# [seqfan] Re: Problem

Tomasz Ordowski tomaszordowski at gmail.com
Tue Jul 21 12:10:00 CEST 2020

```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/
>

```