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    dfsacxzsdefa's Avatar
    dfsacxzsdefa Posts: 5, Reputation: 1
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    #1

    Nov 20, 2010, 08:56 PM
    2^2^2^2^2... for primes
    Let's say we are given the numbers 2, 2^2, 2^(2^2), 2^(2^(2^2)), and so on. Would all these numbers plus one be a prime number? (So far I see that 2^(2^(2*2)) or 2^16 works, but sadly 2^65536 is a little harder)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Nov 21, 2010, 07:10 AM


    No, they are all not primes.

    i.e is not prime.

    But, Mersenne primes have the form

    , where p is prime.

    See here:

    The UCLA Mersenne Prime
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Nov 21, 2010, 08:45 AM

    Um... it's 'plus' one and not minus one... but then, I don't know...

    Wolfram alpha gave the digit as a 19729 digit number :eek:
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