  Using new and archival observations made with the Swift satellite and other
facilities, we examine 147 X-ray sources selected from the ROSAT All-Sky-Survey
Bright Source Catalog (RASS/BSC) to produce a new limit on the number of
isolated neutron stars (INSs) in the RASS/BSC, the most constraining such limit
to-date. Independent of X-ray spectrum and variability, the number of INSs is
<=48 (90% confidence). Restricting attention to soft (having an effective
temperature of < 200 eV), non-variable X-ray sources -- as in a previous study
-- yields an all-sky limit of <=31 INSs. In the course of our analysis, we
identify five new high-quality INS candidates for targeted follow-up
observations. A future all-sky X-ray survey with eROSITA, or another mission
with similar capabilities, can be expected to increase the detected population
of X-ray-discovered INSs from the 8 to 50 in the BSC, to (for a disk
population) 240 to 1500, which will enable a more detailed study of neutron
star population models.
