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How many prime divisors does (10^263-1)/9 have?

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  • Anonymous
    6 years ago
    Favorite Answer

    Your number is 111111....1 (263 1's). If a number consists of a sequence of n 1's and n = st where s is prime, then 1111...1 (s 1's) divides n. Your n = 263 is a prime number, so it has no st decomposition. So a sequence of 263 1's is a prime number. However, this argument is heuristic and does not satisfy my notions of rigour.

  • 6 years ago

    Sorry to answer my own question, but I found the answer online, here:

    http://stdkmd.com/nrr/repunit/tm.cgi?p=3

    And the answer is that (10^263-1)/9 has 3 prime divisors, so it is neither prime nor semi-prime.

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