Question 23
Magalí's calculator has a special button ⋆ that works as follows. Every time she presses ⋆, the calculator multiplies the number on the screen by itself, then adds 6, and finally shows the result on the screen. For example, if the number on the screen is $11$ and Magalí presses ⋆, the number that will appear on the screen is $11 \times 11 + 6 = 127$. Magalí chooses a prime number, writes it on the calculator, and presses the ⋆ button many times. The ⋆ button gets blocked when a number that is not prime appears on the screen. What is the greatest number of times that she can press the ⋆ button?