use strict;
use warnings;

my $THRESHOLD = 2.5;

 LOG_ENTRY:
    while (my $line = <DATA>) {
        if ($line =~ /^(\d+)/) {
            my $stamp = $1;
            if ($stamp > $THRESHOLD) {
                process_line( $line );
                last LOG_ENTRY;
            }
        }
        else {
            warn "Bad line: $line";
        }
    }

while (my $line = <DATA>) {
    process_line( $line );
}

exit(0);

sub process_line {
    print $_[0];
}

__DATA__
1 llama
2 alpaca
3 camel
4 badger
[download]

prints:

3 camel
4 badger
[download]

HTH.