Prison Break

I saw them put someone in jail. Can you find out who it is? They said this is the best prison ever built. You sure can’t break it, can you?

Prime-Roll

We built a random number generator and it just rolls dice in the background and prints the result of the roll. We love prime numbers so a dice with (10^9)+7 (a famous prime number) sides is used. To simulate random behaviour, the machine rolls the dice n number of times, where n equals the 2^((10^9)+7) (th) prime number. We want to know the probability of the largest result among all these rolls being a prime number too. You can stop the machine from rolling dices till the Heat Death of the universe by telling us the answer beforehand. Calculate the first 10 digits after the decimal place.

No-DIStractions

I see all, I read all, but I shall not speak until I am asked to. Ask me, and thou shall recieve.

Machine-Fix

We ran a code on a machine a few years ago. It is still running however we forgot what it was meant for. It completed n=523693181734689806809285195318 iterations of the loop and broke down. We want the answer but cannot wait a few more years. Find the answer after n iterations to get the flag.