# [seqfan] Re: Problem

Tomasz Ordowski tomaszordowski at gmail.com
Sun Jul 26 09:43:21 CEST 2020

```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/
>>>
>>

```