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Math Help - please help!

  1. #1
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    please help!

    hi, I am having trouble proving or disproving these two:

    First:

    If p is a prime number, must 2^p - 1 also be prime? Prove or give a counterexample.

    Second:

    If n is a nonnegative integer, must 2^(2^n) + 1 be prime? Prove of give a couterexample.

    Thank you so much.
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  2. #2
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    Quote Originally Posted by dahamalian2000
    hi, I am having trouble proving or disproving these two:

    First:

    If p is a prime number, must 2^p - 1 also be prime? Prove or give a counterexample.
    <br />
p=11,\  2^p-1=2047=23 \times 89<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by dahamalian2000

    Second:

    If n is a nonnegative integer, must 2^(2^n) + 1 be prime? Prove of give a couterexample.
    <br />
n=5,\ 2^{2^n}+1=2^{32}+1=4294967297=641  \times 6700417<br />

    RonL
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  4. #4
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    Thanks! But do you know a way to generally disprove it, using variables?

    Thank again,
    David
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  5. #5
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    Quote Originally Posted by dahamalian2000
    Thanks! But do you know a way to generally disprove it, using variables?

    Thank again,
    David
    No

    RonL
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  6. #6
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    Quote Originally Posted by dahamalian2000
    Thanks! But do you know a way to generally disprove it, using variables?

    Thank again,
    David
    NOT even Fermat himself had a way to disprove it with
    variables.
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