Eratosthenes lived between 276 and 194 B.C. He didn't discover prime numbers; he devised a simple way to determine what numbers are prime in a given range.
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Prime numbers are not invented.
One
A sieve.
No, although he did devise a way to predict them.
One method for finding prime numbers is called the "Sieve of Eratosthenes" because it basically "sifts" through the numbers looking for numbers that are not not prime.