I have found this, but I am not sure about it (especially because it contains an error
Quote:
If p==1 mod 4 then k==3 or 0 mod 4. If p==3 mod 4 then k==0 or 1 mod 4
This gives us a nice try 2, skip 2 type pattern, so all that we have to do
is set the initial value the factor, then add 2p or 4p according to the
pattern.

Now, the 4p in that last part should be 6p. Is this statement correct? I am guessing in your statements that you say that p = 2qk+1, and this quote says that p is the exponent of the Mersenne.