Your example is superfluous. The access modifier is already publicly available, and specifying it again is pointless.
However, the real problem is that C # allows you to specify more restrictive modifiers, so the following code is illegal:
private int Number {public get; set;}
This has a side effect, also being illegal if you specify the same level (i.e. public and open). This should be more restrictive.
You can also specify only one modifier, because otherwise it is pointless to put an access modifier in this property.
public int Number {protected get; private set;}
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