The usefulness in writing a program that will find, store and make a list of prime numbers is that you will then search for better algorithms, faster ones. The challenge in factoring numbers is that it is extremly time consuming given large enough products. That fact is the core of cipher algorithms like RSA. An RSA cipher can be broken, sure, but only by factoring N which is the product of two giant primes. I gather that today's N would take a single computer many, MANY times the age of the universe to factor N, but it can be done. Theoretically.
Another thing is the list: If you want to look into primes and their nature, a list of every prime from 2 to [whatever] could prove interesting.
So, all in all I'd say a program like that has its fields of application.
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Je Suis Charlie
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