I looked at my copy of Guy Ottewell and Fred Schaaf's 'Mankinds Comet' published in 1985, ISBN 0-934546-15-0 which gives the orbits for this comet to the year 2134. Here are the years of closest approach to the Earth:
Year.............Distance in AU 1404 BC 0.033 164 BC 0.107 374 AD 0.0884 607 AD 0.0897 837 AD 0.0334 1910 AD 0.1514And here are the nearest distances and dates for the next apparitions:
Year...............Distance April 10, 1986 0.4174 July 29, 2061 0.4773 May 7, 2134 0.0925Clearly, Halley's has been within 0.08 AU or 7.2 million miles of the Earth several times, but given its current path, it is not likely to get close enough to be a problem for the forseeable future.