s/^\D*\d+// # 'first few digits'
Even if this interpretation is correct (and I agree with erix that it’s unlikely), there is no warrant in the OP to remove the non-digit prefix. So the regex would need to be: s/^(\D*)\d+/$1/. For example:
23:21 >perl -wE "$f = 'xyz20130101Customer100.imp'; $f =~ s/^(\D*)\d+/
+$1/; say $f;"
Update (2nd January, 2013):
Thank-you Anonymous Monk for the improvement below using \K: shorter and “much more efficient”, according to perlre. I’ve learned something useful!
Hope that helps,