Correlation to a Single Gene

I am trying to find a way to perform pairwise correlations against one
gene in a matrix rather than computing every pairwise correlation.  I am
interested in how 1 transcription factor correlates to every gene in a
matrix of 55 experiments (columns) by 23,000 genes (rows), performing
the correlation by rows.  Trying to perform every pairwise correlation
in this fashion is too memory intensive for any computer I am currently
using so I am wondering if anyone had a method for doing pairwise
correlations to a single gene or if there is a preexisting package in R
that might address this.

Damion Nero
Plant Molecular Biology Lab
Department of Biology 
New York University