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Thread: prove,,,

  1. March 1st 2010, 02:44 AM #1
    flower3
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    prove,,,

    for n \in \mathbb{N} Let \ p_n \ be the n^{th} prime (thus \ , p_1=2,p_2=3,p_3=5,p_4=7,p_5=11,...):
    prove that \ p_n \leq p_1 p_2 p_3...p_{n-1} +1 , n \geq 3
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  2. March 1st 2010, 09:02 AM #2
    qmech
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    Suppose the next prime wasn't less or equal to your number (A= product of primes + 1). Is A prime? Clearly none of the primes less than A divide it (they all leave a remainder of 1). You have a contradiction.
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