Use of new Mersenne conjecture ?

[bhelmes]

A peaceful night for you,

Is there a relationship between the primes of the form
2^p-1 and (2^p+1)/3.

Or in other words, there are two quadratic polynomials:
f(n)=2n^2-1 =(sqrt (2)n-1)*(sqrt (2)n+1) and
f(m)=2m^2+1=(sqrt (2)m-i)*(sqrt (2)m+i) (i is the complex part)

Both could be used for primesieving by a described algorithm:

http://devalco.de/quadr_Sieb_2x%5E2-1.php
http://devalco.de/quadr_Sieb_2x%5E2+1.php

Is there a conection between these two prime generators
what the new Mersenne conjecture suggest ?

Greetings from the primes
Bernhard