FANDOM


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

121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212,121,212

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

See also Edit

Numbers by André Joyce

Repunits: twenty-twos · thirty-threes · forty-fours · fifty-fives · sixty-sixes · seventy-sevens · eighty-eights · ninety-nines · eleventy-elevens · twelvety-twelves
Googo- series: googoli · googolij · googoliji · googoliv · googolv · googolvi · googolvij · googolix · googolex · googolxi · googolxij · googolxiv · googolxix · googoc · googoci · googocli · googoclij · googocliji · googocliv · googoclix · googoclex · googoclexi · googoclexij · googoclexiji · googoclexiv · googoclexvy · googoclexvi · googoclexvij · googoclexviji · googoclexix · googoclexxi · googoclexxij · googoclexxiji · googoclexxiv · googoclexxix · googoccy · googocci · googoccij · googocciji · googocciv · googoccyv · googoccyvi · googoccyvij · googoccyviji · googoccix · googoccyx · googoccyxi · googoccyxij · googoccyxiji · googoccyxiv · googoccyxvy · googoccyxvi · googoccyxvij · googoccyxviji · googoccyxix · googoccyxex · googoccyxxiji · googoccyxexij · googoccyxexiji · googoccyxexvy · googoccyxexvij · googoccyxexix · googoccyxelv · googoccyxelviji · googoccelx · googoccelxi · googoccelxij · googoccelxiji · googoccelxiv · googoccelxvy · googoccelxvi · googoccelxvij · googoccelxviji · googoccelxix · googoccelxex · googoccelxxi · googoccelxxij · googoccelxxiji · googoccic · googodiji · googoxem · googoim · googom · googomi · googomij · googolmox · googomiv · googomvi · googomvij · googomxi · googomxij · googomxox · googomxiv · googomxix · googomump · googolbar
Googoo- series: googool · googooli · googoolij · googooliv · googoolv · googoolvi · googoolvij · googoolix · googoolxiv · googoolxix · googooci · googoocij · googoociv · googoocvi · googoocvij · googoocix · googoocxi · googoocxij · googoocxix · googoocxex · googoocxexviji · googoocli · googooclij · googoocliv · googooclix · googooccij · googoocciv · googooccix · googooccli · googoocclvi · googood · googoodi · googoodij · googoodiv · googoodvi · googoodvij · googoodix · googoodxi · googoodxij
Googoople- series: googovplev · googovplevi · googovplevij · googovplexi · googovplexij · googovplexiv · googovplexvi · googovplexvij · googovplexix · googovplexxi · googovplexxij
Googgoo- series: googgol · googgool · geegeel · geeggeel · geiggeil · geiggeim
Googodul series: googodul · goodugol · googogoogol · dugoogol · dugoogodul · dugoodugol · dugoodugodul
Googolplux series: googolplux · googolpluc · googolplum
Googool-n-plex series: googolundeciplex · googolduodeciplex · googoltriskaidekaplex · googoltetrakaidekaplex · googolpentakaidekaplex · googolhexakaidekaplex · googolheptakaidekaplex
Factorial series: lexexfa · lexxifa · lexxijfa · lexxijifa · lexxivfa · lexexvy · lexexvi · lexexvij · lexexviji · lexxixfa · lexxexfa · lexxexifa · lexxexijfa · lexxexijifa · lexxexivfa · lexxexvyfa · lexxexvifa · lexxexvijfa

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