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interests / rec.puzzles / Re: if p is prime, then so is (2^p - 1)

if p is prime, then so is (2^p - 1)

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Subject: if p is prime, then so is (2^p - 1)
From: henha...@gmail.com (henh...@gmail.com)
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by: henh...@gmail.com - Sat, 13 Aug 2022 18:08 UTC

(no need to "wait a few days, before..." ------ this must've be known for Centuries)

Are the following both true ?

A. if p is prime, then so is (2^p - 1)

---------- for what kind of P does this fail ?

B. if (2^p - 1) is prime, then so is p.

( 2018年2月現在、50個のメルセンヌ素数が発見されている。 )

Re: if p is prime, then so is (2^p - 1)

<20220813192851.93149508f0078d44009809fb@127.0.0.1>

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From: adm...@127.0.0.1 (Kerr-Mudd, John)
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Subject: Re: if p is prime, then so is (2^p - 1)
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by: Kerr-Mudd, John - Sat, 13 Aug 2022 18:28 UTC

On Sat, 13 Aug 2022 11:08:53 -0700 (PDT)
"henh...@gmail.com" <henhanna@gmail.com> wrote:

> (no need to "wait a few days, before..." ------ this must've be known for Centuries)
>
>
> Are the following both true ?
>
> A. if p is prime, then so is (2^p - 1)
>
> ---------- for what kind of P does this fail ?
>
>
> B. if (2^p - 1) is prime, then so is p.
>
>
It's quite a Little Puzzle

https://en.wikipedia.org/wiki/Fermat%27s_little_theorem

Please try harder.

--
Bah, and indeed Humbug.

Re: if p is prime, then so is (2^p - 1)

<td8uvs$2tbcs$1@dont-email.me>

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From: esos...@comcast-dot-net.invalid (Eric Sosman)
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Subject: Re: if p is prime, then so is (2^p - 1)
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by: Eric Sosman - Sat, 13 Aug 2022 19:45 UTC

On 8/13/2022 2:28 PM, Kerr-Mudd, John wrote:
> On Sat, 13 Aug 2022 11:08:53 -0700 (PDT)
> "henh...@gmail.com" <henhanna@gmail.com> wrote:
>
>> (no need to "wait a few days, before..." ------ this must've be known for Centuries)
>>
>>
>> Are the following both true ?
>>
>> A. if p is prime, then so is (2^p - 1)
>>
>> ---------- for what kind of P does this fail ?
>>
>>
>> B. if (2^p - 1) is prime, then so is p.
>>
>>
> It's quite a Little Puzzle
>
> https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
>
>
>
> Please try harder.

.... or at least let it marin-ate a bit longer.

--
esosman@comcast-dot-net.invalid
Look on my code, ye Hackers, and guffaw!

Subject	Author
if p is prime, then so is (2^p - 1)	henh...@gmail.com
Re: if p is prime, then so is (2^p - 1)	Kerr-Mudd, John
Re: if p is prime, then so is (2^p - 1)	Eric Sosman