> Am I missing something here, or is my evaluation correct. If the

> latter is true then any benefit of using PMPQS or PPMPQS is surely

> outweighed by the fact that the eventual chance of finding a factor

> is not 50% but maybe 12.5% or even as low as 0.78125% ?

It's conventional to "divide" the quadratic residue by the large prime

once relations have been combined in this manner. "Divide", of course,

means "multiply by the multiplactive inverse". Having performed this

operation, discard both identical copies of the large prime from the

combined relation.

You should find that this returns the probability back to 50%. Think

about it!

Paul