I used a similar idea but did as follows:

my $file = '...the OPs File example..." #used as a string
                                        # to simplify my
                                        # test
my @gi_ids = $file =~/gi\|(\d+)\|/g;
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That leaves the list @gi_ids containing all of the gi id's that were in the string (i.e., it finds 4 gi id's in the OPs example).

Just another possible strategy. It looks to me like all of the respondents' ideas would work fine. Mine is just another variation.

Hope that helps.