Again thank you very much for the link, I will also ask there, but still my question remains open … thanks. ]]>

Btw. first question is equivalent to asking if 2^(m-1)-1 = k^2/2, which is the same as asking if there is a Mersenne prime which is even. The only prime which is even is 2, and that is not a Mersenne prime. ]]>

Some more comments to the references:

– [1]: Remove “Pages”.

– [3]: Remove “pp.”.

– [11]: Remove “pp.”.

– [21] Remove “pp.”.

*[Changed, thanks -T.]*

Best Regard, Tao and community

Hi!

I am a Yeisson Acevedo, currently I am

master student in applied mathematics at the Eafit University (Colombia),

I am interested in number theory and I would like to ask you a question that has to do with my object of study that I do not know if it is relevant or not to publish a possible paper, and i would like to ask the favor if you give me your opinions about the next questions:

1) is there a Mersenne Prime such that $M_p = k^2+1$ for some Integer k?

2) Is there a Mersenne prime who is at the same time Germain’s prime?

3) Is there a Mersenne prime who is at the same time Fermat’s prime?

4) Is there a Mersenne prime who is at the same time Wagstaff prime?

5) Is there a Mersenne prime who is at the same time Wodall prime?

6) Is it possible to estimate if around a Mersenne prime there are close primes? That is to say, is Mp +- 2 a prime number?, is Mp +- 4 a prime number?

We want to know if they are important or not in the academic field of number theory and please excuse us for making them spend their time. Thank you.

Pdt: For us, from here in Colombia, the results shared and commented in this blog have been very useful to think about several application problems that go hand in hand with the theory of numbers, although it is not our object of direct study if we use many of your results, so thank you very much for everything.

Knowledge is built in community.

]]>*[The most recent version of the writeup is at https://github.com/km-git-acc/dbn_upper_bound/blob/master/Writeup/debruijn.pdf – T.]*

*[Thanks, this will be updated in the next revision of the slides. -T]*