I'm having trouble understanding the steps this paper makes to come to the conclusion $p_{f}(d) \sim e^d\sqrt{d}$
Marek Wolf, First occurrence of a given gap between consecutive primes, preprint, April 1997, IFTUWr 911/97 (Citeseer^x)
In particular, line 6 where it relates his result on the partial Brun's sums to first occurrence prime gaps. And also the following quadratic.
moreover it seems to be inconsistent with his previous paper in line (4) as it ignores some terms in line 28 of this one.
Marek Wolf, Generalized Brun's constants, preprint, March 1997, IFTUWr 910/97 (Citeseer^x)