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What are all the primes?
That's an infinite list.
Which set of numbers includes prime numbers only?
The set of primes would be one. The set of Mersenne primes is another. The set of all primes below 50 is another. And so on. A set which includes all primes, and only them, is the set of numbers having exactly 2 factors.
List all of each number then identify each number prime or composite?
There are infinitely many numbers, and these comprise infinitely many primes and composites. It is not possible to list them all.
Can you list all the composite numers numbers?
NO because there is an infinite number of them, just like there is an infinite number of primes. In fact, if there is an infinite number of primes there must be an infinite number of composite numbers too... do you see why?
What purpose does sieve of Eratosthenes?
it is a brute force way to find all the primes in a given range. Remove all the composites, and you are left with the primes
