The more expensive LM117 can use a resistor value as high as 240 ohms for R3. The LM317 uses 120 ohms so that its voltage doesn't rise without any other load. Then the R4 pot should be 2.5K.
The 3K resistor won't be enough of a load for an LM317 with 240 ohms as R3 at low output voltages and might waste power at high output voltages.
Connect the power LED and its current limiting resistor (a power resistor) to the unregulated 32VDC supply across the 6000uF capacitor.