- --- In primenumbers@yahoogroups.com,

Bill Bouris <leavemsg1@...> wrote:

> I think that proves it

http://primes.utm.edu/notes/proofs/MerDiv2.html proves that

if p = 3 mod 4 and p is prime,

then 2p+1 is prime iff 2p+1|2^p-1

Bill claims that

if p = 1 mod 4 and p is prime,

then 2p+1 is prime iff 2p+1|2^p+1

and his facsimile proof looks good to me.

If Chris agrees, than he might like to add

Bill's case to the Euler-Lagrange page, above.

David - --- In primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> http://primes.utm.edu/notes/proofs/MerDiv2.html proves that

Henri has remarked (off list) that he had already given

> if p = 3 mod 4 and p is prime,

> then 2p+1 is prime iff 2p+1|2^p-1

>

> Bill claims that

> if p = 1 mod 4 and p is prime,

> then 2p+1 is prime iff 2p+1|2^p+1

>

> and his facsimile proof looks good to me.

essentially the same proof as Bill, in 1998:

http://www.primenumbers.net/Henri/us/NouvTh1us.htm

It's always good to see clear minds agreeing.

David