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• ## Re: [PrimeNumbers] Re: A question

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• ... PRP27 = 643679794963466223081509857 PRP28 = 2496022367830647867616317307 PRP44 = 20316223246552213835636779619145529457704309 [Non-text portions of this
Message 1 of 12 , Oct 1, 2011
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>
> I have now run into a brick wall:
> u[28]=326408399720836161014262419152749\
> 231088487789442706259494316079679210912\
> 54869713984092316692981590
> and pari-Gp is struggling to factorise the 98-digit integer (u[28]+1).
>

PRP27 = 643679794963466223081509857
PRP28 = 2496022367830647867616317307
PRP44 = 20316223246552213835636779619145529457704309

[Non-text portions of this message have been removed]
• ... Thanks, Bernardo. Now do you feel like factorising the 98+27=125-digit integer (u[29]+1) ... Mike
Message 2 of 12 , Oct 1, 2011
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--- In primenumbers@yahoogroups.com, Bernardo Boncompagni <RedGolpe@...> wrote:
>
> >
> > I have now run into a brick wall:
> > u[28]=326408399720836161014262419152749\
> > 231088487789442706259494316079679210912\
> > 54869713984092316692981590
> > and pari-Gp is struggling to factorise the 98-digit integer (u[28]+1).
> >
>
> PRP27 = 643679794963466223081509857
> PRP28 = 2496022367830647867616317307
> PRP44 = 20316223246552213835636779619145529457704309
>

Thanks, Bernardo.

Now do you feel like factorising the 98+27=125-digit integer (u[29]+1)
:-)

Mike
• ... Somebody has been here before, carried it up to 256 digits, and saved it all in the factordb http://factorization.ath.cx/index.php?id=1100000000024656542
Message 3 of 12 , Oct 1, 2011
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• ... We only need the smallest factor which is trivially found by trial factoring to be 103. The sequence of smallest prime factors is the Euclid-Mullin
Message 4 of 12 , Oct 1, 2011
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Mike wrote:
> Now do you feel like factorising the 98+27=125-digit integer (u[29]+1)

We only need the smallest factor which is trivially found by trial
factoring to be 103.
The sequence of smallest prime factors is the Euclid-Mullin sequence.
See for example http://oeis.org/A000945 and
http://en.wikipedia.org/wiki/Euclid%E2%80%93Mullin_sequence

The smallest missing prime in the 47 known terms is 31.

--
Jens Kruse Andersen
• ... It is notable that only one known factorization is incomplete: http://www.rieselprime.de/Others/EuclidMullin.htm and in that case it suffices to show that
Message 5 of 12 , Oct 1, 2011
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"Jens Kruse Andersen" <jens.k.a@...> wrote:

> The sequence of smallest prime factors is the Euclid-Mullin sequence.
> See for example http://oeis.org/A000945 and
> http://en.wikipedia.org/wiki/Euclid%E2%80%93Mullin_sequence

It is notable that only one known factorization is incomplete:
http://www.rieselprime.de/Others/EuclidMullin.htm
and in that case it suffices to show that the composite
co-factor has no prime divisor less than 127.

David
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