FANDOM


Eleventy-elevens is a positive integer formed by concatenating 110 (eleventy) copies of the digits "11."[1] Its decimal representation is:

1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

By expressing this number as a partial sum of the geometric series 1 + 10 + 100 + ..., we can derive a simple closed-form expression \((10^{220} - 1)/9\).

Its prime factorization is 112 × 23 × 41 × 89 × 101 × 271 × 331 × 661 × 1,321 × 3,541 × 4,093 × 5,171 × 8,779 × 9,091 × 18,041 × 21,649 × 27,961 × 62,921 × 148,721 × 513,239 × 83,251,631 × 1,052,788,969 × 1,056,689,261 × 1,121,407,321 × 20,163,494,891 × 318,727,841,165,674,579,776,721 × 1,300,635,692,678,058,358,830,121 × 1,395,900,370,916,327,245,555,441,901 × 36,380,545,029,953,205,956,377,406,702,261.

SourcesEdit

  1. Googology
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