We report the discovery of four isolated millisecond pulsars found as
part of the Parkes 436 MHz survey of the southern sky. Three of the pu
lsars, PSRs J1024-0719, J1744-1134, and J2124-3358, are close to the S
un (d < 360 pc) and have very low luminosities, less than or similar t
o 0.5 mJy kpc(2). The other, PSR J0711-6830, is of intermediate lumino
sity. The four least luminous millisecond pulsars presently known are
all isolated objects, even though more than 75% of the known disk mill
isecond pulsars are binary. A Kolmogorov-Smirnov analysis confirms tha
t the luminosity distributions of the binary and isolated millisecond
pulsars are different at the 99.5% confidence level. We can find no si
mple explanation for this fact. The low-luminosity millisecond pulsars
reported here exacerbate the birthrate discrepancy with their assumed
progenitors, the low-mass X-ray binaries. None of the pulsars exhibit
s any evidence of a planetary system such as that observed around PSR
B1257+12, indicating that planetary formation around millisecond pulsa
rs is rare.