[seqfan] Re: Glued primes

[Max Alekseyev]

On Sun, Nov 23, 2008 at 10:56 AM, Max Alekseyev <maxale at gmail.com> wrote:
> On Sun, Nov 23, 2008 at 10:51 AM, Artur <grafix at csl.pl> wrote:
>> Dear Max,
>> Thank you for example!
>> http://www.research.att.com/~njas/sequences/A003537
>> that mean that all 7 primes numbers from A003537 are glued only for
>> 2^(29*k)-1
>> and these will be occured for every 2^(29*k)-1  where k=1,2,3,4,5,6,7,...
>> but what with 2^58*k+1=5*107367629*536903681 ????
>
> These prime will divide 2^m + 1 as soon as m is an odd multiple of 29,
> i.e., m=29, 3*29, 5*29, ...

Ops. Please ignore this comment.
They will never divide any 2^m + 1.

For a prime p to divide 2^m + 1, it is necessary that the order of 2
modulo p is an even number.
While in this case the order equals 29.

Regards,
Max