Every Mersenne number of index $n >2$
`$$
M_n = 2^n-1
$$`
is represented by the quadratic polynomial 
$$
Q(x,y) = 28x^2+4y^2+28x+4y+7
$$


e.g.,


`$$
M_3=Q(0,0), M_4=Q(0,1), M_5=Q(0,2),M_6=Q(1,0),
$$
$$
M_7=Q(0,5),M_8=Q(2,4),M_9=Q(3,6),M_{10}=Q(1,15).
$$`


Since it is believed that there are an infinity of Mersenne primes, this polynomial should
represent an infinity of prime numbers.


Question: It is true that this polynomial represents an infinity of prime numbers ?
(Probably unrelated with Mersenne primes).



Mersenne numbers represented by a Quadratic polynomial in two variables
I think this was proved by Iwaniec (for any quadratic in two variables satisfying the obvious necessary conditions).


