One interesting application of HUGE prime numbers is in encryption. Many systems used nowadays for encryption use more or less random prime numbers, of over a hundred digits each.
This is by no means the only practical application of prime numbers. More examples of practical uses can be found here: http://en.wikipedia.org/wiki/Prime_number#Applications
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A diagram is not needed because 2 is a prime number whose only factors are itself and one which makes it a prime number in common with all other prime numbers.
It is: 2*5*7 = 70 and no exponents are needed
7 is a prime number!
109 is a prime number.
167 is a prime number.