  We present a detailed study of the Orion B clouds (d~400 pc), imaged with the
PACS/SPIRE cameras at 70-500 $\mu$m by the Herschel Gould Belt survey (HGBS).
We release new high-res. maps of column density and dust temperature. In the
filamentary sub-regions NGC2023/2024, NGC2068/2071, and L1622, 1768 starless
dense cores were identified, ~28-45% of which are self-gravitating prestellar
cores. A total of 76 protostellar dense cores were also found. The typical
lifetime of the prestellar cores was found to be $t_{\rm
pre}=1.7_{-0.6}^{+0.8}$ Myr. The prestellar core mass function (CMF) peaks at
~0.5 $M_\odot$ and is consistent with a power law with log slope -1.27$\pm$0.24
at the high-mass end, compared to the Salpeter slope of -1.35. In this region,
we confirm the existence of a transition in prestellar core formation
efficiency (CFE) around a fiducial value A_V_bg~7 mag in background visual
extinction, similar to the trend observed with Herschel in other clouds. This
is not a sharp threshold, but a smooth transition between a regime with very
low prestellar CFE at A_V_bg<5 and a regime with higher, roughly constant CFE
at A_V_bg$\gtrsim$10. The total mass in the form of prestellar cores represents
only ~20% of the dense molecular cloud gas at A_V_bg$\gtrsim$7 mag. About
60-80% of the prestellar cores are closely associated with filaments, and this
fraction increases up to >90% when a more complete sample of filamentary
structures is considered. Interestingly, the median separation between nearest
core neighbors corresponds to the typical inner filament width of ~0.1 pc
commonly observed in nearby molecular clouds. Analysis of the CMF observed as a
function of background cloud column density shows that the most massive
prestellar cores are spatially segregated in the highest column density areas,
and suggests that both higher- and lower-mass prestellar cores may form in
denser filaments.
