Determining voltage by arc length
There is a big difference in dielectric Breakdown Voltage BDV for smooth parallel surfaces and point sources from sharp wire tips due to the E-field gradient force effects on ionization.
Yes 30kV/cm or 3kV/mm is true for smooth area surfaces.
But for wire tips it is 10kV/cm or 1kV/mm  This also raises the resistance and this begins arcing with a lower current, which is less visible.
This of course varies with dust , humidity and pressure.
This BDV has nothing to do with the &quot;holding current&quot; gap which may be increased after conduction occurs.