paul.Jobling@W...> wrote:
> Hi Norman,
>
> > It is just a conjecture!
>
> It has no prime factors<2 billion (unless I have done the coding
wrong) - do
> you intend to spend the time PRPing it? I am not sure that there is
any hope
> of proving primality, unfortunately, though.
>
> Regards,
>
> Paul.
>
>
> __________________________________________________
> Virus checked by MessageLabs Virus Control Centre.
• Correction: It was a 733Mhz Pentium III and not a 933Mhz. So I say go ahead and run a PRP test through pfgw.exe; let us know if it is a probable prime or not.
Message 6 of 6 , May 2, 2002
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Correction:
It was a 733Mhz Pentium III and not a 933Mhz. So I say go ahead and
run a PRP test through pfgw.exe; let us know if it is a probable
prime or not.

william
--- In primenumbers@y..., "wfgarnett3" <wfgarnett3@y...> wrote:
> Hi,
>
> Running the "prp -m" command in the latest development version of
> OpenPFGW on around a PIII 933Mhz shows 5 days for 4194304 and 24
days
> for 8388608. Your number is in between there. Plus, if you have
an
> Athlon or Pentium IV, it would be faster. I would say go ahead and
> run a PRP test through OpenPFGW, and let us know if it is indeed a
> probable prime. It would lend more credibility to your
conjecture.
> I would try to get a special version of OpenPFGW that will save
your
> progress every so often so you don't lose your work. Best wishes.
>
> william
>
>
>
> --- In primenumbers@y..., "Paul Jobling" <Paul.Jobling@W...> wrote:
> > Hi Norman,
> >
> > > It is just a conjecture!
> >
> > It has no prime factors<2 billion (unless I have done the coding
> wrong) - do
> > you intend to spend the time PRPing it? I am not sure that there
is
> any hope
> > of proving primality, unfortunately, though.
> >
> > Regards,
> >
> > Paul.
> >
> >
> > __________________________________________________
> > Virus checked by MessageLabs Virus Control Centre.
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