Exclude the primary attendee count from the confirmation page and adjust the price to exclude the primary attendee. Requires Event Espresso 3.1.34.P or later.

exclude_primary.php

//Calculate number of attendees, minus the primary attendee
function espresso_exclude_primary_attendee() {
    $sql = " AND is_primary = '0' ";
    return $sql;
}
add_filter('filter_hook_espresso_payment_page_count_attendees_sql_where', 'espresso_exclude_primary_attendee', 10);

//Make the primary attendee free
function espresso_primary_attendee_is_free($registration_id) {
    global $wpdb;
    $SQL = " UPDATE " . EVENTS_ATTENDEE_TABLE . " ";
    $SQL .= "SET final_price = '0.00', orig_price = '0.00' ";
    $SQL .= "WHERE registration_id = %s AND is_primary = '1'";
    $wpdb->query( $wpdb->prepare( $SQL, $registration_id ));
}
add_action('action_hook_espresso_confirmation_page_before', 'espresso_primary_attendee_is_free', 10, 1);

//Changes the primary attendee count to 0 on the confirmation display page
function espresso_adjust_primary_attendee_count() {
    return 0;
}
add_filter('action_hook_espresso_confirmation_page_primary_attendee_count', 'espresso_primary_attendee_count', 10);