Reggie, is it truly your contention that if any time elapses between the death of one Pope and the election of another, the line is "broken?"
If this is the case, allow me to save you the trouble since I doubt Pope Linus assumed the role immediately and exactly coinciding with the death of Peter. Heck, the line was broken again just twenty five years ago since -as I recall- several days (weeks) passed between the death of John Paul the I and John Paul II.