This is a very hot summer in Rome and you don't know what to do. You are the best detective in town but no crime seems to happen. You are all the day in front of your PC trying to solve some puzzles about parties and elephants but you can't find any solution so far. You are on the way to solving the 20th when a young policeman rushes into your room and gives you a letter.
"Get the hell out! I had the solution of that devilish puzzle and now it is gone! Get out!"
He can't understand your frustration and closes the door as fast as he could. Anyway, you opened up the letter and started to read:
Rome, 22/7/14 AHAHA Mr. Rossi, I have planted a bomb into the Colosseum! It will explode tonight at 24:00. I know you are a puzzle-lover, so I would give you a chance to defuse it. Go there and and follow the instructions, every clue is important, so be focused! You will find a 6-fold piece of paper with some hints to crack the bomb! Good Luck! The evil bomber
"Accipicchia [Oh my gosh]" you said "I need to move!"
You started to run to the Colosseum and after 20 minutes you found the bomb and the instruction. There is a keyboard and a monitor linked to the bomb. On the screen, you can see a textbox which allows you to type in just 4 characters and big red text saying: "Enter the password".
You opened up the piece of paper and started to read the hint.
Let's do some math: 2^2 = ... 3^2 = ... 5^2 = ... 7^2 = ... 11^2 = ... You can choose to stop here or keep on with all the prime numbers you can evaluate! Now you should know the password! The evil bomber
You started to think about for a while and after 20 minutes you started to type the solution that came up in your mind. After you pressed enter, on the screen you saw "The bomb has been defused!"
"Perbacco [My goodnees], I made it! Now I need to find the solution of the 20th party!".
What is the password and how did he come up with that?
Let's add some hints to help you to find the right solution.
The evil bomber is a PhD in Math, but he did not find any job and he started his career as a terrorist. Loving numbers, every number he gave are there for a reason, but one, just to make him struggle a little more.
Mr. Rossi is a fan of Math History, he loves HSM too. He found in a while which "subject" of the hints the evil bomber gave to him. It was easy, every numbers are linked univocally to that subject. It was easy to type the right answer this way.
During his PhD, the evil bomber studied a lot Euler, Reimann, and their Euler-Reimann Z function. He found with joy they are related to PI.
You can find at prodotto di Eulero the relation between primes and $\pi$. If you want more, you can see this one and read the demostration here
Anyway guys, I actually hope you had fun with this riddle as I had!