Exploring Mersenne primes 2^p -1

Just a note:
My app "Touch Integers ℤ (+ - × ÷)" is useful to explore the Mersenne primes:
Here there's a tiny exploration from 2^2 -1 to 2^23 -1.
We found all numbers prime, except when p==11 and p==23
Like everybody knows:

The search is made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

https://play.google.com/store/apps/details?id=com.nummolt.touch.integers

http://www.nummolt.com

///////     UPDATE:  (August 2016)    ////////

Same exploration on Wagstaff Prime Numbers:  

 

 Woodall Primes:

 

     

Euler's Lucky numbers:

 

   

And Goldbach's Conjecture:

 
 

The exploration has been made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

https://play.google.com/store/apps/details?id=com.nummolt.touch.integers

http://www.nummolt.com