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Math Help - prime numbers

  1. #1
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    prime numbers

    In proving that there are infinitely many primes, one could define a function  f: \mathbb{N} \to \mathbb{N} by  f(n) = n!+1 and show that (1)  f(n) > n for all  n \in \mathbb{N} , (2)  f(n) is either prime or composite and (3)  f(n) has prime factors greater than  n if  f(n) is composite.

    So in general can we find a function  f: \mathbb{N} \to \mathbb{N} defined by  f(n) = n! + a and choose  a accordingly to satisfy the above conditions? Could we define a function  f: \mathbb{N} \to \mathbb{N} in another way that satisfies the above condtions?
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  2. #2
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    keep in mind that n! +a where a is between 2 and n
    are always composite numbers
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  3. #3
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    Uggg, just never mind. No helpful thoughts... I'm thinking some more.
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