UKHeliBob:
Your connections are the same as mine but I am using a Nano
Mm, I came up with another idea. The code I use to read the NUID is an example of the MFRC522 library. However, the code from that website runs on the library you can add by downloading the zip file. Maybe that is where it goes wrong? I added the library by downloading the zip file and click on 'Sketch' --> 'Include Library' --> 'Add .ZIP library' --> Selecting the zip file. Did I made a mistake here?
And one more question. In the circuit, I only included the MFRC522 reader that I connected to my Teensy. The circuit of that site is also using LED and a TIP31 transistor. Although, I thought the code should just work, only without turning on a LED, right? Did you also only used the MFRC522 reader with your Arduino Nano?