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math

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the sum of the digits of a two digit prime number is substracted from the number. prove that the difference cannot be a prime number.

  • math - ,

    adding the digits produces a result that is the remainder when the number is divided by 9.

    So, assuming that the prime number p = 9m+n
    the sum of the digits is also n

    so, p-n = 9m, not a prime

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