What is the largest difference between two consecutive prime number?

Discussion in 'General Math' started by Larry, Dec 14, 2008.

  1. Larry

    Larry Guest

    Hi:

    We know that the smallest difference between two consecutive prime number is
    1 which occurs between 2 and 3. But what is the largest difference between
    two consecutive prime number? Or such difference can be infinity large?
     
    Larry, Dec 14, 2008
    #1
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  2. Larry

    Virgil Guest

    While the set of such a differences is not bounded above, there is no
    infinite value in that set.
     
    Virgil, Dec 14, 2008
    #2
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  3. Larry

    N. Silver Guest

    There are arbitrarily large sequences of consecutive composite numbers.
    Suppose we want a collection of n-1 consecutive composites.
    Consider the sequence n!+2, n!+3,..., n!+n. The first is term is divisible
    by 2, the second by 3, the third by 4, and so on.
     
    N. Silver, Dec 15, 2008
    #3
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