R3 does not work as intended.
1V5 / 15k = 100uA
So you'll need 100 of them to get to your minimum of 10mA
A simpler option would be to remove R3 and use lower values for R1 and R2.
Also:
The minimum load current for the LM317L is 2.5mA (Checked TI datasheet) Other manufacturers of LM317 variants may deviate.
Another easy project with an LM317 is to make a current source / sink with a single resistor.
If you calibrate it to 1A or 100mA, you can use it to make 4 point measurements on low value resistors with a simple power supply and a regular DMM.