I have a chart like the one pictured, with the following "tick intervals":
0, 1-10000,10001-20000,20000-30000 and 30000+
What is a consistent way of labeling the x-axis? I am not pleased with how the 0 and 1 are placed and expressed.
In your example, the special space allotted for the range of values between 0 and 1 indicate they have some special significance. Again, without more context it is hard to say if that is needed, but if it isn't particularly important range of values, I suggest that you not highlight that range specially in order to give the range 0-10K the same significance as other ranges. Alternatively, if that range is so very important, then maybe it warrants two separate charts.
Update: Since we now know that the range is not that important but the values that are exactly zero are important, I would use color to highlight those. I have updated the mockup below.
I'd also consider using an abbreviation of the axis labels here because the vast majority of the "ink" on your labels are just zeros. So if you could, for example, replace "10 000" with "10K" and your audience would understand it equally well I would definitely do that.