  Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a
constant factor of the conjectured asymptotic result for the second moment for
primes in an individual arithmetic progression in short intervals. Previous
results were averaged over all progression of a given modulus. The method uses
a short divisor sum approximation for the von Mangoldt function, together with
some new results for binary correlations of this divisor sum approximation in
arithmetic progressions.
