# [seqfan] Re: Problem

W. Edwin Clark wclark at mail.usf.edu
Mon Jul 27 08:26:35 CEST 2020

```My Maple program is still running for p = 94603 and now it has passed n =
160000 without
finding any primes of the form (p+1)2^n - 1.  To check the primality of the
number I
use Maple's probabilistic primality test (isprime) ---so I don't collect
any information

On Sun, Jul 26, 2020 at 11:46 PM Tomasz Ordowski <tomaszordowski at gmail.com>
wrote:

> Hello Edwin and Allan!
>
> Thank you for your active interest in the topic.
>
> Let LPF(n) be the Least Prime Factor of n. The provable theorems:
> (1) There are no primes p such that LPF((p+1)2^n-1) < p for all n > 0.
> (2) There are no primes p such that LPF((p-1)2^n+1) < p for all n > 0.
>
> Have a nice Sunday!
>
> Thomas
>
> niedz., 26 lip 2020 o 09:41 Tomasz Ordowski <tomaszordowski at gmail.com>
> napisał(a):
>
> > Hello Edwin and Allan!
> >
> > Thank you for your active interest in the topic.
> >
> > Let LPF(n) be the Least Prime Factor of n. The provable theorems:
> > (1) There are no primes p such that LPF((p+1)2^n-1) < p for all n > 0.
> > (2) There are no primes p such that LPF((p-1)2^n+1) < p for all n > 0.
> >
> > Have a nice Sunday!
> >
> > Thomas
> >
> > pt., 24 lip 2020 o 23:14 W. Edwin Clark <wclark at mail.usf.edu>
> napisał(a):
> >
> >> For the prime p = 94603 and for n from 1 to 100000, (p+1) 2^n - 1 is
> >> composite, says Maple.
> >> This prime appears twice in the OEIS if you don't count A094603.  See
> >> http://oeis.org/search?q=94603&language=english&go=Search   Note this
> >> search doesn't
> >> include things like the sequence of primes.
> >>
> >> 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/
>

```