[seqfan] Re: Problem

[Jack Brennen]

You will find that for p = 94603 and n = 237504, that you get a prime.

I didn't do the prime search myself, just a web search.  This problem, 
in a different restated way, was discussed on mersenneforum.org back in 
2007:

https://www.mersenneforum.org/showthread.php?p=116340#post116340

You will see there that 23651*2^237506-1 was found to be prime, which is 
another way of writing the number I alluded to on the first line.



On 7/27/2020 2:26 AM, W. Edwin Clark wrote:
> 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
> about LPF((p+1)2^n - 1).
>
> 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
>>>>>
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>>>>>
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