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

From henhanna@gmail.com@21:1/5 to All on Sat Aug 13 11:08:53 2022
(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。 )

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• From Kerr-Mudd, John@21:1/5 to henh...@gmail.com on Sat Aug 13 19:28:51 2022
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

--
Bah, and indeed Humbug.

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• From Eric Sosman@21:1/5 to John on Sat Aug 13 15:45:00 2022
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