if statement syntax. Wrong output

x=11

for n in range(1,x+1):
    #print(n)
    if (x%n)==0:
        if n == 1 and n==x:
            print(f"{x} is a prime number")
            break       
        else:
            #print(n)
            print(f"{x} is not a prime number")
            break

the output is: 11 is not a prime number. According to my knowledge the logic is correct but why this wrong output.