# [seqfan] Re: [manumit at protonmail.com: A216189 update]

Hugo Pfoertner yae9911 at gmail.com
Tue Oct 9 22:00:16 CEST 2018

```At least the shown numbers are confirmed to be PRPs by using Jean Penné's
LLR (Lucas, Lehmer, Riesel) program, see http://jpenne.free.fr/index2.html .
2^277244-175709 is base 3-Fermat PRP! (83459 decimal digits)
2^277244-175709 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13)
2^649662-170531 is base 3-Fermat PRP! (195568 decimal digits)
2^649662-170531 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13)
2^728277-183313 is base 3-Fermat PRP! (219234 decimal digits)
2^728277-183313 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13)
2^743592-134579 is base 3-Fermat PRP! (223844 decimal digits)
2^743592-134579 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13)
2^861987-134557 is base 3-Fermat PRP! (259484 decimal digits)
2^861987-134557 is Fermat, Lucas and Frobenius PRP! (P = 6, Q = 6, D = 12)

It is therefore safe to remove the 5 terms 134557, ..., 183313 from the
sequence. I've performed a corresponding edit, please check. This is the
funny case, where the sequence is "extended" by deleting terms. Eventually
it is expected that all shown terms would be eliminated and the first term
will become the proved A076337(1)=509203.

Hugo Pfoertner

On Tue, Oct 9, 2018 at 8:27 PM Fred Lunnon <fred.lunnon at gmail.com> wrote:

>   Sounds like 007's controller --- hope you had appropriate security
> clearance!
>
> WFL
>
>
>
> On 10/9/18, Joerg Arndt <arndt at jjj.de> wrote:
> > I got this message from someone who apparently does not
> > want me to know who he is.
> > As I do not particularly care about A216189, I'd like
> > to leave it to a volunteer to decipher the message
> > and possibly edit the sequence.
> >
> > Best regards,   jj
> >
> >
> > ----- Forwarded message from M <manumit at protonmail.com> -----
> >
> > Date: Mon, 08 Oct 2018 21:07:16 +0000
> > From: M <manumit at protonmail.com>
> > To: "arndt at jjj.de" <arndt at jjj.de>
> > Reply-To: M <manumit at protonmail.com>
> > Subject: A216189 update
> > X-Spam-Score: -2.2 (--)
> >
> > Hallo,
> >
> > I have tested the larger n's to k=1e6.
> > 5 n's can be removed:
> > PRP's
> > 2^277244-175709
> > 2^649662-170531
> > 2^728277-183313
> > 2^743592-134579
> > 2^861987-134557
> >
> > I found this sequence from
> > https://en.wikipedia.org/wiki/Riesel_number#The_dual_Riesel_problem
> >
> > pub   rsa2048 2018-10-01 [SC]
> >       8681D9A1E866162CC29975CD090894AC3F78BFCC
> > uid           "manumit at protonmail.com" <manumit at protonmail.com>
> > sub   rsa2048 2018-10-01 [E]
> >
> >
> >
> > ----- End forwarded message -----
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```