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Twelvety-twelves is a positive integer formed by concatenating 120 (twelfty) copies of the digits "12."[1] Its decimal representation is:

121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212

By expressing this number as a partial sum of the geometric series 12 + 1,200 + 120,000 + ..., we can derive a simple closed-form expression \(12(100^{120} - 1)/99\).

Its prime factorization is 22 × 32 × 7 × 13 × 17 × 31 × 37 × 41 × 61 × 73 × 101 × 137 × 211 × 241 × 271 × 2,161 × 3,541 × 9,091 × 9,901 × 27,961 × 1,676,321 × 2,906,161 × 4,188,901 × 5,070,721 × 5,882,353 × 39,526,741 × 99,990,001 × 1,132,716,961 × 5,964,848,081 × 9,999,999,900,000,001 × 19,721,061,166,646,717,498,359,681 × 281,259,985,248,437,790,051,014,401 × 31,388,506,438,433,752,927,908,678,241 × 1,000,099,99,999,899,989,999,000,000,010,001.

SourcesEdit

  1. Googology
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