||28.60 |- |14||16383||35504586||2167.160227||4392.129||2.0267||0.771695||46.10 ||29.52 |- |15||32767||134736824||4111.967040||8153.054||1.9828||0.776437||47.21 ||29.15 |- |16||65535||513758796||7839.456718||15225.43||1.9422||0.781064||49.13 ||28.17 |- |17||131071||1964413592||14987.40066||28576.97||1.9067||0.785401||50.43 ||29.55 |- |18||262143||7529218208||28721.79768||53869.76||1.8756||0.789561||51.17 ||30.67 |- |19||524287||28935644342||55190.46694||101930.9||1.8469||0.793536||52.62 ||31.45 |- |20||1048575||111393101150||106232.8409||193507.1||1.8215||0.797351||53.74 ||31.83 |- |21||2097151||429685077652||204889.9090||368427.6||1.7982||0.801018||54.97 ||32.18 |- |22||4194303||1660388309120||395867.5158||703289.4||1.7766||0.804543||56.24 ||33.65 |- |23||8388607||6425917227352||766029.1187||1345633||1.7566||0.807936||57.19 ||34.32 |- |24||16777215||24906872655990||1484565.386||2580070||1.7379||0.811204||58.49 ||34.43 |- |25||33554431||96666595865430||2880889.140||4956372||1.7204||0.814351||59.52 ||35.76 |- |26||67108863||375619048086576||5597160.066||9537863||1.7041||0.817384||60.49 ||36.73 |} Prevailing interval For all numbers and all but positive integers (a "prevailing" majority): with the constant Lower bounds For any sufficiently large number and for any , there are at most positive integers such that . Minimal order For any sequence of positive integers, any constant , and any sufficiently large : Small values For a constant and any sufficiently large positive , there exists an integer such that Moreover, is of the form for some square-free integer . Image of the function The set of values of the Carmichael function has counting function where Use in cryptography The Carmichael function is important in cryptography due to its use in the RSA encryption algorithm. See also Carmichael number Notes References Modular arithmetic Functions and mappings