# [seqfan] Re: Problem

Allan Wechsler acwacw at gmail.com
Wed Jul 22 08:10:30 CEST 2020

```I concur. But establishing the premise will be very hard. If it could be
proved that every prime had a prime Sophie Germain extension, then the
infinitude of the Mersenne primes would be a trivial corollary.

On Wed, Jul 22, 2020, 12:40 AM Tomasz Ordowski <tomaszordowski at gmail.com>
wrote:

> Theorem:
> If, for every prime p,
> (p+1)2^n-1 is prime for some n > 0,
> then it is prime for infinitely many n.
>
> T. Ordowski
>
>
> pon., 20 lip 2020 o 21:06 <israel at math.ubc.ca> napisał(a):
>
> > See sequence A257495. The b-file goes up to 7075 with no 0's, i.e. none
> of
> > the first 7075 primes has the property.
> >
> > Cheers,
> > Robert
> >
> > On Jul 20 2020, Robert Dougherty-Bliss wrote:
> >
> > >Dear Thomas,
> > >
> > >You may already be aware, but none of the first 100 primes (<= 541)
> > >satisfy this property.
> > >
> > >Amazingly, the earliest counterexample for p = 73 is the following
> > integer:
> > >
> > >
> > >
> >
> 12525084203259602214176345117827991857573063437151079650189656689252041617399
> >
> > >
> >
> 16118618976873174436648194378202145606096817433350319763375794132326993383200
> >
> > >
> >
> 14217732225003163760036417965916387747831867749318699104524437655151695087826
> >
> > >
> >
> 47278357731824391729532319069188907350539418959168425940169356532195426353195
> >
> > >
> >
> 84257183520755212129194474630919879413057346247800071524008686049488780942766
> >
> > >
> >
> 38123436651683349651892026768245860789398297612527549211852109219078820059778
> >
> > >
> >
> 19346432242814374609091413789240598598335924463948419947004368457022517766034
> >
> > >
> >
> 95591799870311650343246943884972083691195975663585667560716289785503524182355
> >
> > >
> >
> 53897768571561351251352502155056787443177087759615376430034900988921205572639
> >
> > >
> >
> 317118528079725593399200244440233458975807425711011346463660588817113315016703
> > >
> > >Robert
> > >
> > >
> > >Robert
> > >
> > >
> > >On Sun, Jul 19, 2020 at 2:28 AM Tomasz Ordowski
> > ><tomaszordowski at gmail.com> wrote:
> > >>
> > >> Dear SeqFans!
> > >>
> > >> Let a(0) = p and a(n) = 2 a(n-1) + 1. Note that a(n) = (p+1) 2^n - 1.
> > >> Are there primes p such that a(n) is composite for every n > 0 ?
> > >>
> > >> Best regards,
> > >>
> > >> Thomas Ordowski
> > >> _______________________
> > >> https://en.wikipedia.org/wiki/Riesel_number
> > >>
> > >> --
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >--
> > >Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```