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Math Help - Positive Cube

  1. #1
    Member Rimas's Avatar
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    Positive Cube

    What is the sum of three smallest prime numbers each of which is two more than a perfect positive cube?
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  2. #2
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    Hello, Rimas!


    What is the sum of three smallest prime numbers each of which
    is two more than a perfect positive cube?
    What have you tried?

    If you examine the first few cubes, you'll trip over the answer . . .

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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Rimas View Post
    What is the sum of three smallest prime numbers each of which is two more than a perfect positive cube?
    Clumsy fingers and being abducted by aliens resulted in my not posting this when I thought I has so here it is again:

    24547

    RonL

    (or I might have already posted it in an alternate reality)
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  4. #4
    Junior Member Dragon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, Rimas!


    What have you tried?

    If you examine the first few cubes, you'll trip over the answer . . .

    Thanks i think the answer is 81
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  5. #5
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    Hello again, Rimas!

    Am I reading it wrong?
    It is very simple . . .


    What is the sum of three smallest prime numbers each of which
    is two more than a perfect positive cube?

    \begin{array}{cc} \text{cube} & \text{two more} \\<br />
1^3 = 1 & 3 \\ 2^3 = 8  & \not1\!\!\!\!\not0 \\ 3^3 = 27 & 29 \\ 4^3 = 64 & \not6\!\!\!\not6 \\ 5^3 = 125 & 127 \end{array}


    Therefore: . 3 + 29 + 127\;=\;157

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  6. #6
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    Hi:

    The positive cubes are (1, 8, 27, 64, 125, 216, ...) 1 + 2 = 3, 27 + 2 = 29, and 2 + 125 = 127. As each is prime, the sum in question is 3 + 29 + 127 = 159.

    Regards,

    Rich B.
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