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Math Help - Prove that (product of primes between n and 2n) > 2^n

  1. #1
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    Prove that (product of primes between n and 2n) > 2^n

    I've read that a weak but explicit version of the Prime Number Theorem states that the product of primes between n and 2n (inclusive) is at least 2^n for all n \geq 1. I don't think this proof can be elementary (although if someone can prove it below then that would be great!) but is this a standard result? If so, where can I find a proof? I've searched but haven't managed to find anything.
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  2. #2
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    Quote Originally Posted by Newtonian View Post
    I've read that a weak but explicit version of the Prime Number Theorem states that the product of primes between n and 2n (inclusive) is at least 2^n for all n \geq 1. I don't think this proof can be elementary (although if someone can prove it below then that would be great!) but is this a standard result? If so, where can I find a proof? I've searched but haven't managed to find anything.

    Between 8 and 16 there are only two primes: 11 and 13, and 11\cdot 13 = 143 < 2^8 = 256

    Tonio
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  3. #3
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    That's a very good point...
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